DigitalTwinDrivenGreenPerformanceEvaluation...

Research ArticleDigital Twin Driven Green Performance EvaluationMethodology of Intelligent Manufacturing Hybrid ModelBasedonFuzzyRough-SetsAHPMultistageWeightSynthesis andPROMETHEE II

Lianhui Li 123 Chunlei Mao4 Hongxia Sun1 Yiping Yuan 5 and Bingbing Lei 26

1College of Mechatronic Engineering North Minzu University Yinchuan 750021 China2Ningxia Key Laboratory of Intelligent Information and Big Data Processing North Minzu University Yinchuan 750021 China3Institute of Physical Internet Jinan University Zhuhai 519070 China4Nanjing Automation Institute of Water Conservancy and Hydrology Nanjing 210012 China5School of Mechanical Engineering Xinjiang University Urumqi 830046 China6School of Computer Science and Engineering North Minzu University Yinchuan 750021 China

Correspondence should be addressed to Bingbing Lei x_generation126com

Received 24 March 2020 Accepted 22 June 2020 Published 16 July 2020

Guest Editor Baogui Xin

Copyright copy 2020 Lianhui Li et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

e design planning and implementation of intelligent manufacturing are mainly carried out from the perspectives of meetingthe needs of mass customization improving manufacturing capacity and innovating business pattern currently Environmentaland social factors should be systematically integrated into the life cycle of intelligent manufacturing In view of this a greenperformance evaluation methodology of intelligent manufacturing driven by digital twin is proposed in this paper Digital twinframework which constructs the bidirectional mapping and real-time data interaction between physical entity and digital modelprovides the green performance evaluation with a total factor virtual image of the whole life cycle to meet the monitoring andsimulation requirements of the evaluation information source and demand Driven by the digital twin framework a novel hybridMCDMmodel based on fuzzy rough-sets AHP multistage weight synthesis and PROMETHEE II is proposed as the methodologyfor the green performance evaluation of intelligent manufacturing e model is tested and validated on a study of the greenperformance evaluation of remote operation and maintenance service project evaluation for an air conditioning enterpriseTesting demonstrates that the proposed hybrid model driven by digital twin can enable a stable and reasonable evaluation result Asensitivity analysis was carried out by means of 27 scenarios the results of which showed a high degree of stability

1 Introduction

e concept of intelligent manufacturing rose in the 1980sIts emergence and development are closely related to thefour industrial revolutions and the development of relatedtechnologies and industries First of all the first and secondindustrial revolutions brought manufacturing industry intothe era of mechanization and electrification With the in-vention and application of atomic energy and electroniccomputer technology the third industrial revolutionappeared In the same period terms representing new

manufacturing paradigms such as flexible manufacturingcells (FMCs) [1] flexible manufacturing systems (FMSs) [2]computer integrated manufacturing (CIM) [3] and intel-ligent manufacturing system (IMS) [4] are emerging grad-ually After more than 40 years of development and progressintelligent manufacturing has gradually evolved from con-cept to industrialization and integrated into the emergingfourth industrial revolution

At present the design and implementation of intelligentmanufacturing are mainly carried out from the perspectivesof meeting the needs of mass customization improving

HindawiComplexityVolume 2020 Article ID 3853925 24 pageshttpsdoiorg10115520203853925

manufacturing capacity and innovating business pattern Insome theoretical research and practice green or even sus-tainability has also been brought into the intelligentmanufacturing paradigm But most of them focus on theoptimization of energy consumption in the manufacturingprocess For example cloud platform is used for promotingresource sharing and improving application efficiency ofmanufacturing system [5] combining big data technology inthe product life cycle to achieve sustainable intelligentmanufacturing is proposed [6] big data method was used forenergy efficiency optimization [7] anomaly detection [8]and energy consumption monitoring [9] in intelligentmanufacturing process and through the analysis of relevantliterature it can be seen that there is no clear definition ofgreen intelligent manufacturing in the current academiccircle and few research studies systematically integratedenvironmental and social factors into the design planningand implementation of intelligent manufacturing [10 11]On the one hand the current research and practice pay moreattention to the core business and competitive elements (forexample productivity improvement personalized custom-ization and intelligent services) On the other hand theimprovement of the environment and social impact of in-telligent manufacturing may conflict with the realization ofother elements and even may bring a lot of investment costse research on the green of intelligent manufacturing is stillin the exploratory stage

At present there are many researches on performanceevaluation of intelligent manufacturing focusing on thefollowing aspects

e first aspect is overall performance evaluation ofintelligent manufacturing enterprises Gong [12] introduceda three-tier index system to evaluate the performance ofenterprise intelligent manufacturing by using the compre-hensive scoring method of experts which covers manyaspects of enterprise performance but does not involveenvironmental performance and only uses an overall sat-isfaction degree for the evaluation of employees Jia and Shi[13] use the DEA model of cross efficiency to measure theperformance of some listed intelligent manufacturing en-terprises which can evaluate the overall economic perfor-mance of enterprises but cannot pay attention to the detailsof intelligent manufacturing itself and does not consider theenvironmental factors

In the second aspect enterprisersquos intelligentmanufacturing capability is assessed Yi et al [14] establishedthe evaluation model of enterprise intelligent manufacturingcapability based on tensor analysis and measured the en-terprise intelligent manufacturing capability from threedimensions of life cycle system level and intelligent func-tion Similarly Ding et al [15] put forward the intelligentmanufacturing capability maturity model from three di-mensions of manufacturing resources manufacturing as-surance and intelligent promotion which can supportenterprises to describe their comprehensive level of intel-ligent manufacturing Qu et al [16] used Douglas produc-tion function and seemingly unrelated regression (SUA)analysis to evaluate the production capacity of intelligentmanufacturing enterprises so as to compare its advantages

and disadvantages with traditional manufacturing capacitySchumacher et al [17] proposed an empirical model toevaluate the industry 40 maturity of discrete manufacturingenterprise in which nine dimensions and sixty-two indi-cators were established for evaluation including the items ofthe impact on employees and products

e third aspect is environment and social impact as-sessment of intelligent manufacturing ere are few re-search studies on intelligent manufacturing environmentand social impact assessment e above two aspects or partof the performance assurance research of intelligentmanufacturing involved environmental and social dimen-sions but it was often described as a macromethod onlyincluding environmental or social factors as a macro-indicator [18]

In addition Mashhadi and Behdad [19] summarized theshortcomings of traditional life cycle assessment (LCA) inthe assessment of the environment impact of intelligentmanufacturing combined with the characteristics of intel-ligent manufacturing and put forward the assessmentconcept based on product characteristics data It is mainly ascheme of data collection and real-time assessment by usingthe new generation of information technology rather thanstudying specific assessment methods Peruzzini et al [20]used social life cycle assessment (SLCA) to evaluate theimpact of the implementation of intelligent manufacturingon the society but it only focuses on the general socialimpact not the special impact of intelligent manufacturingon employees or users

By creating the virtual model of physical entity in adigital way and simulating the behavior of physical entity bymeans of data digital twin has the characteristics of real-time synchronization faithful mapping and high fidelitythrough the means of virtual real interaction feedback datafusion analysis and decision iteration selection optimization[21] Digital twin can promote the interaction and inte-gration of physical world and information world and in-crease or expand new capabilities for physical entity [22] Inthis study digital twin mainly focuses on obtaining thevirtual image of all factors in the whole life cycle of intel-ligent manufacturing project to meet the monitoring andsimulation requirements of the evaluation informationsource and demand for the green evaluation of intelligentmanufacturing Based on digital twin technology [21 22]the complete and dynamic mapping interaction betweenphysical entity and digital model in green performanceevaluation of intelligent manufacturing can be realized Andthen how to comprehensively master the multidimensionalinfluencing factors and their coupling relationship forcomparative analysis is the key problem in green perfor-mance evaluation of intelligent manufacturing

Multicriteria decision-making (MCDM) [23 24] byusing the experience and wisdom of experts is a feasiblemethod to comprehensively consider the multidimensionalinfluencing factors and their coupling relationship that affectthe green performance evaluation In the existing similarevaluation problem and its solution the value or importanceof a factor is usually evaluated by one expert in numericalnumber form which is unreasonable due to the preferences

2 Complexity

of individual expert and the fuzziness of expert judgment[25 26] Additionally the green performance evaluation ofintelligent manufacturing includes multidimensionalinfluencing factors with complex coupling relationship andthese factors and their relationship are dynamic evolutionerefore it is difficult for a single expert to achieve accuratejudgment with the numerical number form as the judgmentopinion while integrating the fuzzy number form judgmentof multiple experts is more reasonable Trapezoid fuzzynumber which is a key definition in fuzzy theory can reflectthe internal uncertainty of expertrsquos judgment [27 28] Toexpress the expert judgment value about the value or im-portance of the index using trapezoid fuzzy number canbetter describe the uncertainty e single weight methodcannot fully reflect the weight information e weightsobtained by the multiple weight method should besynthesized

To sum up there is a lack of special systematic andobjective research to evaluate the green performance ofintelligent manufacturing e existing studies prove thenecessity of green performance evaluation of intelligentmanufacturing and provide reference for the study of thispaper Additionally digital twin can provide an overallinformation framework for this study In view of this thispaper constructs an overall information framework drivenby digital twin for the green performance of intelligentmanufacturing In this framework the digital twin system isformed by mapping and interacting between intelligentmanufacturing entity and intelligent manufacturing modelAll activities in the life cycle of intelligent manufacturingentity interact with the model in real time and both physicalentity and digital model provide a source of digital twin dataWith the full mastery of digital twin data by multiple expertsa novel hybrid MCDM model based on fuzzy rough-setsAHP multistage weight synthesis and PROMETHEE II(FRSA-MSWS-PII) is proposed as the methodology for thegreen performance evaluation of intelligent manufacturing

e rest of this work is arranged as follows overallframework driven by digital twin is stated in Section 2Section 3 builds the novel hybrid MCDM model (FRSA-MSWS-PII) for the green performance evaluation of intel-ligent manufacturing which include three phases multi-expert judgment integration based on fuzzy rough-sets AHPmultistage weight synthesis and intelligent manufacturingproject evaluation by PROMETHEE II case study is given inSection 4 by an application of remote operation andmaintenance service project evaluation for an air condi-tioning enterprise Section 5 presents a discussion of theresults and validation of the FRSA-MSWS-PII model finallySection 6 summarizes the conclusion

2 Overall Framework

On the basis of digital twin technology [21 22] the bidi-rectional mapping and real-time data interaction are con-structed between physical entity and digital modelerefore the comprehensive data integration and fusion ofphysical entity and digital model can be realized and formthe digital twin data that can support and drive the green

performance evaluation methodology In addition the greenperformance evaluation methodology results in an optimalproject alternative selection which can interact with thephysical entity and digital model and provide the physicalentity and digital model with the support of decision-making e overall framework built in this paper is drivenby digital twin As shown in Figure 1 it consists of threelayers which are the digital twin concept layer informationlayer and methodology layer

e bidirectional mapping and real-time data interactionbetween physical entity and digital model are defined the-oretically in the digital twin concept layer In the design stageof intelligent manufacturing project multiple project al-ternatives are produced in general All of them meet theactual demands After that in the test running stage theoriginal intelligent manufacturing project will be adjustedand optimized iteratively Finally an optimal alternative isdetermined and put into formal running stage Additionallythe data of formal running stage will also be fed back to assistin the selection optimization of design stage

Intelligent manufacturing project entity really exists inthe physical world while intelligent manufacturing projectmodel is a real and complete digital mirror image of in-telligent manufacturing project entity Intelligentmanufacturing project model can integrate all influencingfactors related to green performance evaluation of intelligentmanufacturing project At the same time it is a dynamicmodel which can describe the dynamic evolution of thewhole life cycle including but not limited to the design testrunning and formal running stages

3 Hybrid MCDM Model (FRSA-MSWS-PII)

31 Fundamental Concepts e fundamental concepts inthe proposed hybrid model mainly include two aspectstrapezoid fuzzy number (TFN) related to fuzzy mathematicsrough approximation set (RAS) and rough boundary in-terval (RBI) related to rough-sets theory [27 28]

311 Trapezoid Fuzzy Number (TFN) A TFN is defined asfollows

1113957a (α χ δ β) (1)

Its membership function f1113957a(x) R⟶ [0 1] is definedas follows

f1113957a(x)

x minus αχ minus α

αlexle χ

1 χ le xle δ

x minus βδ minus β

δ lexle β

0 xlt α orxgt β

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(2)

where x isin R αle χ le δ le β and α and β are the lower boundand upper bound of 1113957a respectively Especially when χ δ 1113957a

Complexity 3

degenerates into a triangular fuzzy number whenα χ δ β 1113957a degenerates into a real number

e graph of function f1113957a(x) is shown in Figure 2e TFN is characterized by specific arithmetic opera-

tions that differ from those dealing with typical real num-bers e arithmetic operations between two TFNs1113957a1 (α1 χ1 δ1 β1) and 1113957a2 (α2 χ2 δ2 β2) (α1 χ1 δ1 β1 α2χ2 δ2 β2isin R+ λgt0) are carried out using the followingexpressions

(1) Addition of two TFNs ldquooplusrdquo1113957a1 oplus 1113957a2 α1 + α2 χ1 + χ2 δ1 + δ2 β1 + β2( 1113857 (3)

(2) Multiplication of two TFNs ldquootimesrdquo1113957a1 otimes 1113957a2 α1 middot α2 χ1 middot χ2 δ1 middot δ2 β1 middot β2( 1113857 (4)

(3) Multiplication of a real number and a TFN ldquootimesrdquo

λotimes 1113957a1 λ middot α1 λ middot χ1 λ middot δ1 λ middot β1( 1113857 (5)

(4) Reciprocal of a TFN ldquominus1rdquo

1113957a1( 1113857minus 1

βminus11 δminus1

1 χminus11 αminus1

11113872 1113873 (6)

(5) Division of two TFNs ldquordquo

1113957a11113957a2

α1β2

χ1δ2

δ1χ2

β1α2

1113888 1113889 (7)

(6) Barycenter of a TFN ldquo⊙rdquo

⊙1113957a1 δ12 + β12 minus α12 minus χ12( 1113857 + δ1 middot β1 minus α1 middot χ1( 1113857

3 δ1 + β1 minus α1 minus χ1( 1113857 (8)

Digital twin data

Dat

adr

ivin

g

Hybrid model based on fuzzy rough-sets AHP multi-stage weight synthesis and PROMETHEE II( hybrid FRSA-MSWS-PII model )

Dat

adr

ivin

g

Multistage weightsynthesis Fuzzy rough-sets AHP

Multiexpertjudgementintegration

Physical world Digital world

Digital twin

Mapping

Interacting

PROMETHEE II

Green performance evaluation

Dat

adr

ivin

g

Itera

tive o

ptim

izat

ion

Itera

tive o

ptim

izat

ion

Inte

ract

ing

Inte

ract

ing

Dig

ital t

win

conc

ept

laye

rIn

form

atio

nla

yer

Met

hodo

logy

laye

r

Index sys

tem

Entity Model

Figure 1 Green performance evaluation framework of intelligent manufacturing driven by digital twin

4 Complexity

On the basis of the membership function of trapezoidfuzzy number shown by formula (2) a real number a can beconverted to trapezoid fuzzy number 1113957a [27 28] For ex-ample 11139572(1 32 52 3) For trapezoid fuzzy number 1113957a itsmembership function f1113957a(x) is shown in Figure 3 ecommonly used nine-level scale assessment comments areextremely superior (ES) strongly superior (SS) obviouslysuperior (OS) weakly superior (WS) equal (E) weaklyinferior (WI) obviously inferior (OI) strongly inferior (SI)and extremely inferior (EI) e corresponding assessmentvalues are 9 7 5 3 1 13 15 17 and 19 in order ecommonly used nine-level scale assessment comments andcorresponding assessment values are converted to thetrapezoid fuzzy number form as ES 1113957911139571 SS 1113957811139572 OS 1113957711139573WS1113957611139574 E 1113957511139575 WI 1113957411139576 OI 1113957311139577 SI 1113957211139578 and EI 1113957111139579 emembership functions of nine-level trapezoid fuzzy numberscales are shown in Figure 4

According to the arithmetic rules of trapezoid fuzzynumber shown by formulas (3)ndash(8) the trapezoid fuzzynumber values of nine-level scales are shown in Table 1

312 Rough Approximation Set (RAS) and Rough BoundaryInterval (RBI) According to rough-sets theory the defini-tions of RAS and RBI are given as follows

(1) Rough approximation set (RAS)e domain φwhich is a nonempty finite set containsall objects All objects in φ belong to n divisions ieD1 D2 Dn e set of divisions in φ is as follows

D D1 D2 Dn1113864 1113865 (9)

Here D1 D2 Dn have an order relationship asD1 ltD2 lt ltDnFor a division Dw(1lewle n) its upper RAS (URAS) isdefined as follows

URAS Sw( 1113857 Y isin K | K isin DandKgeDw1113864 1113865 (10)

And its lower RAS (LRAS) is defined as follows

LRAS Sw( 1113857 Y isin K|K isin DandKleDw1113864 1113865 (11)

where Y is any object in φ(2) Rough boundary interval (RBI)

e mathematical characteristics of division Sw canbe embodied by its RBI which is composed of lowerrough limit (LRL) and upper rough limit (URL) SoRBI of Sw is defined as follows

RBI Sw( 1113857 LRL Sw( 1113857URL Sw( 11138571113858 1113859 (12)

LRL(Sw) and URL(Sw) are expressed as follows

LRL Sw( 1113857 1

Num LRAS Sw( 1113857( 11138571113944

YisinLRAS Sw( )

Y (13)

URL Sw( 1113857 1

Num URAS Sw( 1113857( 11138571113944

YisinURAS Sw( )

Y (14)

where Num(LRAS(Sw)) and Num(URAS(Sw)) are thenumbers of objects contained in the LRAS and URAS of Swrespectively

e arithmetic operations between two RBIs RBI(Sw)

[LRL(Sw)URL(Sw)] and RBI(Su) [LRL(Su)URL(Su)]

(LRL(Sw)URL(Sw) LRL(Su) andURL(Su) isin R+ λgt0) arecarried out using the following expressions

(1) Addition of two RBIs ldquooplusrdquoRBI Sw( 1113857oplusRBI Su( 1113857 LRL Sw( 1113857 + LRL Su( 1113857URL Sw( 1113857 + URL Su( 11138571113858 1113859

(15)

(2) Multiplication of two RBIs ldquootimesrdquoRBI Sw( 1113857otimesRBI Su( 1113857 LRL Sw( 1113857 middot LRL Su( 1113857URL Sw( 1113857 middot URL Su( 11138571113858 1113859

(16)

(3) Multiplication of a real number and an RBI ldquootimesrdquoλotimesRBI Sw( 1113857 λ middot LRL Sw( 1113857 λ middot URL Sw( 11138571113858 1113859 (17)

32 Evaluation Index System Considering the typical en-vironmental problems and the special influence of mainstakeholders of intelligent manufacturing the index systemof green performance evaluation of intelligentmanufacturing is constructed through the summary of theexisting research as shown in Figure 5 By integrating thetarget dimension and index of the green performanceevaluation of intelligent manufacturing the index system inthis paper mainly constructs the three-level standardizedframework

In Figure 5 the target level is green performance eval-uation of intelligent manufacturing the dimension level hasthree elements general environmental effect (dimension 1)social effect on employees (dimension 2) and social effect onusers (dimension 3) the index level has nine indexes

~fa(x)

a

xβδχα0

1~

Figure 2 e membership function graph of triangular fuzzynumber

Complexity 5

Furthermore in the index level exhaustion of resources andenergy (index 1) destruction of ecological environment(index 2) and hazards to human health (index 3) belong todimension 1 physical health effects (index 4) mental healtheffects (index 5) and impact on employee development(index 6) belong to dimension 2 physical health effects

0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

a = 1a = 2a = 3

a = 4a = 5a = 6

a = 7a = 8a = 9

Figure 3 Membership functions of trapezoid fuzzy numbers 1113957a (a 1ndash9)

0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

EISIOI

WIEWS

OSSSES

Figure 4 Membership functions of nine-level trapezoid fuzzy number scales (EI-ES)

Table 1 e trapezoid fuzzy number values of nine-level scales

Nine-level scale Trapezoid fuzzy number valueEI (01111 01111 01765 02500)SI (01111 01765 03333 04286)OI (02500 03333 05385 06667)WI (04286 05385 08182 10000)E (10000 10000 10000 10000)WS (10000 12222 18571 23333)OS (15000 18571 30000 40000)SS (23333 30000 56667 90000)ES (40000 56667 90000 90000)

Dimen

sionIn

dex

Targ

et

12

3

1

3 2

4

5

67

8

9

Figure 5 ree-level standardized framework for the indexsystem

6 Complexity

(index 7) mental health effects (index 8) and impact on userdevelopment (index 9) belong to dimension 1

33 Ce Process of Proposed Hybrid Model is paperpresents a digital twin driven green performance evaluationmethodology of intelligent manufacturing by introducingthe hybrid model (FRSA-MSWS-PII) as shown in Figure 6Fuzzy numbers are used to deal with uncertainty of expertjudgment in the group decision-making process while RBIis used to integrate the judgments of multiple experts Phase1 includes the expert judgment of assessment index value byapplying the fuzzy rough-sets AHP model which results inthe creation of input data required for the multistage weightsynthesis model (phase 2) and PROMETHEE II model(phase 3) In phase 2 the multiple objective weights arebased on the assessment index values from phase 1 while themultiple subjective weights are based on expertsrsquo judgmentabout the importance of assessment index e output dataof phase 2 are the final synthesized weights which are theinput data of phase 3

e FRSA-MSWS-PII model which is the subject matterof this paper represents a novel approach for dealing withuncertainty in green performance evaluation of intelligentmanufacturing based on fuzzy rough-sets AHP multistageweight synthesis and PROMETHEE II For defining thefinal rank of intelligent manufacturing project alternativesthe FRSA-MSWS-PII method is used e following threesections deal with the algorithms for the FRSA-MSWS-PIImodel

331 Multiexpert Judgment Integration Based on FuzzyRough-Sets AHP To achieve multiexpert judgment inte-gration there are two preconditions (1) there are N indexesindex 1 index 2 index N which constitute the index setis I Here N 9 and index 1 index 2 index N representthe indexes shown in Figure 5 (2) ere are q experts toassess the sustainable performance of l intelligentmanufacturing project alternatives As shown in Figure 6the fuzzy rough-sets AHP for multiexpert judgment inte-gration which is phase 1 of the hybrid model is to obtain theindex value of intelligent manufacturing project alternativesIts process is as follows

Experts judge the performance of all intelligentmanufacturing project alternatives on any index based ontheir experiences and wisdom On index t (t 1 2 N)the fuzzy reciprocal judgment matrix given by expert k(k 12 q) is as follows

1113957Φkt

1113957ϕkt

111113957ϕkt

12 middot middot middot 1113957ϕkt

1l

1113957ϕkt

211113957ϕkt


2l

⋮ ⋮ ⋮1113957ϕkt

l11113957ϕkt

l2 middot middot middot 1113957ϕkt

ll

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(18)

where 1113957ϕkt

ij is the fuzzy score of intelligent manufacturingproject alternative i relative to intelligent manufacturing

project alternative j given by expert k on index t and1113957ϕkt

ji 11113957ϕkt

ij According to the table the set of the nine-level scales is

SCA EI SI OI WI E WS OS SS ES and the set oftrapezoid fuzzy number values of nine-level scales is TFN-SCA (01111 01111 01765 02500) (01111 0176503333 04286) (02500 03333 05385 06667) (0428605385 08182 10000) (10000 10000 10000 10000)(10000 12222 18571 23333) (10000 12222 1857123333) (23333 30000 56667 90000) (40000 5666790000 90000)

From the perspective of judgment comment 1113957ϕkt

ij isin SCAwhich represents the evaluation of performance of intelli-gent manufacturing project alternative i relative to intelli-gent manufacturing project alternative j given by expert k onindex t while from the perspective of judgment value 1113957ϕkt

ij isinTFN-SCA which is a trapezoid fuzzy number and can berepresented as follows

1113957ϕkt

ij αktij χkt

ij δktij βkt

ij1113872 1113873 (19)

Especially when i j 1113957ϕkt

ij (1 1 1 1)Consistency inspection is carried out after all experts

finish their judgment If any fuzzy reciprocal judgmentmatrix fails to pass the consistency inspection the corre-sponding expert should adjust his judgment matrix ebasic idea of consistency inspection for fuzzy reciprocaljudgment matrix is using formula (8) to convert trapezoidfuzzy number to real number and then fuzzy reciprocaljudgment matrix 1113957Φkt could be transformed into generaljudgment matrix 1113957Φkt as follows

Φkt

ϕktl1 ϕkt

12 middot middot middot ϕkt1l

ϕkt21 ϕkt


⋮ ⋮ ⋮

ϕktl1 ϕkt

l2 middot middot middot ϕktll

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(20)

Consistency index (CI) of Φkt is represented as follows

CIkt

λmax( 1113857kt

minus l

l minus 1 (21)

where (λmax)kt is the maximum eigenvalue of Φkt

Usually consistency ratio (CR) is used to evaluate theconsistency of reciprocal judgment matrix ForΦkt its CR isrepresented as follows

CRktCIkt

RIkt (22)

where RIkt is a random index (RI) that depends on thedimension l of Φkt e specific value of RI is shown inTable 2

When CRktgt01 the judgment logic of expert k on indexIt is inconsistent and Φkt fails to pass the consistency in-spection As a result expert k should adjust his judgmentprocess and give a new judgment matrix

Ulteriorly the group judgment matrix is constructed asfollows

Complexity 7

1113957Θt

1113957ρt11 1113957ρt

12 middot middot middot 1113957ρt1l

1113957ρt21 1113957ρt


⋮ ⋮ ⋮

1113957ρtl1 1113957ρt

l2 middot middot middot 1113957ρtll

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(23)

Element 1113957ρtij is a set which can be represented as follows

1113957ρtij 1113957ϕ1t

ij 1113957ϕ2t

ij 1113957ϕqt

ij1113882 1113883 (24)

In 1113957ρtij the fuzzy RBI of 1113957ϕkt

ij is obtained according torelated concepts given by formulas (8)ndash(13) as follows

RBI 1113957ϕkt

ij1113874 1113875 LRL 1113957ϕkt

ij1113874 1113875URL 1113957ϕkt

ij1113874 11138751113876 1113877

1

Num LRAS 1113957ϕkt

ij1113874 11138751113874 11138751113944

Yisin1113957ρt

ij

Yle1113957ϕkt

ij

Y1

Num URAS 1113957ϕkt

ij1113874 11138751113874 11138751113944

Yisin1113957ρt

ij

Yge1113957ϕkt

ij

Y

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(25)

Intelligent manufacturing program alternatives Index system

Fuzzy reciprocal judgement matrix

Consistency inspection

Group judgement matrix

RBI judgement matrix

LRL matrix and URL matrix

Eigenvectors corresponding to the maximum eigenvalue

Average of two eigenvectors

Multiple objective weights Multiple subjective weights

Objective weight synthesis Subjective weight synthesis

Total synthesis

Preference function between two alternatives on one index

Weighted preference function between two alternatives on all

indexes

Outflow and inflow of an alternative

Preference net flow of an alternative

Index value matrix

Final synthesized weight

Priority ranking results of all alternatives

Experts judgement

Phas

e 1 f

uzzy

roug

h-se

ts A

HP

Phas

e 2 m

ultis

tage

wei

ght

synt

hesis

Phas

e 3 P

ROM

ETH

EE II

Yes

No

Figure 6 e process of the proposed FRSA-MSWS-PII model

Table 2 e specific value of RI

Dimension l 1 2 3 4 5 6 7 8 9RI 000 000 058 090 112 124 132 141 145

8 Complexity

Based on the arithmetic operation rule of RBI shown byformulas (16)ndash(18) RBI of 1113957ρt

ij is obtained as follows

RBI 1113957ρtij1113872 1113873 LRL 1113957ρt

ij1113872 1113873URL 1113957ρtij1113872 11138731113960 1113961

1q

1113944

q

k1LRL 1113957ϕkt

ij1113874 11138751q

1113944

q

k1URL 1113957ϕkt

ij1113874 1113875⎡⎣ ⎤⎦

(26)

en the RBI judgment matrix is constructed as follows

1113957Λt

RBI 1113957ρt111113872 1113873 RBI 1113957ρt

121113872 1113873 middot middot middot RBI 1113957ρt1l1113872 1113873

RBI 1113957ρt211113872 1113873 RBI 1113957ρt


⋮ ⋮ ⋮

RBI 1113957ρtl11113872 1113873 RBI 1113957ρt

l21113872 1113873 middot middot middot RBI 1113957ρtll1113872 1113873

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(27)

1113957Λt is decomposed into LRL matrix and URL matrix asfollows

1113957Λt

LRL

LRL 1113957ρt111113872 1113873 LRL 1113957ρt

121113872 1113873 middot middot middot LRL 1113957ρt1l1113872 1113873

LRL 1113957ρt211113872 1113873 LRL 1113957ρt


⋮ ⋮ ⋮

LRL 1113957ρtl11113872 1113873 LRL 1113957ρt

l21113872 1113873 middot middot middot LRL 1113957ρtll1113872 1113873

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(28)

1113957Λt

URL

URL 1113957ρt111113872 1113873 URL 1113957ρt

121113872 1113873 middot middot middot URL 1113957ρt1l1113872 1113873

URL 1113957ρt211113872 1113873 URL 1113957ρt


⋮ ⋮ ⋮URL 1113957ρt

l11113872 1113873 URL 1113957ρtl21113872 1113873 middot middot middot URL 1113957ρt

ll1113872 1113873

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(29)

Based on the barycenter operation shown by formula (8)1113957Λt

LRL and 1113957Λt

URL are converted into real number forms ΛtLRL

andΛtURLe eigenvectors of Λt

LRL andΛtURL corresponding

to the maximum eigenvalue are obtained respectively asfollows

Eig ΛtLRL1113872 1113873 Eig1 Λ

tLRL1113872 1113873Eig2 Λ

tLRL1113872 1113873 Eigl Λ

tLRL1113872 11138731113960 1113961

(30)

Eig ΛtURL1113872 1113873 Eig1 Λ

tURL1113872 1113873Eig2 Λ

tURL1113872 1113873 Eigl Λ

tURL1113872 11138731113960 1113961

(31)

After averaging the two eigenvectors shown in formulas(29) and (30) an average vector is obtained as follows

Eig ΛtAver1113872 1113873 Eig1 Λ

tAver1113872 1113873Eig2 Λ

tAver1113872 1113873 Eigl Λ

tAver1113872 11138731113960 1113961

(32)

where Eigi(ΛtAver) (12)(Eigi(Λt

LRL) + Eigi(ΛtURL))

e index value of alternate intelligent manufacturingproject i on index t is obtained as Eigi(Λt

Aver) After solvingthe index values of l intelligent manufacturing project al-ternates on other indexes by similar way the index valuematrix of l intelligent manufacturing project alternates on allindexes is obtained as X [xit]ltimesN where xit Eigi(Λt

Aver)

332 Multistage Weight Synthesis Solving index weight isthe key step of comprehensive decision of green

performance evaluation of intelligent manufacturingGenerally there are three methods to determine indexweight subjective weight method objective weight methodand synthesis weight method e subjective weight methodgenerally uses the knowledge and experience of experts butthe evaluation results are not scientific because of subjec-tivity the objective weight method determines the weightaccording to the degree of difference between indexes butoften ignores the importance of the indexes themselves thesynthesis weight method is usually composed of a variety ofsubjective and objective weight methods which can offsetthe shortcomings of different weight methods

In the aspect of index weight solving for green perfor-mance evaluation of intelligent manufacturing in order toavoid the instability of assessment result caused by singleweight and make the weight setting of assessment indexmore fair and reasonable a multistage synthesis weightmethod is proposed to solve index weight e proposedmethod has three stages of weight synthesis and there areseveral substages in each stage of weight synthesis

As shown in Figure 7 the proposed multistage weightsynthesis method has a detailed process as follows

(1) Stage 1 subjective weight synthesisSubjective weight methods mainly include complexnetworks method ANPmethod and Delphi methode principle and solution process of these methodsare as follows

(i) Complex networks method By complex net-works method the determination of indexweight is regarded as the evaluation of nodeimportance in complex networks e index canbe treated as node in complex networks and thenetwork attributes (degree centrality between-ness centrality and closeness centrality) of anode describe its importance in the networkfrom different aspects (local attribute propa-gation attribute and global attribute)ereforewe use expert evaluation to determine whetherthere is a relationship between two indexesregardless of the direction of the relationshipBased on this an undirected network with indexas node is established en the degree cen-trality betweenness centrality and closenesscentrality of each node are computed Taking thenetwork attributes of index as criterion the netflow of each index is calculated by the PreferenceRanking Organization Method for EnrichmentEvaluations II (PROMETHEE II) method erelative net flow of an index is obtained bycalculating the relative difference between its netflow and the minimum net flow and then therelative net flow of all indexes is normalized toget the index weight e process of complexnetworks method is shown in Figure 8

(ii) ANP method e ANP structure of deter-mining the subjective weight of green perfor-mance evaluation of intelligent manufacturing is

Complexity 9

SW

Substage

Substage

Substage

Substage

OW3

Substage

OWg

OWSu

bstage

TW

Stage 1

sub

jective w

eigh

t syn

thesis

Stage 2

objectiv

e weigh

t syn

thesis

Stage 3 total synthesis

Complex networks method

ANP method

Delphi method

Entropy method

CRITIC method

Standard deviationmethod

Subjective weight methods Objective weight methods

OW1 OW2SW1

SW3

SW2

SWh

Figure 7 e process of multistage weight synthesis

Is there relationship between two indexes

Establish an undirected network with index as node

Compute the degree centrality betweenness centrality and closeness centrality of each node

Calculate the net flow of each index is by PROMETHEE II

Obtain the relative net flow of an index by calculating the relative difference between its net flow and the minimum net flow and normalize it

Subjective weight vector

Figure 8 e process of obtaining subjective weight by complex networks method

10 Complexity

set up as shown in Figure 9 e control layeronly has one element the overall goal (greenperformance evaluation of intelligentmanufacturing) and the network layer has threeelement groups corresponding to three perfor-mance dimensions Each element group affectseach other and contains different elements eelements in the same element group also affecteach other Based on the expertsrsquo evaluation ofthe importance and influence among the in-dexes the weights of the indexes are determinedby the classical ANP method

(iii) Delphi method It usually relies on the knowl-edge experience and specialty of experts toscore the indexes of the evaluation object sep-arately and generally adopts the percentagegrading system and then takes the average valueof all expertsrsquo scores as the weight of the eval-uation index is method has convenient op-eration easy investigation procedure andsimple calculationIt is assumed that the subjective weight vectorsobtained by h different methods are as follows

SW1 sw1

1 sw12 sw1

N1113960 1113961T

SW2 sw2

1 sw22 sw2

N1113960 1113961T

middot middot middot

SWh swh

1 swh2 swh

N1113960 1113961T

(33)

In the subjective weight synthesis stage there are h minus 1substages and each substage corresponds to a syn-thesis Taking the synthesis of SW1 and SW2 as anexample their synthesized weight vectorSW1∘2 [sw1∘2

1 sw1∘22 sw1∘2

N ]T is defined as follows

SW1∘2 τ1SW

1+ τ2SW

2 (34)

where τ1 and τ2 are the synthesis coefficients corre-sponding to SW1 and SW2 andτ1 ge 0 τ2 ge 0 and τ1 + τ2 1According to index value matrix X [xit]ltimesN theweight contribution difference degree of SW1 and SW2

is defined as follows

ξ1∘2 1113944l

i11113944

N

t1τ1sw

1t xit minus τ2sw

2t xit1113872 1113873

2 (35)

erefore a weight synthesis optimization model isestablished to balance the weight contribution of SW1

and SW2 as follows

min ξ1∘2

st τ1 ge 0 τ2 ge 0 τ1 + τ2 1(36)

Two synthesis coefficients are solved as follows

τ1 1113936

li1 1113936

Nt1 xit1113872 1113873

2sw2

t sw1t + sw2

t( 1113857

1113936li1 1113936

Nt1 xit1113872 1113873

2sw1

t + sw2t( 1113857

τ2 1 minus τ1

(37)

SW1∘2 and SW3 are synthesized in the same way andtheir synthesized weight vector is obtained as SW1∘2∘3According to the process of subjective weight synthesisstage shown in Figure 1 the synthesized subjectiveweight vector can be obtained in the end as follows

SW1∘2∘∘h sw1∘2∘∘h

1 sw1∘2∘∘h2 sw1∘2∘∘h

N1113960 1113961T (38)

(2) Stage 2 objective weight synthesisObjective weight methods mainly include entropymethod CRITIC method and standard deviationmethod e principle and solution process of thesemethods are as follows

(i) Entropy method In information theory entropy isa measure of uncertainty which determines theweight according to the variation in index Gen-erally the smaller the entropy of an index thegreater the variation degree in the index the morethe information it provides and the greater itsweight on the contrary the larger the entropy of anindex the smaller the variation degree of the indexthe less information it provides and the smaller itsweight Entropymethod calculates the weight of anindex based on its information quantity

(ii) CRITIC method Its basic idea is to compre-hensively measure the weight of the indexthrough the contrast intensity within the indexand the conflict between the indexes Contrast

Overall goal

Index 1

Index 3

Index 2

Index 7

Index 9

Index 8

Index 4

Index 6

Index 5

Dimension 1

Dimension 2 Dimension 3

Control layer

Network layer

Figure 9 e ANP structure

Complexity 11

intensity is presented in the form of standarddeviation while conflict is determined by thecorrelation between indexes

(iii) Standard deviation method is method usesthe standard deviation of an index to determineits weight If an index has a larger standarddeviation which means that the index is moredifferent in value its weight will be larger Bynormalizing the standard deviations of all in-dexes the weights of indexes can be obtainedAccording to the process of objective weightsynthesis stage shown in Figure 1 by the sameway with the solving process of synthesizedsubjective weight vector the synthesized ob-jective weight vector also can be obtained in theend as follows

OW1∘2∘∘g ow1∘2∘∘g

1 ow1∘2∘∘g2 ow1∘2∘∘g

N1113960 1113961T

(39)

(3) Stage 3 total synthesisUnder the premise of obtaining synthesized sub-jective weight SW1∘2∘∘h and synthesized objectiveweight OW1∘2∘∘g total synthesis of subjective andobjective weight is carried out using the same weightsynthesis optimization model shown by formula(35) and the vector TW [tw1 tw2 twN]T isobtained as follows

TW τswSW1∘2∘∘h

+ τowOW1∘2∘∘g

(40)

where τsw and τow are the subjective synthesis coeffi-cient and objective synthesis coefficient and they arecorresponding to SW1∘2∘∘h and OW1∘2∘∘g respec-tively Here τsw ge 0 τow ge 0 and τsw + τow 1

333 Intelligent Manufacturing Project Evaluation byPROMETHEE II Traditional object assessment methods in-clude TOPSIS (Technique for Order Preference by Similarity toan Ideal Solution) [28] VIKOR (VlseKriterijumska Opti-mizacija I Kompromisnoresenje) [29] AHP and other mixed-model MCDM methods ese methods have decision com-pensation in the assessment and decision-making process thatis the high value of one index can remedy the low value ofother indexes In this part PROMETHEE II [30] is used toassess the green performance and sort several intelligentmanufacturing projectse core idea of thismethod is that thelevel is not lower than the relationship By PROMETHEE IIthe priority function is used to compare the intelligentmanufacturing projects one by one to determine the prioritysequence of all intelligent manufacturing projects which canavoid the influence of decision compensation on the assess-ment results of intelligentmanufacturing projectsismethodfully considers the objective facts of the existence of thepreference of the decision-maker making the decision-makingresults more convincing

In PROMETHEE II there are many common criteria todetermine the preference function Compared with others theGaussian preference function has nonlinear characteristicswhich is more in line with the actual decision-making envi-ronmenterefore this paper chooses the preference functionin the form of Gaussian criteria e index values of intelligentmanufacturing projects i andm (im 1 2 l and inem) inindex t are xit and xmt respectively On index t the preferencefunction of intelligent manufacturing project i compared withintelligent manufacturing project m is defined as follows

pt(i m) 0 xit minus xmt le 0

1 minus eminus xitminus xmt( )22η2 xit minus xmt gt 0

⎧⎨

⎩ (41)

where the value of parameter η is 02Under the condition of considering all indexes the

weighted preference degree of intelligent manufacturingproject i compared with intelligent manufacturing projectmis expressed as follows

p(i m) 1113944N

t1wt middot pt(i m) (42)

e outflow Ω+i and inflow Ωminus

i of intelligentmanufacturing project i can be obtained as follows

Ω+i 1113944

l

m1mneip(i m)

Ωminusi 1113944

l

m1mneip(m i)

(43)

where p(m i) represents the weighted preference degree ofintelligent manufacturing project m compared with intel-ligent manufacturing project i under the condition ofconsidering all indexes

e degree of intelligent manufacturing project i su-perior to other projects can be represented by outflow Ω+

i and the degree of intelligent manufacturing project i inferiorto other projects can be represented by inflowΩminus

i ereforethe preference net flow of intelligent manufacturing project iis represented as follows

Ωi Ω+i minusΩminus

i (44)

e net flow is the main basis for the PROMETHEE IImethod to measure the advantages and disadvantages of theintelligent manufacturing projects e priority rankingresults of all intelligent manufacturing projects can be ob-tained by comparing the net flow values

4 Case Study Application of the FRSA-MSWS-PII Model for Green PerformanceEvaluation of Intelligent ManufacturingProject for an Air Conditioning EnterpriseDriven by Digital Twin

e remote operation and maintenance service project is akey component of the intelligent manufacturing strategy foran air conditioning enterprise is section will evaluate the

12 Complexity

green performance of the remote operation and mainte-nance service project alternatives to obtain the optimal onefrom multiple alternatives e enterprise has built thedigital twin system of its intelligent manufacturing projectwhich can provide the digital twin data of whole life cycle forgreen performance evaluation ere are ten alternatives ofintelligent manufacturing project of remote operation andmaintenance service which are Alter 1 Alter 2 Alter10ree experts participate in the index value calculation ofintelligent manufacturing project alternatives For index 1the fuzzy reciprocal assessment matrices given by threeexperts are 1113957Φ11

[1113957ϕ11ij ]10times10 1113957Φ21

[1113957ϕ21ij ]10times10 and

1113957Φ31 [1113957ϕ31

ij ]10times10 Due to limited space and without losinggenerality only 1113957Φ11 is given as follows

1113957Φ11

E OS E WS OS E ES WS OS E

OI E OI WI E E SI OI WI WI

E OS E WS E OS WS SS E OS

WI WS WI E WS OS E WS E SS

OI E OI WI E EI E SI WI WI

E E OI OI ES E E SI SI EI

EI SS WI E SS E E SS OS E

WI OS SI WI SS SS SI E WI WS

OI WS E E WS SS OI WS E SI

E WS OI SI WS ES E WI SS E

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(45)

rough consistency inspection three matrices 1113957Φ111113957Φ21 and 1113957Φ31 can pass the inspection en the groupjudgment matrix 1113957Θ1 [1113957ρ1ij]10times10 is constructed based on1113957Φ11 1113957Φ21 and 1113957Φ31 and 1113957ρ1ij 1113957ϕ11

ij 1113957ϕ21ij 1113957ϕ31

ij1113882 1113883 For example

1113957ρ112 1113957ϕ1112

1113957ϕ2112

1113957ϕ31121113882 1113883 OSEOS (10000 12222

18571 23333) (10000 10000 10000 10000) (1000012222 18571 23333) Based on formulas (11)ndash(13) therough boundary interval of 1113957ϕ11

12 OS in 1113957ρ112

1113957ϕ1112

1113957ϕ2112

1113957ϕ31121113882 1113883 is obtained as RBI(1113957ϕ11

12) [LRL(1113957ϕ1112)

URL(1113957ϕ1112)] [(10000 11481 15714 18889) (10000

12222 18571 23333)] while RBI(1113957ϕ2112)

[LRL(1113957ϕ2112)URL(1113957ϕ21

12)] [(10000 10000 10000 10000)(10000 11481 15714 18889)] and RBI(1113957ϕ31

12)

[LRL(1113957ϕ3112)URL(1113957ϕ31

12)] [(10000 11481 15714 18889)(10000 12222 18571 23333)] According to the arithmeticoperation rules shown in formulas (14)ndash(16) the rough

boundary interval of 1113957ρ112 1113957ϕ1112

1113957ϕ2112

1113957ϕ31121113882 1113883 can be obtained

as RBI(1113957ρ112) [(10000 10988 13809 15926) (1000011975 17619 21852)]

e rough boundary intervals of other elements in 1113957Θ1

[1113957ρ1ij]10times10 can be obtained by the same way e RBIjudgment matrix is constructed as 1113957Λ1 [RBI(1113957ρ1ij)]10times10en 1113957Λ1 is decomposed into LRL matrix 1113957Λ1LRL and URLmatrix 1113957Λ1URL 1113957Λ1LRL is shown in Tables 3 and 4 while 1113957Λ1URL isshown in Tables 5 and 6

According to formula (8) 1113957Λ1LRL and 1113957Λ1URL are convertedinto real number forms Λ1LRL shown in Table 7 and Λ1URLshown in Table 8

e eigenvectors of Λ1LRL and Λ1URL corresponding to the

maximum eigenvalue are obtained respectively asEig(Λ1LRL) and Eig(Λ1URL) After averaging the two eigen-vectors an average vector is obtained asEig(Λ1Aver) [03353 03039 03235 03009 03108 0335402915 03100 03234 03214]T

e index value of ten intelligent manufacturing projectalternatives on index 1 is obtained as Eig(Λ1Aver) Aftersolving the index values of ten intelligent manufacturingproject alternatives on other indexes by the same way theindex value matrix of ten intelligent manufacturing projectalternatives on all indexes is obtained as X [xit]10times9 asshown in Table 9

Subjective weight solved by the complex networksmethod ANP method and Delphi method is shown inTable 10 while objective weight solved by the entropymethod CRITIC method and standard deviation method isshown in Table 11

As shown in Figure 10 the weight synthesis has threestages Stage 1 and stage 2 have two substages respectively

e synthesized weight obtained in each stage is shownin Table 12

According to formulas (40) and (41) the weightedpreference degree matrix is obtained as shown in Table 13

According to formulas (42) and (43) the outflow inflownet flow and final rank are obtained as shown in Table 14

5 Discussion of the Results

In order to make a final selection of the optimal alternativesit is necessary to assess the reliability of the results obtainedby the initial model e most common means of assessingthe reliability of the results is to compare them with otherMCDM techniques e discussion of the results is pre-sented using the comparison of three MCDM methods(PROMETHEE II TOPSIS and VIKOR) ese methodswere chosen because they have so far given stable and re-liable results [27ndash30] TOPSIS and VIKOR methods weremodified using fuzzy rough-sets AHP and multistage weightsynthesis techniques proposed in this paper which are calledFRSA-MSWS-TOPSIS and FRSA-MSWS-VIKOR esetwo modified models are compared with the proposedFRSA-MSWS-PII Additionally the models for comparison(FRSA-MSWS-TOPSIS and FRSA-MSWS-VIKOR) are di-vided into multiple submodels which are with synthesis ofdifferent quantity weights In the second part of this sectiona sensitivity analysis [31 32] of the proposed FRSA-MSWS-PII model was carried out through 27 scenarios

Complexity 13

51 Comparing the Ranks of Different ModelsFRSA-MSWS-TOPSIS model and FRSA-MSWS-TOPSISmodel are divided into multiple submodels All modelsincluding the proposed model (model 1) are as follows

(1) Model 1 proposed model (FRSA-MSWS-PII) withsynthesis of six weights (SW1 SW2 SW3+OW1OW2 OW3)

(2) Model 2 FRSA-MSWS-TOPSIS with synthesis oftwo weights

Model 21 SW1+OW1

Model 22 SW1+OW2

Model 23 SW2 +OW2

Model 24 SW2 +OW3

Model 25 SW3 +OW1

Model 26 SW3 +OW3

(3) Model 3 FRSA-MSWS-VIKOR with synthesis oftwo weights

Model 31 SW1 +OW1

Model 32 SW1 +OW2

Model 33 SW2 +OW2

Model 34 SW2 +OW3

Model 35 SW3 +OW1

Model 36 SW3 +OW3

Table 3 LRL matrix 1113957Λ1LRL (part 1 columns 1ndash5)

Alter 1 2 3 4 5

1 (1 1 1 1) (10000 10988 1380915926)

(11037 16779 1869419372)

(06468 17128 1854018657)

(09951 13021 1357217378)

2 (05336 05676 1039713301) (1 1 1 1) (04684 09725 11776

13317)(08246 10541 10761

16594)(05427 08139 09974

13416)

3 (11489 14540 1456115842)

(04953 05825 0856816916) (1 1 1 1) (08178 11612 12975

19428)(10195 10630 15027

19814)

4 (07188 10560 1695217386)

(09026 11191 1423414681)

(07571 09762 1027212090) (1 1 1 1) (05961 11055 11799

13777)

5 (05566 09454 1272814644)

(06137 09540 1273613970)

(14355 14538 1502519150)

(11477 11610 1391314760) (1 1 1 1)

6 (08475 14009 1741017550)

(10563 11164 1723718260)

(07848 10350 1675119214)

(07092 16417 1786119843)

(04996 13061 1402814263)

7 (06408 06771 0743107685)

(11400 12236 1280515275)

(05379 07261 1007412589)

(06112 11761 1496918638)

(06579 07795 0914913757)

8 (05216 06006 0879217264)

(10414 11301 1636616826)

(08778 15035 1549516198)

(06862 08049 1730018657)

(04572 06153 1651119409)

9 (11202 12001 1371513804)

(09248 11256 1142512045)

(10368 12759 1448717079)

(07720 09169 1359914148)

(12160 15583 1657518508)

10 (04973 11939 1225016033)

(07335 08219 1343916985)

(12856 14828 1483115321)

(05005 13199 1487218169)

(06924 10332 1449417761)


Alter 6 7 8 9 10

1 (08231 14384 1498019344)

(07973 08449 1485117588)

(04518 10495 1383418698)

(10328 10413 1067112811)

(10170 10771 1145016334)

2 (05954 06653 0747615292)

(06231 06613 1217515019)

(13189 15298 1768618909)

(04508 13995 1791419844)

(06138 06702 0708014125)

3 (05483 15937 1783718983)

(04979 06576 0725310678)

(05462 09109 0964719929)

(05753 05893 1428216547)

(04660 09057 0974116068)

4 (07969 09776 1357219376)

(06649 12982 1830919369)

(08275 09925 1712118904)

(06747 13023 1348517974)

(05677 06411 0821910728)

5 (12083 12108 1849219144)

(07146 08002 0802911253)

(06222 11302 1852619686)

(06320 07937 1384415524)

(08933 09312 1100123003)

6 (1 1 1 1) (05999 12586 1717217181)

(11534 14559 1690519581)

(08006 10462 1353613637)

(09830 15819 1727819731)

7 (04849 08541 1371317175) (1 1 1 1) (05054 09498 11806

16663)(07472 09787 13915

15946)(05912 07424 08956

13431)

8 (10599 12561 1490715989)

(05189 08263 1135716201) (1 1 1 1) (04803 11356 15093

15413)(12220 13407 17600

18463)

9 (05794 14202 1474515811)

(04763 06373 1349118889)

(04891 11740 1454717554) (1 1 1 1) (05341 07245 09628

14774)

10 (08962 10925 1545719992)

(08964 15462 1581016611)

(09733 13922 1598916593)

(05296 15882 1688418302) (1 1 1 1)

14 Complexity

Table 5 URL matrix 1113957Λ1URL (part 1 columns 1ndash5)

Alter 1 2 3 4 5

1 (1 1 1 1) (10000 11975 1761921852)

(13959 18678 2560629058)

(08786 22426 2668147228)

(14288 24658 2817839657)

2 (13456 19678 2514228548) (1 1 1 1) (11568 14847 25474

30198)(10122 10903 28725

48158)(08339 08947 15098

26066)

3 (14519 15936 2003424383)

(18749 24067 2843532298) (1 1 1 1) (13095 18756 19465

34211)(08830 27474 28092

41440)

4 (09330 16784 1959125506)

(08341 11678 1246129649)

(09159 28247 2893638990) (1 1 1 1) (09411 22048 23311

23398)

5 (16968 23804 2604048683)

(09998 17316 1919225134)

(12597 13015 1319723604)

(15705 22564 2494625479) (1 1 1 1)

6 (19121 19896 2080927139)

(16729 24921 2578739713)

(15206 17650 2276843007)

(14500 19317 2093727454)

(09090 15973 1608518771)

7 (08938 14201 2197430621)

(10727 18788 2676644705)

(11865 12597 1538946016)

(15736 20361 2419824402)

(09572 10258 1333527689)

8 (09447 14976 2328628905)

(12111 17803 1877535145)

(10618 11577 2241228931)

(09720 19844 2659229915)

(09858 24791 2598127111)

9 (08528 11187 1690118615)

(19187 19237 2598841383)

(15716 27271 2865831107)

(13071 16180 1836026575)

(15352 16308 2337227600)

10 (21417 21589 2790444097)

(08631 15053 1877827503)

(10816 11919 1518729980)

(12190 16116 1813649229)

(12200 13066 1742218604)


Alter 6 7 8 9 10

1 (10856 14359 2278023293)

(08282 15578 2285725171)

(17336 18140 1817440347)

(12599 12930 1567629902)

(21814 24984 2852348855)

2 (19559 19668 2694528364)

(10309 11247 1217418890)

(20821 25939 2733849534)

(17569 18550 1960925630)

(09146 20622 2848638604)

3 (25282 26897 2956229657)

(14502 14629 2198328661)

(09020 14561 1911939980)

(10401 19743 2791342684)

(09066 21276 2269430096)

4 (13612 19131 2452837361)

(11284 13665 1868026496)

(12325 13524 2155327878)

(15721 21685 2676729556)

(10085 12046 1327917180)

5 (12671 15430 1612327801)

(14844 15762 1746528314)

(13677 16992 1901321088)

(14527 15013 1733229330)

(11802 12257 1554719670)

6 (1 1 1 1) (11297 22511 2389429781)

(09836 13593 1751326157)

(13540 14390 1914221576)

(10371 20850 2793944945)

7 (11553 14880 1550817356) (1 1 1 1) (11869 14414 18417

23879)(13343 13919 28183

40151)(17366 20025 23034

35067)

8 (11300 15650 1901020894)

(15903 23132 2419924578) (1 1 1 1) (13946 15279 16276

17335)(13428 20892 24250

35989)

9 (24919 27597 2961132421)

(16795 18655 2658726980)

(15653 20299 2673326790) (1 1 1 1) (10599 27767 29745

30679)

10 (12209 18226 2480726000)

(10587 16723 2024723236)

(10306 10814 2009028380)

(09603 09948 2556447606) (1 1 1 1)

Table 7 Real number form matrix Λ1LRL

Alter 1 2 3 4 5 6 7 8 9 101 1 15314 16206 14502 13533 14101 12253 11829 11195 124672 08732 1 09696 11815 09277 09341 10056 16240 13692 090033 13962 09456 1 13245 14052 13976 07491 11550 10641 100244 12965 12240 09899 1 10433 12840 14147 13558 12670 078295 10521 10520 16035 12950 1 15459 08802 13835 10907 138236 14157 14310 13540 14816 11058 1 13005 15629 11353 154467 07071 13030 08849 12772 09513 11062 1 10778 11772 090948 09719 13723 13468 12719 11681 13485 10335 1 11417 154179 12668 10891 13683 11145 15616 12089 10983 11979 1 0940810 11048 11561 14336 12495 12373 13923 13778 13899 13436 1

Complexity 15

Table 9 Index value matrix X [xit]10times9

Index 1 Index 2 Index 3 Index 4 Index 5 Index 6 Index 7 Index 8 Index 9Alter 1 03353 08333 09152 02143 09220 06691 01878 03506 05922Alter 2 03039 09618 09684 02419 09735 09615 05368 08203 02277Alter 3 03235 04796 09242 08130 09635 06902 01321 08642 09406Alter 4 03009 07109 07820 07688 04530 06899 02541 07354 01286Alter 5 03108 03492 01416 01874 08411 07253 03854 09552 01310Alter 6 03354 04949 04434 07890 08157 02682 05408 05010 06817Alter 7 02915 07384 07792 03484 07117 06896 02464 02071 05485Alter 8 03100 09638 04063 06267 03014 07761 03296 05554 07292Alter 9 03234 09018 09634 05925 02248 02344 03318 08566 03289Alter 10 03214 08329 03192 09363 04150 02769 03260 03260 05260

Table 8 Real number form matrix Λ1URL

Alter 1 2 3 4 5 6 7 8 9 101 1 19481 21786 26741 26765 17774 17807 25275 18617 321432 21596 1 20555 25039 15031 23644 13543 32199 20662 241493 18819 25825 1 22090 26034 27819 20116 21619 25455 204334 17712 16605 25614 1 18669 24042 17760 18956 23310 132615 30017 17821 16409 21853 1 18684 19738 17633 19750 149446 22110 27231 25680 20662 14638 1 21489 17024 17196 263857 19067 25757 23581 21032 16022 14725 1 17266 24189 244278 19157 21776 18503 21235 20933 16615 21507 1 15697 239049 13786 27131 25055 18854 20731 28643 22239 22266 1 2358710 29505 17620 17784 25948 15328 20168 17550 17606 23935 1

Table 10 Subjective weight

Index 1 Index 2 Index 3 Index 4 Index 5 Index 6 Index 7 Index 8 Index 9Complex networks method (SW1) 00685 00309 01646 00656 00258 01591 01396 02425 01034ANP method (SW2) 00284 00913 00711 01715 01104 01162 01852 01049 01209Delphi method (SW3) 00830 00497 00607 00970 01141 01530 01323 00875 02226

Table 11 Objective weight

Index 1 Index 2 Index 3 Index 4 Index 5 Index 6 Index 7 Index 8 Index 9Entropy method (SW1) 01154 01133 01099 01091 01108 01111 01117 01110 01077CRITIC method (SW2) 01077 01153 01024 01189 01066 01143 01163 01116 01069Standard deviation method (SW3) 00072 01070 01515 01388 01416 01226 00663 01306 01344

SW3

SW2SW1

OW3

OW1 OW2

Subs

tage

1-1

Subs

tage

1-2

Subs

tage

2-1

Subs

tage

2-2

TW

Stage 1 Stage 2

Stage 3

SW1∘2 OW1∘2

SW1∘2∘3 OW1∘2∘3

Figure 10 e weight synthesis process

16 Complexity

(4) Model 4 FRSA-MSWS-TOPSIS with synthesis ofthree weights

Model 41 SW1 SW2 +OW1

Model 42 SW2 SW3+OW2


Model 44 SW1+OW1 OW2



(5) Model 5 FRSA-MSWS-VIKOR with synthesis ofthree weights







(6) Model 6 FRSA-MSWS-TOPSIS with synthesis offour weights

Model 61 SW1 SW2 +OW1 OW2

Model 62 SW1 SW2+OW2 OW3





(7) Model 7 FRSA-MSWS-VIKOR with synthesis offour weights







(8) Model 8 FRSA-MSWS-TOPSIS with synthesis offive weights

Model 81 SW1 SW2 SW3+OW1 OW2



Model 84 SW1 SW2 +OW1 OW2 OW3



Table 14 e outflow inflow net flow and final rank

Outflow Inflow Net flow Final rankAlter 1 20998 20036 00962 4Alter 2 33781 14468 19313 2Alter 3 36129 10577 25552 1Alter 4 20032 21477 minus01445 5Alter 5 16731 32940 minus16208 10Alter 6 23546 25657 minus02111 6Alter 7 17805 24108 minus06302 8Alter 8 22557 21512 01045 3Alter 9 20233 25379 minus05145 7Alter 10 16088 31748 minus15660 9

Table 12 e synthesized weight obtained in each stage

Synthesis coefficients Index 1 Index 2 Index 3 Index 4 Index 5 Index 6 Index 7 Index 8 Index 9Substage 1ndash1 SW1∘2 03131 and 06869 00409 00724 01004 01384 00839 01296 01709 01480 01154Substage 1ndash2 SW1∘2∘3 06181 and 03819 00570 00638 00852 01226 00954 01385 01562 01249 01564Substage 2ndash1 OW1∘2 07110 and 02890 01132 01139 01077 01119 01096 01120 01130 01111 01075Substage 2ndash2 OW1∘2∘3 04289 and 05711 00527 01100 01327 01273 01279 01181 00864 01222 01228Stage 3 TW 03509 and 06491 00542 00937 01161 01256 01165 01252 01108 01232 01346

Table 13 e weighted preference degree matrix

Alter 1 Alter 2 Alter 3 Alter 4 Alter 5 Alter 6 Alter 7 Alter 8 Alter 9 Alter 10Alter 1 0 01097 00784 02744 03406 03040 01158 02275 03077 03417Alter 2 03107 0 02633 03761 03417 04448 04223 03916 02909 05367Alter 3 03512 02610 0 02990 04132 04260 04460 04158 04229 05779Alter 4 02334 01217 00645 0 03146 03027 02314 01943 02120 03286Alter 5 01696 00251 00751 01781 0 02308 01711 02242 02525 03466Alter 6 02542 02477 00974 02982 03858 0 03120 01972 03178 02443Alter 7 00306 01140 00698 01867 03491 02484 0 01980 02872 02967Alter 8 02483 02347 01425 02035 04120 02161 02838 0 02529 02619Alter 9 02567 01170 01293 01556 03694 02919 02656 01974 0 02404Alter 10 01489 02158 01373 01762 03675 01012 01628 01051 01939 0

Complexity 17

(9) Model 9 FRSA-MSWS-VIKOR with synthesis offive weights

Model 91 SW1 SW2 SW3 +OW1 OW2



Model 94 SW1 SW2+OW1 OW2 OW3



(10) Model 10 FRSA-MSWS-TOPSIS with synthesis ofsix weights (SW1 SW2 SW3+OW1 OW2 OW3)

(11) Model 11 FRSA-MSWS-VIKOR with synthesis ofsix weights (SW1 SW2 SW3+OW1 OW2 OW3)

Ranking of the alternatives according to the models usedin order to assess the reliability of the results shows thatalternative 3 remained in the first place for the majority ofthemodels (Tables 15ndash19)ere was a change in the rankingof alternative 3 using the FRSA-MSWS-TOPSIS model andFRSA-MSWS-TOPSIS model whereby alternatives 3 and 2changed places for the majority of the models

In order to establish the connection between the resultsobtained using 51 different models (Tables 15ndash19) Spear-manrsquos correlation coefficient (SCC) was used SCC of ranksis a useful and important indicator for determining the linkbetween the results obtained by different models [31ndash33]Additionally the case in this study has ordinal variables orranked variables while SCC is suitable for use in this sit-uation In this paper SCC was used to define the statistical

significance of the difference between the ranks obtained bydifferent models e results of the comparison of ranksusing SCC are shown in Tables 20ndash24

e SCC values from Tables 20ndash24 which are with theaverage values of 064 074 077 090 and 092 (all greaterthan 060) show a high correlation between the ranks amongthe models examined In addition the average value of SCCtends to increase when the number of synthesized weightsincreases which reveals that the model tends to be stable whenmore weights are synthesized Based on recommendations byGhorabaee et al [33] when all SCC values are greater than 08an extremely high correlation is shown In our case when thenumber of synthesized weights is 6 all of the SCC values aresignificantly greater than 08 (Table 24) and the average value is092 when the number of synthesized weights is 5 most of theSCC values are significantly greater than 08 (Table 23) and theaverage value is 090 when the number of synthesized weightsis 4 most of the SCC values are also significantly greater than08 (Table 22) and the average value is 077 (slightly less than08) erefore we can conclude that there is a very highcorrelation (closeness) between the proposed FRSA-MSWS-PII model and the other models for the treatment of uncer-tainty (fuzzy and rough) especially when the number ofsynthesized weights is more than 4

52 Sensitivity Analysis Since the results of MCDM modelsdepend to a great extent on the values of the weight coef-ficients of the assessment index this section shows

Table 15 Comparison of the ranks of alternatives according to models 1 2 and 3

Model 1Model 2 Model 3

21 22 23 24 25 26 31 32 33 34 35 36Alter 1 4 6 6 6 6 4 4 7 7 9 8 2 2Alter 2 2 2 2 2 2 3 2 1 1 3 4 3 3Alter 3 1 1 1 1 1 1 1 2 2 6 1 1 1Alter 4 5 3 3 5 5 7 7 3 3 2 3 9 9Alter 5 10 7 7 10 10 10 10 9 9 10 10 10 10Alter 6 6 8 8 3 3 5 5 5 6 1 2 4 4Alter 7 8 9 9 9 9 6 6 10 10 8 7 6 5Alter 8 3 5 5 4 4 2 3 6 5 4 6 5 6Alter 9 7 4 4 8 7 9 8 4 4 7 9 8 8Alter 10 9 10 10 7 8 8 9 8 8 5 5 7 7




18 Complexity








Model 1 Model 10 Model 11Alter 1 4 4 3Alter 2 2 2 2Alter 3 1 1 1Alter 4 5 6 5Alter 5 10 10 10Alter 6 6 5 4Alter 7 8 8 9Alter 8 3 3 6Alter 9 7 7 8Alter 10 9 9 7

Table 20 Correlation of the ranks in the models 1 2 and 3

Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36

Model 1 1 078 078 088 090 090 094 076 079 038 058 077 071Model21 mdash 1 1 061 068 048 059 087 090 021 035 032 027

Model22 mdash mdash 1 061 068 048 059 087 090 021 035 032 027

Model23 mdash mdash mdash 1 099 083 084 079 078 067 084 073 067

Model24 mdash mdash mdash mdash 1 082 085 084 083 065 079 072 066

Complexity 19

sensitivity analysis of the results when there is a change inthe weights of the assessment index

Sometimes the ranks of the alternatives change as a resultof very small changes in the weight coefficients ereforethe results of MCDM models as a rule are accompanied byan analysis of their sensitivity to these changes is sectionpresents a sensitivity analysis of the ranking of the alter-natives to changes in the weight coefficients of the assess-ment index carried out through 27 scenarios (Tables 25ndash27)

e scenarios for the sensitivity analysis were groupedinto three phases In each phase of the sensitivity analysis

the weight coefficients of the assessment index are increasedrespectively by 25 50 and 75 One assessment index isfavoured per scenario for each of nine scenarios in the phaseand its weight coefficient is increased by the given values Inthe same scenario the weight coefficients of the remainingassessment index were each reduced by the correspondingratios Changes in the ranking of the alternatives for thescenarios are shown in Tables 25ndash27

e results (Tables 25ndash27) show that the allocation ofdifferent weights to the assessment index through the sce-narios leads to a change in the ranking of the alternatives

Table 20 Continued

Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36

Model25 mdash mdash mdash mdash mdash 1 098 047 050 032 059 088 083

Model26 mdash mdash mdash mdash mdash mdash 1 058 060 031 056 089 085

Model31 mdash mdash mdash mdash mdash mdash mdash 1 099 059 061 038 033

Model32 mdash mdash mdash mdash mdash mdash mdash mdash 1 055 056 037 031

Model33 mdash mdash mdash mdash mdash mdash mdash mdash mdash 1 077 014 009

Model34 mdash mdash mdash mdash mdash mdash mdash mdash mdash mdash 1 049 048

Model35 mdash mdash mdash mdash mdash mdash mdash mdash mdash mdash mdash 1 099

Model36 mdash mdash mdash mdash mdash mdash mdash mdash mdash mdash mdash mdash 1


Model1

Model41

Model42

Model43

Model44

Model45

Model46

Model51

Model52

Model53

Model54

Model55

Model56













20 Complexity


Model1

Model61

Model62

Model63

Model64

Model65

Model66

Model71

Model72

Model73

Model74

Model75

Model76














Model1

Model81

Model82

Model83

Model84

Model85

Model86

Model91

Model92

Model93

Model94

Model95

Model96













Complexity 21


Model 1 Model 10 Model 11Model 1 1 099 088Model 10 mdash 1 089Model 11 mdash mdash 1

Table 25 Scenarios for the sensitivity analysis (phase I 25)

tw1lowast 125 tw2lowast1 25 tw3lowast125 tw4lowast125 tw5lowast125 tw6lowast125 tw7lowast125 tw8lowast125 tw9lowast125Alter 1 4 4 3 8 3 3 5 7 4Alter 2 2 2 2 3 2 1 1 1 2Alter 3 1 1 1 1 1 2 2 2 1Alter 4 5 5 4 5 8 5 4 3 7Alter 5 10 10 9 10 6 7 10 5 10Alter 6 6 7 5 2 4 8 3 8 5Alter 7 8 8 7 9 5 6 7 9 6Alter 8 3 3 8 4 7 4 6 6 3Alter 9 7 6 6 7 9 9 8 4 8Alter 10 9 9 10 6 10 10 9 10 9


tw1lowast 150 tw2lowast150 tw3lowast150 tw4lowast150 tw5lowast150 tw6lowast150 tw7lowast150 tw8lowast150 tw9lowast150Alter 1 4 4 3 8 3 4 6 7 4Alter 2 2 1 2 5 2 1 1 1 2Alter 3 1 2 1 1 1 2 2 2 1Alter 4 5 5 4 4 7 5 4 3 7Alter 5 10 10 9 10 5 7 10 5 10Alter 6 6 8 7 2 4 8 3 8 5Alter 7 8 7 6 9 6 6 7 9 6Alter 8 3 3 8 3 8 3 5 6 3Alter 9 7 6 5 7 9 9 8 4 8Alter 10 9 9 10 6 10 10 9 10 9



Table 28 Correlations in the ranking of 27 scenarios

Scenario SCC Scenario SCC Scenario SCCS1 100 S10 100 S19 100S2 099 S11 095 S20 093S3 081 S12 077 S21 077S4 073 S13 068 S22 058S5 064 S14 059 S23 059S6 084 S15 085 S24 085S7 085 S16 087 S25 090S8 061 S17 061 S26 059S9 094 S18 094 S27 092

22 Complexity

which confirms that the model is sensitive to changes in theweight coefficients By comparing the alternatives which areranked first (Alter 3 and Alter 2) in scenarios 1ndash27 with theinitial ranking (Table 14) it is can be seen that the rank of thehighest ranked alternative is confirmed Analyzing theranking through 27 scenarios also shows that alternativeAlter 3 holds its rank in 16 scenarios while in 11 scenariosit is ranked second e alternative ranked second (Alter 2)holds its rank in 13 scenarios while it is ranked first in 11scenarios Changing the weights of the assessment indexesthrough the scenarios leads to changes in the ranking of theremaining alternatives However these changes were notdrastic which also confirms the correlation of the ranksthrough the scenarios (Table 28)

e SCC values were obtained by comparing the initialranks of the FRSA-MSWS-PII model (Table 14) with thoseobtained through the scenarios (Tables 25ndash27) By analyzingthe results (Table 28) we can conclude that there is a highcorrelation of the ranks since in 15 scenarios the value ofSCC is greater than 080 while in the remaining scenarios itis greater than 055e average value of SCC through all thescenarios is 081 which indicates a high average correlationOn this basis we can conclude that there is satisfactorycloseness of the ranks and that the proposed ranking isconfirmed and credible

6 Conclusions

In future manufacturing industry there is no doubt aboutthat green intelligent manufacturing is the target direction ofsustainable development e key point of green intelligentmanufacturing is to achieve a reasonable balance of envi-ronmental social and economic performance ofmanufacturing system and a sustainable development ofconsumption and production Obviously some technicaland policy support are required Driven by digital twinsystem this paper focuses on the methodology from theperspective of green performance evaluation of intelligentmanufacturing to promote the transformation ofmanufacturing industry to green intelligent manufacturing

Because the contribution in this paper is just a pilotstudy on the social influence evaluation for intelligentmanufacturing there are many future works that should becarried out in the future It is only a performance evalu-ation model based on MCDM and the mechanism thathow multiple factors affect the green performance of in-telligent manufacturing has not been studied deeply Inaddition the development of intelligent manufacturingwill pay more attention to the impact on people in thefuture In the final analysis whether intelligentmanufacturing can provide human with a well-being workand comfortable life will be explored Human-orientedgreen performance evaluation methodology of intelligentmanufacturing is necessary to study in the future Forexample the long-term and cumulative impact of intel-ligent manufacturing on human beings should be evalu-ated with the coordination of intelligence and economy ofintelligent manufacturingen a green maturity model ofintelligent manufacturing in the whole life cycle can be

built based on the decision-making support from the greenperformance evaluation

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interest

Authorsrsquo Contributions

Lianhui Li and Bingbing Lei are the principal investigators ofthe study Bingbing Lei assisted Lianhui Li to propose thenovel hybrid model Chunlei Mao and Hongxia Sundesigned the case study and checked the manuscript YipingYuan processed the data and did the data analysis work inthe case study

Acknowledgments

e authors thank assistant editor for the useful suggestionswhich improve the quality of this researchis research wasfunded by e ird Batch of Ningxia Youth TalentsSupporting Project (TGJC2018048) Ningxia Natural Sci-ence Foundation (NZ17111 and 2020AAC03202) NationalNatural Science Foundation of China (51875251) Guang-dong Special Support Talent Program-Innovation and En-trepreneurship Leading Team (2019BT02S593) NationalKey Research and Development Plan (2019YFB2102000)and Youth Project with Special Fund for Basic ScientificResearch Business Expenses of Central Level Public WelfareScientific Research Institutes (Y919008)

References

[1] H Feng L Xi L Xiao T Xia and E Pan ldquoImperfect pre-ventive maintenance optimization for flexible flowshopmanufacturing cells considering sequence-dependent groupschedulingrdquo Reliability Engineering amp System Safety vol 176pp 218ndash229 2018

[2] G Mejıa and J Pereira ldquoMultiobjective scheduling algorithmfor flexible manufacturing systems with Petri netsrdquo Journal ofManufacturing Systems vol 54 pp 272ndash284 2020

[3] J Delaram and O F Valilai ldquoAn architectural solution forvirtual computer integrated manufacturing systems using ISOstandardsrdquo Scientia Iranica vol 26 no 6 pp 3712ndash37272018

[4] Q Guo and M Zhang ldquoA novel approach for multi-agent-based Intelligent Manufacturing Systemrdquo Information Sci-ences vol 179 no 18 pp 3079ndash3090 2009

[5] A Simeone ldquoResource efficiency optimization engine in smartproduction networks via intelligent cloud manufacturingplatformsrdquo Procedia Cirp vol 78 pp 19ndash24 2018

[6] S Ren Y Zhang Y Liu T Sakao D Huisingh andC M V B Almeida ldquoA comprehensive review of big dataanalytics throughout product lifecycle to support sustainablesmart manufacturing a framework challenges and futureresearch directionsrdquo Journal of Cleaner Production vol 210pp 1343ndash1365 2019

Complexity 23

[7] S Wang W D Liang and X T Cai ldquoBig data enabled in-telligent immune system for energy efficient manufacturingmanagementrdquo Journal of Cleaner Production vol 195 no 9pp 507ndash520 2018

[8] T F Edgar and E N Pistikopoulos ldquoSmart manufacturingand energy systemsrdquo Computers amp Chemical Engineeringvol 114 pp 130ndash144 2018

[9] S Jia R Tang and J Lv ldquoerblig-based energy demandmodeling methodology of machining process to supportintelligent manufacturingrdquo Journal of IntelligentManufacturing vol 25 no 5 2014

[10] K-D oben S Wiesner and S T Wiesner ldquoIndustrie 40and smart manufacturing-a review of research issues andapplication examplesrdquo International Journal of AutomationTechnology vol 11 no 1 pp 4ndash16 2017

[11] A Wuest ldquoFundamentals of smart manufacturing a multi-thread perspectiverdquo Annual Reviews in Control vol 47pp 214ndash220 2019

[12] B Gong ldquoe discussion on evaluation index and the as-sessment method of intelligent manufacturingrdquo Applicationof Electronic Technique vol 41 no 11 pp 6ndash8 2015

[13] J Y Jia and J Shi ldquoReview on middle managers performanceappraisalrdquo in Proceedings of the International Conference onEducation Management Arts Economics and Social Sciencevol 1 Atlantis Press Paris France pp 695ndash700 2016

[14] W Yi Pe Dong and J Wang ldquoResearch on evaluation modelof enterpri es intelligent manufacturing capacity based onhigh order tensor analysisrdquo Industrial Technology amp Economyvol 37 no 1 pp 11ndash16 2018

[15] D Xue-hong S Li L I Min et al ldquoResearch on intelligentmanufacturing capability maturity evaluation based on BPneural networkrdquo Journal of Qingdao University (NaturalScience Edition) vol 32 no 3 pp 20ndash25 2019

[16] Y Qu Y Shi K Guo and Y Zheng ldquoHas ldquointelligentmanufacturingrdquo promoted the productivity of manufacturingsector--evidence from Chinarsquos listed firmsrdquo Procedia Com-puter Science vol 139 pp 299ndash305 2018

[17] A Schumacher W S Erol and W Sihn ldquoA maturity model forassessing industry 40 readiness and maturity of manufacturingenterprisesrdquo Procedia CIRP vol 52 pp 161ndash166 2016

[18] K Jung K W Morris S Leong and H Cho ldquoMappingstrategic goals and operational performance metrics for smartmanufacturing systemsrdquo Procedia Computer Science vol 44pp 184ndash193 2015

[19] A R Mashhadi and S Behdad ldquoUbiquitous life cycle as-sessment (U-LCA) a proposed concept for environmentaland social impact assessment of industry 40rdquoManufacturingLetters vol 15 pp 93ndash96 2018

[20] M Peruzzini F Gregori A Luzi M Mengarelli andM Germani ldquoA social life cycle assessment methodology forsmart manufacturing the case of study of a kitchen sinkrdquoJournal of Industrial Information Integration vol 7 pp 24ndash32 2017

[21] K Zhang T Qu D Zhou H Jiang and Y Lin ldquoDigital twin-based opti-state control method for a synchronized pro-duction operation systemrdquo Robotics and Computer-IntegratedManufacturing vol 63 no 11 pp 1ndash15 2019

[22] J Leng D Yan Q Liulowast et al ldquoDigital twin-driven jointoptimization of packing and storage assignment in large-scaleautomated high-rise warehouserdquo International Journal ofComputer Integrated Manufacturing vol 21 no 8pp 2490ndash2509 2019

[23] F Meng H J Tang and H Fujita ldquoLinguistic intuitionisticfuzzy preference relations and their application to multi-

criteria decision makingrdquo Information Fusion vol 46pp 77ndash90 2019

[24] Y Qin X Cui M Huang et al ldquoArchimedean muirheadaggregation operators of q-rung orthopair fuzzy numbers formulticriteria group decision makingrdquo Complexity vol 2019Article ID 3103741 33 pages 2019

[25] F Meng and X Chen ldquoInterval-valued intuitionistic fuzzymulti-criteria group decision making based on cross entropyand 2-additive measuresrdquo Soft Computing vol 19 no 7pp 2071ndash2082 2015

[26] T-L Nguyen ldquoMethods in ranking fuzzy numbers a unifiedindex and comparative reviewsrdquo Complexity vol 2017Article ID 3083745 13 pages 2017

[27] L-Y Li J-C Hang Y Gao and C Y Mu ldquoUsing an inte-grated group decision method based on SVM TFN-RS-AHPand TOPSIS-CD for cloud service supplier selectionrdquoMathematical Problems in Engineering vol 2017 Article ID3143502 14 pages 2017

[28] L H Li J C Hang H X Sun and L Wang ldquoA conjunctivemultiple-criteria decision-making approach for cloud servicesupplier selection of manufacturing enterpriserdquo Advances inMechanical Engineering vol 9 no 3 pp 1ndash15 2017

[29] W Yang and Y Pang ldquoHesitant interval-valued pythagoreanfuzzy VIKOR methodrdquo International Journal of IntelligentSystems vol 34 no 5 pp 754ndash789 2019

[30] H J Zhang Y Zhou and Q H Gan ldquoAn extendedPROMETHEE-II-based risk prioritization method forequipment failures in the geothermal power plantrdquo Inter-national Journal of Fuzzy Systems vol 2 no 8 pp 2490ndash25092019

[31] Pamucar ldquoNovel approach to group multi-criteria decisionmaking based on interval rough numbers hybrid DEMATEL-ANP-MAIRCA modelrdquo Expert Systems with Applicationvol 88 pp 58ndash80 2017

[32] D Pamucar I Petrovic and G Cirovic ldquoModification of theBest-Worst andMABACmethods a novel approach based oninterval-valued fuzzy-rough numbersrdquo Expert Systems withApplication vol 91 pp 89ndash106 2018

[33] M K Ghorabaee E K Zavadskas Z Turskis et al ldquoA newcombinative distance-based assessment(codas) method formulti-criteria decision-makingrdquo Economic Computation andEconomic Cybernetics Studies and Research vol 50 no 3pp 25ndash44 2016

24 Complexity

manufacturing capacity and innovating business pattern Insome theoretical research and practice green or even sus-tainability has also been brought into the intelligentmanufacturing paradigm But most of them focus on theoptimization of energy consumption in the manufacturingprocess For example cloud platform is used for promotingresource sharing and improving application efficiency ofmanufacturing system [5] combining big data technology inthe product life cycle to achieve sustainable intelligentmanufacturing is proposed [6] big data method was used forenergy efficiency optimization [7] anomaly detection [8]and energy consumption monitoring [9] in intelligentmanufacturing process and through the analysis of relevantliterature it can be seen that there is no clear definition ofgreen intelligent manufacturing in the current academiccircle and few research studies systematically integratedenvironmental and social factors into the design planningand implementation of intelligent manufacturing [10 11]On the one hand the current research and practice pay moreattention to the core business and competitive elements (forexample productivity improvement personalized custom-ization and intelligent services) On the other hand theimprovement of the environment and social impact of in-telligent manufacturing may conflict with the realization ofother elements and even may bring a lot of investment costse research on the green of intelligent manufacturing is stillin the exploratory stage

At present there are many researches on performanceevaluation of intelligent manufacturing focusing on thefollowing aspects

e first aspect is overall performance evaluation ofintelligent manufacturing enterprises Gong [12] introduceda three-tier index system to evaluate the performance ofenterprise intelligent manufacturing by using the compre-hensive scoring method of experts which covers manyaspects of enterprise performance but does not involveenvironmental performance and only uses an overall sat-isfaction degree for the evaluation of employees Jia and Shi[13] use the DEA model of cross efficiency to measure theperformance of some listed intelligent manufacturing en-terprises which can evaluate the overall economic perfor-mance of enterprises but cannot pay attention to the detailsof intelligent manufacturing itself and does not consider theenvironmental factors

In the second aspect enterprisersquos intelligentmanufacturing capability is assessed Yi et al [14] establishedthe evaluation model of enterprise intelligent manufacturingcapability based on tensor analysis and measured the en-terprise intelligent manufacturing capability from threedimensions of life cycle system level and intelligent func-tion Similarly Ding et al [15] put forward the intelligentmanufacturing capability maturity model from three di-mensions of manufacturing resources manufacturing as-surance and intelligent promotion which can supportenterprises to describe their comprehensive level of intel-ligent manufacturing Qu et al [16] used Douglas produc-tion function and seemingly unrelated regression (SUA)analysis to evaluate the production capacity of intelligentmanufacturing enterprises so as to compare its advantages

and disadvantages with traditional manufacturing capacitySchumacher et al [17] proposed an empirical model toevaluate the industry 40 maturity of discrete manufacturingenterprise in which nine dimensions and sixty-two indi-cators were established for evaluation including the items ofthe impact on employees and products

e third aspect is environment and social impact as-sessment of intelligent manufacturing ere are few re-search studies on intelligent manufacturing environmentand social impact assessment e above two aspects or partof the performance assurance research of intelligentmanufacturing involved environmental and social dimen-sions but it was often described as a macromethod onlyincluding environmental or social factors as a macro-indicator [18]

In addition Mashhadi and Behdad [19] summarized theshortcomings of traditional life cycle assessment (LCA) inthe assessment of the environment impact of intelligentmanufacturing combined with the characteristics of intel-ligent manufacturing and put forward the assessmentconcept based on product characteristics data It is mainly ascheme of data collection and real-time assessment by usingthe new generation of information technology rather thanstudying specific assessment methods Peruzzini et al [20]used social life cycle assessment (SLCA) to evaluate theimpact of the implementation of intelligent manufacturingon the society but it only focuses on the general socialimpact not the special impact of intelligent manufacturingon employees or users

By creating the virtual model of physical entity in adigital way and simulating the behavior of physical entity bymeans of data digital twin has the characteristics of real-time synchronization faithful mapping and high fidelitythrough the means of virtual real interaction feedback datafusion analysis and decision iteration selection optimization[21] Digital twin can promote the interaction and inte-gration of physical world and information world and in-crease or expand new capabilities for physical entity [22] Inthis study digital twin mainly focuses on obtaining thevirtual image of all factors in the whole life cycle of intel-ligent manufacturing project to meet the monitoring andsimulation requirements of the evaluation informationsource and demand for the green evaluation of intelligentmanufacturing Based on digital twin technology [21 22]the complete and dynamic mapping interaction betweenphysical entity and digital model in green performanceevaluation of intelligent manufacturing can be realized Andthen how to comprehensively master the multidimensionalinfluencing factors and their coupling relationship forcomparative analysis is the key problem in green perfor-mance evaluation of intelligent manufacturing

Multicriteria decision-making (MCDM) [23 24] byusing the experience and wisdom of experts is a feasiblemethod to comprehensively consider the multidimensionalinfluencing factors and their coupling relationship that affectthe green performance evaluation In the existing similarevaluation problem and its solution the value or importanceof a factor is usually evaluated by one expert in numericalnumber form which is unreasonable due to the preferences

2 Complexity




2 Overall Framework








1113957a (α χ δ β) (1)


f1113957a(x)


αlexle χ

1 χ le xle δ


δ lexle β

0 xlt α orxgt β

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(2)


Complexity 3









1113957a1( 1113857minus 1

βminus11 δminus1


11113872 1113873 (6)


1113957a11113957a2

α1β2

χ1δ2

δ1χ2

β1α2

1113888 1113889 (7)



3 δ1 + β1 minus α1 minus χ1( 1113857 (8)

Digital twin data

Dat

adr

ivin

g


Dat

adr

ivin

g




Digital twin

Mapping

Interacting

PROMETHEE II


Dat

adr

ivin

g

Itera

tive o

ptim

izat

ion

Itera

tive o

ptim

izat

ion

Inte

ract

ing

Inte

ract

ing

Dig

ital t

win

conc

ept

laye

rIn

form

atio

nla

yer

Met

hodo

logy

laye

r

Index sys

tem

Entity Model


4 Complexity





D D1 D2 Dn1113864 1113865 (9)









LRL Sw( 1113857 1

Num LRAS Sw( 1113857( 11138571113944

YisinLRAS Sw( )

Y (13)

URL Sw( 1113857 1

Num URAS Sw( 1113857( 11138571113944

YisinURAS Sw( )

Y (14)






(15)


(16)




~fa(x)

a

xβδχα0

1~


Complexity 5


0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

a = 1a = 2a = 3

a = 4a = 5a = 6

a = 7a = 8a = 9


0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

EISIOI

WIEWS

OSSSES




Dimen

sionIn

dex

Targ

et

12

3

1

3 2

4

5

67

8

9


6 Complexity






1113957Φkt

1113957ϕkt

111113957ϕkt


1l

1113957ϕkt

211113957ϕkt


2l

⋮ ⋮ ⋮1113957ϕkt

l11113957ϕkt


ll

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(18)

where 1113957ϕkt



ji 11113957ϕkt






1113957ϕkt

ij αktij χkt

ij δktij βkt

ij1113872 1113873 (19)




Φkt

ϕktl1 ϕkt


ϕkt21 ϕkt


⋮ ⋮ ⋮

ϕktl1 ϕkt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(20)


CIkt

λmax( 1113857kt

minus l

l minus 1 (21)



CRktCIkt

RIkt (22)




Complexity 7

1113957Θt

1113957ρt11 1113957ρt


1113957ρt21 1113957ρt


⋮ ⋮ ⋮

1113957ρtl1 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(23)


1113957ρtij 1113957ϕ1t

ij 1113957ϕ2t

ij 1113957ϕqt

ij1113882 1113883 (24)



RBI 1113957ϕkt

ij1113874 1113875 LRL 1113957ϕkt

ij1113874 1113875URL 1113957ϕkt

ij1113874 11138751113876 1113877

1


ij1113874 11138751113874 11138751113944

Yisin1113957ρt

ij

Yle1113957ϕkt

ij

Y1


ij1113874 11138751113874 11138751113944

Yisin1113957ρt

ij

Yge1113957ϕkt

ij

Y

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(25)











Total synthesis



indexes



Index value matrix



Experts judgement

Phas

e 1 f

uzzy

roug

h-se

ts A

HP

Phas

e 2 m

ultis

tage

wei

ght

synt

hesis

Phas

e 3 P

ROM

ETH

EE II

Yes

No



Dimension l 1 2 3 4 5 6 7 8 9RI 000 000 058 090 112 124 132 141 145

8 Complexity



RBI 1113957ρtij1113872 1113873 LRL 1113957ρt

ij1113872 1113873URL 1113957ρtij1113872 11138731113960 1113961

1q

1113944

q

k1LRL 1113957ϕkt

ij1113874 11138751q

1113944

q

k1URL 1113957ϕkt

ij1113874 1113875⎡⎣ ⎤⎦

(26)


1113957Λt

RBI 1113957ρt111113872 1113873 RBI 1113957ρt


RBI 1113957ρt211113872 1113873 RBI 1113957ρt


⋮ ⋮ ⋮

RBI 1113957ρtl11113872 1113873 RBI 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(27)


1113957Λt

LRL

LRL 1113957ρt111113872 1113873 LRL 1113957ρt


LRL 1113957ρt211113872 1113873 LRL 1113957ρt


⋮ ⋮ ⋮

LRL 1113957ρtl11113872 1113873 LRL 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(28)

1113957Λt

URL

URL 1113957ρt111113872 1113873 URL 1113957ρt


URL 1113957ρt211113872 1113873 URL 1113957ρt


⋮ ⋮ ⋮URL 1113957ρt


ll1113872 1113873

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(29)


LRL and 1113957Λt





Eig ΛtLRL1113872 1113873 Eig1 Λ

tLRL1113872 1113873Eig2 Λ

tLRL1113872 1113873 Eigl Λ

tLRL1113872 11138731113960 1113961

(30)

Eig ΛtURL1113872 1113873 Eig1 Λ

tURL1113872 1113873Eig2 Λ

tURL1113872 1113873 Eigl Λ

tURL1113872 11138731113960 1113961

(31)



tAver1113872 1113873Eig2 Λ

tAver1113872 1113873 Eigl Λ

tAver1113872 11138731113960 1113961

(32)





Aver)








Complexity 9

SW

Substage

Substage

Substage

Substage

OW3

Substage

OWg

OWSu

bstage

TW

Stage 1

sub

jective w

eigh

t syn

thesis

Stage 2

objectiv

e weigh

t syn

thesis



ANP method

Delphi method

Entropy method

CRITIC method



OW1 OW2SW1

SW3

SW2

SWh









10 Complexity



SW1 sw1

1 sw12 sw1

N1113960 1113961T

SW2 sw2

1 sw22 sw2

N1113960 1113961T


SWh swh

1 swh2 swh

N1113960 1113961T

(33)


1 sw1∘22 sw1∘2


SW1∘2 τ1SW

1+ τ2SW

2 (34)



ξ1∘2 1113944l

i11113944

N

t1τ1sw

1t xit minus τ2sw

2t xit1113872 1113873

2 (35)


and SW2 as follows

min ξ1∘2

st τ1 ge 0 τ2 ge 0 τ1 + τ2 1(36)


τ1 1113936

li1 1113936

Nt1 xit1113872 1113873

2sw2

t sw1t + sw2

t( 1113857

1113936li1 1113936

Nt1 xit1113872 1113873

2sw1

t + sw2t( 1113857

τ2 1 minus τ1

(37)


SW1∘2∘∘h sw1∘2∘∘h

1 sw1∘2∘∘h2 sw1∘2∘∘h

N1113960 1113961T (38)




Overall goal

Index 1

Index 3

Index 2

Index 7

Index 9

Index 8

Index 4

Index 6

Index 5

Dimension 1


Control layer

Network layer


Complexity 11



OW1∘2∘∘g ow1∘2∘∘g

1 ow1∘2∘∘g2 ow1∘2∘∘g

N1113960 1113961T

(39)




(40)






⎧⎨

⎩ (41)



p(i m) 1113944N




Ω+i 1113944

l

m1mneip(i m)

Ωminusi 1113944

l

m1mneip(m i)

(43)






i (44)




12 Complexity


[1113957ϕ11ij ]10times10 1113957Φ21

[1113957ϕ21ij ]10times10 and

1113957Φ31 [1113957ϕ31


1113957Φ11











⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(45)


ij 1113957ϕ21ij 1113957ϕ31


1113957ρ112 1113957ϕ1112

1113957ϕ2112

1113957ϕ31121113882 1113883 OSEOS (10000 12222


12 OS in 1113957ρ112

1113957ϕ1112

1113957ϕ2112


12) [LRL(1113957ϕ1112)

URL(1113957ϕ1112)] [(10000 11481 15714 18889) (10000

12222 18571 23333)] while RBI(1113957ϕ2112)

[LRL(1113957ϕ2112)URL(1113957ϕ21

12)] [(10000 10000 10000 10000)(10000 11481 15714 18889)] and RBI(1113957ϕ31

12)

[LRL(1113957ϕ3112)URL(1113957ϕ31



1113957ϕ2112

1113957ϕ31121113882 1113883 can be obtained

as RBI(1113957ρ112) [(10000 10988 13809 15926) (1000011975 17619 21852)]














Complexity 13




Model 21 SW1+OW1

Model 22 SW1+OW2

Model 23 SW2 +OW2

Model 24 SW2 +OW3

Model 25 SW3 +OW1

Model 26 SW3 +OW3


Model 31 SW1 +OW1

Model 32 SW1 +OW2

Model 33 SW2 +OW2

Model 34 SW2 +OW3

Model 35 SW3 +OW1

Model 36 SW3 +OW3


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 10988 1380915926)

(11037 16779 1869419372)

(06468 17128 1854018657)

(09951 13021 1357217378)

2 (05336 05676 1039713301) (1 1 1 1) (04684 09725 11776

13317)(08246 10541 10761

16594)(05427 08139 09974

13416)

3 (11489 14540 1456115842)

(04953 05825 0856816916) (1 1 1 1) (08178 11612 12975

19428)(10195 10630 15027

19814)

4 (07188 10560 1695217386)

(09026 11191 1423414681)

(07571 09762 1027212090) (1 1 1 1) (05961 11055 11799

13777)

5 (05566 09454 1272814644)

(06137 09540 1273613970)

(14355 14538 1502519150)

(11477 11610 1391314760) (1 1 1 1)

6 (08475 14009 1741017550)

(10563 11164 1723718260)

(07848 10350 1675119214)

(07092 16417 1786119843)

(04996 13061 1402814263)

7 (06408 06771 0743107685)

(11400 12236 1280515275)

(05379 07261 1007412589)

(06112 11761 1496918638)

(06579 07795 0914913757)

8 (05216 06006 0879217264)

(10414 11301 1636616826)

(08778 15035 1549516198)

(06862 08049 1730018657)

(04572 06153 1651119409)

9 (11202 12001 1371513804)

(09248 11256 1142512045)

(10368 12759 1448717079)

(07720 09169 1359914148)

(12160 15583 1657518508)

10 (04973 11939 1225016033)

(07335 08219 1343916985)

(12856 14828 1483115321)

(05005 13199 1487218169)

(06924 10332 1449417761)


Alter 6 7 8 9 10

1 (08231 14384 1498019344)

(07973 08449 1485117588)

(04518 10495 1383418698)

(10328 10413 1067112811)

(10170 10771 1145016334)

2 (05954 06653 0747615292)

(06231 06613 1217515019)

(13189 15298 1768618909)

(04508 13995 1791419844)

(06138 06702 0708014125)

3 (05483 15937 1783718983)

(04979 06576 0725310678)

(05462 09109 0964719929)

(05753 05893 1428216547)

(04660 09057 0974116068)

4 (07969 09776 1357219376)

(06649 12982 1830919369)

(08275 09925 1712118904)

(06747 13023 1348517974)

(05677 06411 0821910728)

5 (12083 12108 1849219144)

(07146 08002 0802911253)

(06222 11302 1852619686)

(06320 07937 1384415524)

(08933 09312 1100123003)

6 (1 1 1 1) (05999 12586 1717217181)

(11534 14559 1690519581)

(08006 10462 1353613637)

(09830 15819 1727819731)

7 (04849 08541 1371317175) (1 1 1 1) (05054 09498 11806

16663)(07472 09787 13915

15946)(05912 07424 08956

13431)

8 (10599 12561 1490715989)

(05189 08263 1135716201) (1 1 1 1) (04803 11356 15093

15413)(12220 13407 17600

18463)

9 (05794 14202 1474515811)

(04763 06373 1349118889)

(04891 11740 1454717554) (1 1 1 1) (05341 07245 09628

14774)

10 (08962 10925 1545719992)

(08964 15462 1581016611)

(09733 13922 1598916593)

(05296 15882 1688418302) (1 1 1 1)

14 Complexity


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 11975 1761921852)

(13959 18678 2560629058)

(08786 22426 2668147228)

(14288 24658 2817839657)

2 (13456 19678 2514228548) (1 1 1 1) (11568 14847 25474

30198)(10122 10903 28725

48158)(08339 08947 15098

26066)

3 (14519 15936 2003424383)

(18749 24067 2843532298) (1 1 1 1) (13095 18756 19465

34211)(08830 27474 28092

41440)

4 (09330 16784 1959125506)

(08341 11678 1246129649)

(09159 28247 2893638990) (1 1 1 1) (09411 22048 23311

23398)

5 (16968 23804 2604048683)

(09998 17316 1919225134)

(12597 13015 1319723604)

(15705 22564 2494625479) (1 1 1 1)

6 (19121 19896 2080927139)

(16729 24921 2578739713)

(15206 17650 2276843007)

(14500 19317 2093727454)

(09090 15973 1608518771)

7 (08938 14201 2197430621)

(10727 18788 2676644705)

(11865 12597 1538946016)

(15736 20361 2419824402)

(09572 10258 1333527689)

8 (09447 14976 2328628905)

(12111 17803 1877535145)

(10618 11577 2241228931)

(09720 19844 2659229915)

(09858 24791 2598127111)

9 (08528 11187 1690118615)

(19187 19237 2598841383)

(15716 27271 2865831107)

(13071 16180 1836026575)

(15352 16308 2337227600)

10 (21417 21589 2790444097)

(08631 15053 1877827503)

(10816 11919 1518729980)

(12190 16116 1813649229)

(12200 13066 1742218604)


Alter 6 7 8 9 10

1 (10856 14359 2278023293)

(08282 15578 2285725171)

(17336 18140 1817440347)

(12599 12930 1567629902)

(21814 24984 2852348855)

2 (19559 19668 2694528364)

(10309 11247 1217418890)

(20821 25939 2733849534)

(17569 18550 1960925630)

(09146 20622 2848638604)

3 (25282 26897 2956229657)

(14502 14629 2198328661)

(09020 14561 1911939980)

(10401 19743 2791342684)

(09066 21276 2269430096)

4 (13612 19131 2452837361)

(11284 13665 1868026496)

(12325 13524 2155327878)

(15721 21685 2676729556)

(10085 12046 1327917180)

5 (12671 15430 1612327801)

(14844 15762 1746528314)

(13677 16992 1901321088)

(14527 15013 1733229330)

(11802 12257 1554719670)

6 (1 1 1 1) (11297 22511 2389429781)

(09836 13593 1751326157)

(13540 14390 1914221576)

(10371 20850 2793944945)

7 (11553 14880 1550817356) (1 1 1 1) (11869 14414 18417

23879)(13343 13919 28183

40151)(17366 20025 23034

35067)

8 (11300 15650 1901020894)

(15903 23132 2419924578) (1 1 1 1) (13946 15279 16276

17335)(13428 20892 24250

35989)

9 (24919 27597 2961132421)

(16795 18655 2658726980)

(15653 20299 2673326790) (1 1 1 1) (10599 27767 29745

30679)

10 (12209 18226 2480726000)

(10587 16723 2024723236)

(10306 10814 2009028380)

(09603 09948 2556447606) (1 1 1 1)


Alter 1 2 3 4 5 6 7 8 9 101 1 15314 16206 14502 13533 14101 12253 11829 11195 124672 08732 1 09696 11815 09277 09341 10056 16240 13692 090033 13962 09456 1 13245 14052 13976 07491 11550 10641 100244 12965 12240 09899 1 10433 12840 14147 13558 12670 078295 10521 10520 16035 12950 1 15459 08802 13835 10907 138236 14157 14310 13540 14816 11058 1 13005 15629 11353 154467 07071 13030 08849 12772 09513 11062 1 10778 11772 090948 09719 13723 13468 12719 11681 13485 10335 1 11417 154179 12668 10891 13683 11145 15616 12089 10983 11979 1 0940810 11048 11561 14336 12495 12373 13923 13778 13899 13436 1

Complexity 15




Alter 1 2 3 4 5 6 7 8 9 101 1 19481 21786 26741 26765 17774 17807 25275 18617 321432 21596 1 20555 25039 15031 23644 13543 32199 20662 241493 18819 25825 1 22090 26034 27819 20116 21619 25455 204334 17712 16605 25614 1 18669 24042 17760 18956 23310 132615 30017 17821 16409 21853 1 18684 19738 17633 19750 149446 22110 27231 25680 20662 14638 1 21489 17024 17196 263857 19067 25757 23581 21032 16022 14725 1 17266 24189 244278 19157 21776 18503 21235 20933 16615 21507 1 15697 239049 13786 27131 25055 18854 20731 28643 22239 22266 1 2358710 29505 17620 17784 25948 15328 20168 17550 17606 23935 1





SW3

SW2SW1

OW3

OW1 OW2

Subs

tage

1-1

Subs

tage

1-2

Subs

tage

2-1

Subs

tage

2-2

TW

Stage 1 Stage 2

Stage 3

SW1∘2 OW1∘2

SW1∘2∘3 OW1∘2∘3


16 Complexity










































Complexity 17





















18 Complexity










Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36





Complexity 19






Table 20 Continued

Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36










Model1

Model41

Model42

Model43

Model44

Model45

Model46

Model51

Model52

Model53

Model54

Model55

Model56













20 Complexity


Model1

Model61

Model62

Model63

Model64

Model65

Model66

Model71

Model72

Model73

Model74

Model75

Model76














Model1

Model81

Model82

Model83

Model84

Model85

Model86

Model91

Model92

Model93

Model94

Model95

Model96













Complexity 21











22 Complexity



6 Conclusions




Data Availability






Acknowledgments


References







Complexity 23





























24 Complexity




2 Overall Framework








1113957a (α χ δ β) (1)


f1113957a(x)


αlexle χ

1 χ le xle δ


δ lexle β

0 xlt α orxgt β

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(2)


Complexity 3









1113957a1( 1113857minus 1

βminus11 δminus1


11113872 1113873 (6)


1113957a11113957a2

α1β2

χ1δ2

δ1χ2

β1α2

1113888 1113889 (7)



3 δ1 + β1 minus α1 minus χ1( 1113857 (8)

Digital twin data

Dat

adr

ivin

g


Dat

adr

ivin

g




Digital twin

Mapping

Interacting

PROMETHEE II


Dat

adr

ivin

g

Itera

tive o

ptim

izat

ion

Itera

tive o

ptim

izat

ion

Inte

ract

ing

Inte

ract

ing

Dig

ital t

win

conc

ept

laye

rIn

form

atio

nla

yer

Met

hodo

logy

laye

r

Index sys

tem

Entity Model


4 Complexity





D D1 D2 Dn1113864 1113865 (9)









LRL Sw( 1113857 1

Num LRAS Sw( 1113857( 11138571113944

YisinLRAS Sw( )

Y (13)

URL Sw( 1113857 1

Num URAS Sw( 1113857( 11138571113944

YisinURAS Sw( )

Y (14)






(15)


(16)




~fa(x)

a

xβδχα0

1~


Complexity 5


0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

a = 1a = 2a = 3

a = 4a = 5a = 6

a = 7a = 8a = 9


0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

EISIOI

WIEWS

OSSSES




Dimen

sionIn

dex

Targ

et

12

3

1

3 2

4

5

67

8

9


6 Complexity






1113957Φkt

1113957ϕkt

111113957ϕkt


1l

1113957ϕkt

211113957ϕkt


2l

⋮ ⋮ ⋮1113957ϕkt

l11113957ϕkt


ll

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(18)

where 1113957ϕkt



ji 11113957ϕkt






1113957ϕkt

ij αktij χkt

ij δktij βkt

ij1113872 1113873 (19)




Φkt

ϕktl1 ϕkt


ϕkt21 ϕkt


⋮ ⋮ ⋮

ϕktl1 ϕkt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(20)


CIkt

λmax( 1113857kt

minus l

l minus 1 (21)



CRktCIkt

RIkt (22)




Complexity 7

1113957Θt

1113957ρt11 1113957ρt


1113957ρt21 1113957ρt


⋮ ⋮ ⋮

1113957ρtl1 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(23)


1113957ρtij 1113957ϕ1t

ij 1113957ϕ2t

ij 1113957ϕqt

ij1113882 1113883 (24)



RBI 1113957ϕkt

ij1113874 1113875 LRL 1113957ϕkt

ij1113874 1113875URL 1113957ϕkt

ij1113874 11138751113876 1113877

1


ij1113874 11138751113874 11138751113944

Yisin1113957ρt

ij

Yle1113957ϕkt

ij

Y1


ij1113874 11138751113874 11138751113944

Yisin1113957ρt

ij

Yge1113957ϕkt

ij

Y

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(25)











Total synthesis



indexes



Index value matrix



Experts judgement

Phas

e 1 f

uzzy

roug

h-se

ts A

HP

Phas

e 2 m

ultis

tage

wei

ght

synt

hesis

Phas

e 3 P

ROM

ETH

EE II

Yes

No



Dimension l 1 2 3 4 5 6 7 8 9RI 000 000 058 090 112 124 132 141 145

8 Complexity



RBI 1113957ρtij1113872 1113873 LRL 1113957ρt

ij1113872 1113873URL 1113957ρtij1113872 11138731113960 1113961

1q

1113944

q

k1LRL 1113957ϕkt

ij1113874 11138751q

1113944

q

k1URL 1113957ϕkt

ij1113874 1113875⎡⎣ ⎤⎦

(26)


1113957Λt

RBI 1113957ρt111113872 1113873 RBI 1113957ρt


RBI 1113957ρt211113872 1113873 RBI 1113957ρt


⋮ ⋮ ⋮

RBI 1113957ρtl11113872 1113873 RBI 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(27)


1113957Λt

LRL

LRL 1113957ρt111113872 1113873 LRL 1113957ρt


LRL 1113957ρt211113872 1113873 LRL 1113957ρt


⋮ ⋮ ⋮

LRL 1113957ρtl11113872 1113873 LRL 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(28)

1113957Λt

URL

URL 1113957ρt111113872 1113873 URL 1113957ρt


URL 1113957ρt211113872 1113873 URL 1113957ρt


⋮ ⋮ ⋮URL 1113957ρt


ll1113872 1113873

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(29)


LRL and 1113957Λt





Eig ΛtLRL1113872 1113873 Eig1 Λ

tLRL1113872 1113873Eig2 Λ

tLRL1113872 1113873 Eigl Λ

tLRL1113872 11138731113960 1113961

(30)

Eig ΛtURL1113872 1113873 Eig1 Λ

tURL1113872 1113873Eig2 Λ

tURL1113872 1113873 Eigl Λ

tURL1113872 11138731113960 1113961

(31)



tAver1113872 1113873Eig2 Λ

tAver1113872 1113873 Eigl Λ

tAver1113872 11138731113960 1113961

(32)





Aver)








Complexity 9

SW

Substage

Substage

Substage

Substage

OW3

Substage

OWg

OWSu

bstage

TW

Stage 1

sub

jective w

eigh

t syn

thesis

Stage 2

objectiv

e weigh

t syn

thesis



ANP method

Delphi method

Entropy method

CRITIC method



OW1 OW2SW1

SW3

SW2

SWh









10 Complexity



SW1 sw1

1 sw12 sw1

N1113960 1113961T

SW2 sw2

1 sw22 sw2

N1113960 1113961T


SWh swh

1 swh2 swh

N1113960 1113961T

(33)


1 sw1∘22 sw1∘2


SW1∘2 τ1SW

1+ τ2SW

2 (34)



ξ1∘2 1113944l

i11113944

N

t1τ1sw

1t xit minus τ2sw

2t xit1113872 1113873

2 (35)


and SW2 as follows

min ξ1∘2

st τ1 ge 0 τ2 ge 0 τ1 + τ2 1(36)


τ1 1113936

li1 1113936

Nt1 xit1113872 1113873

2sw2

t sw1t + sw2

t( 1113857

1113936li1 1113936

Nt1 xit1113872 1113873

2sw1

t + sw2t( 1113857

τ2 1 minus τ1

(37)


SW1∘2∘∘h sw1∘2∘∘h

1 sw1∘2∘∘h2 sw1∘2∘∘h

N1113960 1113961T (38)




Overall goal

Index 1

Index 3

Index 2

Index 7

Index 9

Index 8

Index 4

Index 6

Index 5

Dimension 1


Control layer

Network layer


Complexity 11



OW1∘2∘∘g ow1∘2∘∘g

1 ow1∘2∘∘g2 ow1∘2∘∘g

N1113960 1113961T

(39)




(40)






⎧⎨

⎩ (41)



p(i m) 1113944N




Ω+i 1113944

l

m1mneip(i m)

Ωminusi 1113944

l

m1mneip(m i)

(43)






i (44)




12 Complexity


[1113957ϕ11ij ]10times10 1113957Φ21

[1113957ϕ21ij ]10times10 and

1113957Φ31 [1113957ϕ31


1113957Φ11











⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(45)


ij 1113957ϕ21ij 1113957ϕ31


1113957ρ112 1113957ϕ1112

1113957ϕ2112

1113957ϕ31121113882 1113883 OSEOS (10000 12222


12 OS in 1113957ρ112

1113957ϕ1112

1113957ϕ2112


12) [LRL(1113957ϕ1112)

URL(1113957ϕ1112)] [(10000 11481 15714 18889) (10000

12222 18571 23333)] while RBI(1113957ϕ2112)

[LRL(1113957ϕ2112)URL(1113957ϕ21

12)] [(10000 10000 10000 10000)(10000 11481 15714 18889)] and RBI(1113957ϕ31

12)

[LRL(1113957ϕ3112)URL(1113957ϕ31



1113957ϕ2112

1113957ϕ31121113882 1113883 can be obtained

as RBI(1113957ρ112) [(10000 10988 13809 15926) (1000011975 17619 21852)]














Complexity 13




Model 21 SW1+OW1

Model 22 SW1+OW2

Model 23 SW2 +OW2

Model 24 SW2 +OW3

Model 25 SW3 +OW1

Model 26 SW3 +OW3


Model 31 SW1 +OW1

Model 32 SW1 +OW2

Model 33 SW2 +OW2

Model 34 SW2 +OW3

Model 35 SW3 +OW1

Model 36 SW3 +OW3


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 10988 1380915926)

(11037 16779 1869419372)

(06468 17128 1854018657)

(09951 13021 1357217378)

2 (05336 05676 1039713301) (1 1 1 1) (04684 09725 11776

13317)(08246 10541 10761

16594)(05427 08139 09974

13416)

3 (11489 14540 1456115842)

(04953 05825 0856816916) (1 1 1 1) (08178 11612 12975

19428)(10195 10630 15027

19814)

4 (07188 10560 1695217386)

(09026 11191 1423414681)

(07571 09762 1027212090) (1 1 1 1) (05961 11055 11799

13777)

5 (05566 09454 1272814644)

(06137 09540 1273613970)

(14355 14538 1502519150)

(11477 11610 1391314760) (1 1 1 1)

6 (08475 14009 1741017550)

(10563 11164 1723718260)

(07848 10350 1675119214)

(07092 16417 1786119843)

(04996 13061 1402814263)

7 (06408 06771 0743107685)

(11400 12236 1280515275)

(05379 07261 1007412589)

(06112 11761 1496918638)

(06579 07795 0914913757)

8 (05216 06006 0879217264)

(10414 11301 1636616826)

(08778 15035 1549516198)

(06862 08049 1730018657)

(04572 06153 1651119409)

9 (11202 12001 1371513804)

(09248 11256 1142512045)

(10368 12759 1448717079)

(07720 09169 1359914148)

(12160 15583 1657518508)

10 (04973 11939 1225016033)

(07335 08219 1343916985)

(12856 14828 1483115321)

(05005 13199 1487218169)

(06924 10332 1449417761)


Alter 6 7 8 9 10

1 (08231 14384 1498019344)

(07973 08449 1485117588)

(04518 10495 1383418698)

(10328 10413 1067112811)

(10170 10771 1145016334)

2 (05954 06653 0747615292)

(06231 06613 1217515019)

(13189 15298 1768618909)

(04508 13995 1791419844)

(06138 06702 0708014125)

3 (05483 15937 1783718983)

(04979 06576 0725310678)

(05462 09109 0964719929)

(05753 05893 1428216547)

(04660 09057 0974116068)

4 (07969 09776 1357219376)

(06649 12982 1830919369)

(08275 09925 1712118904)

(06747 13023 1348517974)

(05677 06411 0821910728)

5 (12083 12108 1849219144)

(07146 08002 0802911253)

(06222 11302 1852619686)

(06320 07937 1384415524)

(08933 09312 1100123003)

6 (1 1 1 1) (05999 12586 1717217181)

(11534 14559 1690519581)

(08006 10462 1353613637)

(09830 15819 1727819731)

7 (04849 08541 1371317175) (1 1 1 1) (05054 09498 11806

16663)(07472 09787 13915

15946)(05912 07424 08956

13431)

8 (10599 12561 1490715989)

(05189 08263 1135716201) (1 1 1 1) (04803 11356 15093

15413)(12220 13407 17600

18463)

9 (05794 14202 1474515811)

(04763 06373 1349118889)

(04891 11740 1454717554) (1 1 1 1) (05341 07245 09628

14774)

10 (08962 10925 1545719992)

(08964 15462 1581016611)

(09733 13922 1598916593)

(05296 15882 1688418302) (1 1 1 1)

14 Complexity


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 11975 1761921852)

(13959 18678 2560629058)

(08786 22426 2668147228)

(14288 24658 2817839657)

2 (13456 19678 2514228548) (1 1 1 1) (11568 14847 25474

30198)(10122 10903 28725

48158)(08339 08947 15098

26066)

3 (14519 15936 2003424383)

(18749 24067 2843532298) (1 1 1 1) (13095 18756 19465

34211)(08830 27474 28092

41440)

4 (09330 16784 1959125506)

(08341 11678 1246129649)

(09159 28247 2893638990) (1 1 1 1) (09411 22048 23311

23398)

5 (16968 23804 2604048683)

(09998 17316 1919225134)

(12597 13015 1319723604)

(15705 22564 2494625479) (1 1 1 1)

6 (19121 19896 2080927139)

(16729 24921 2578739713)

(15206 17650 2276843007)

(14500 19317 2093727454)

(09090 15973 1608518771)

7 (08938 14201 2197430621)

(10727 18788 2676644705)

(11865 12597 1538946016)

(15736 20361 2419824402)

(09572 10258 1333527689)

8 (09447 14976 2328628905)

(12111 17803 1877535145)

(10618 11577 2241228931)

(09720 19844 2659229915)

(09858 24791 2598127111)

9 (08528 11187 1690118615)

(19187 19237 2598841383)

(15716 27271 2865831107)

(13071 16180 1836026575)

(15352 16308 2337227600)

10 (21417 21589 2790444097)

(08631 15053 1877827503)

(10816 11919 1518729980)

(12190 16116 1813649229)

(12200 13066 1742218604)


Alter 6 7 8 9 10

1 (10856 14359 2278023293)

(08282 15578 2285725171)

(17336 18140 1817440347)

(12599 12930 1567629902)

(21814 24984 2852348855)

2 (19559 19668 2694528364)

(10309 11247 1217418890)

(20821 25939 2733849534)

(17569 18550 1960925630)

(09146 20622 2848638604)

3 (25282 26897 2956229657)

(14502 14629 2198328661)

(09020 14561 1911939980)

(10401 19743 2791342684)

(09066 21276 2269430096)

4 (13612 19131 2452837361)

(11284 13665 1868026496)

(12325 13524 2155327878)

(15721 21685 2676729556)

(10085 12046 1327917180)

5 (12671 15430 1612327801)

(14844 15762 1746528314)

(13677 16992 1901321088)

(14527 15013 1733229330)

(11802 12257 1554719670)

6 (1 1 1 1) (11297 22511 2389429781)

(09836 13593 1751326157)

(13540 14390 1914221576)

(10371 20850 2793944945)

7 (11553 14880 1550817356) (1 1 1 1) (11869 14414 18417

23879)(13343 13919 28183

40151)(17366 20025 23034

35067)

8 (11300 15650 1901020894)

(15903 23132 2419924578) (1 1 1 1) (13946 15279 16276

17335)(13428 20892 24250

35989)

9 (24919 27597 2961132421)

(16795 18655 2658726980)

(15653 20299 2673326790) (1 1 1 1) (10599 27767 29745

30679)

10 (12209 18226 2480726000)

(10587 16723 2024723236)

(10306 10814 2009028380)

(09603 09948 2556447606) (1 1 1 1)


Alter 1 2 3 4 5 6 7 8 9 101 1 15314 16206 14502 13533 14101 12253 11829 11195 124672 08732 1 09696 11815 09277 09341 10056 16240 13692 090033 13962 09456 1 13245 14052 13976 07491 11550 10641 100244 12965 12240 09899 1 10433 12840 14147 13558 12670 078295 10521 10520 16035 12950 1 15459 08802 13835 10907 138236 14157 14310 13540 14816 11058 1 13005 15629 11353 154467 07071 13030 08849 12772 09513 11062 1 10778 11772 090948 09719 13723 13468 12719 11681 13485 10335 1 11417 154179 12668 10891 13683 11145 15616 12089 10983 11979 1 0940810 11048 11561 14336 12495 12373 13923 13778 13899 13436 1

Complexity 15




Alter 1 2 3 4 5 6 7 8 9 101 1 19481 21786 26741 26765 17774 17807 25275 18617 321432 21596 1 20555 25039 15031 23644 13543 32199 20662 241493 18819 25825 1 22090 26034 27819 20116 21619 25455 204334 17712 16605 25614 1 18669 24042 17760 18956 23310 132615 30017 17821 16409 21853 1 18684 19738 17633 19750 149446 22110 27231 25680 20662 14638 1 21489 17024 17196 263857 19067 25757 23581 21032 16022 14725 1 17266 24189 244278 19157 21776 18503 21235 20933 16615 21507 1 15697 239049 13786 27131 25055 18854 20731 28643 22239 22266 1 2358710 29505 17620 17784 25948 15328 20168 17550 17606 23935 1





SW3

SW2SW1

OW3

OW1 OW2

Subs

tage

1-1

Subs

tage

1-2

Subs

tage

2-1

Subs

tage

2-2

TW

Stage 1 Stage 2

Stage 3

SW1∘2 OW1∘2

SW1∘2∘3 OW1∘2∘3


16 Complexity










































Complexity 17





















18 Complexity










Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36





Complexity 19






Table 20 Continued

Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36










Model1

Model41

Model42

Model43

Model44

Model45

Model46

Model51

Model52

Model53

Model54

Model55

Model56













20 Complexity


Model1

Model61

Model62

Model63

Model64

Model65

Model66

Model71

Model72

Model73

Model74

Model75

Model76














Model1

Model81

Model82

Model83

Model84

Model85

Model86

Model91

Model92

Model93

Model94

Model95

Model96













Complexity 21











22 Complexity



6 Conclusions




Data Availability






Acknowledgments


References







Complexity 23





























24 Complexity









1113957a1( 1113857minus 1

βminus11 δminus1


11113872 1113873 (6)


1113957a11113957a2

α1β2

χ1δ2

δ1χ2

β1α2

1113888 1113889 (7)



3 δ1 + β1 minus α1 minus χ1( 1113857 (8)

Digital twin data

Dat

adr

ivin

g


Dat

adr

ivin

g




Digital twin

Mapping

Interacting

PROMETHEE II


Dat

adr

ivin

g

Itera

tive o

ptim

izat

ion

Itera

tive o

ptim

izat

ion

Inte

ract

ing

Inte

ract

ing

Dig

ital t

win

conc

ept

laye

rIn

form

atio

nla

yer

Met

hodo

logy

laye

r

Index sys

tem

Entity Model


4 Complexity





D D1 D2 Dn1113864 1113865 (9)









LRL Sw( 1113857 1

Num LRAS Sw( 1113857( 11138571113944

YisinLRAS Sw( )

Y (13)

URL Sw( 1113857 1

Num URAS Sw( 1113857( 11138571113944

YisinURAS Sw( )

Y (14)






(15)


(16)




~fa(x)

a

xβδχα0

1~


Complexity 5


0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

a = 1a = 2a = 3

a = 4a = 5a = 6

a = 7a = 8a = 9


0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

EISIOI

WIEWS

OSSSES




Dimen

sionIn

dex

Targ

et

12

3

1

3 2

4

5

67

8

9


6 Complexity






1113957Φkt

1113957ϕkt

111113957ϕkt


1l

1113957ϕkt

211113957ϕkt


2l

⋮ ⋮ ⋮1113957ϕkt

l11113957ϕkt


ll

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(18)

where 1113957ϕkt



ji 11113957ϕkt






1113957ϕkt

ij αktij χkt

ij δktij βkt

ij1113872 1113873 (19)




Φkt

ϕktl1 ϕkt


ϕkt21 ϕkt


⋮ ⋮ ⋮

ϕktl1 ϕkt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(20)


CIkt

λmax( 1113857kt

minus l

l minus 1 (21)



CRktCIkt

RIkt (22)




Complexity 7

1113957Θt

1113957ρt11 1113957ρt


1113957ρt21 1113957ρt


⋮ ⋮ ⋮

1113957ρtl1 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(23)


1113957ρtij 1113957ϕ1t

ij 1113957ϕ2t

ij 1113957ϕqt

ij1113882 1113883 (24)



RBI 1113957ϕkt

ij1113874 1113875 LRL 1113957ϕkt

ij1113874 1113875URL 1113957ϕkt

ij1113874 11138751113876 1113877

1


ij1113874 11138751113874 11138751113944

Yisin1113957ρt

ij

Yle1113957ϕkt

ij

Y1


ij1113874 11138751113874 11138751113944

Yisin1113957ρt

ij

Yge1113957ϕkt

ij

Y

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(25)











Total synthesis



indexes



Index value matrix



Experts judgement

Phas

e 1 f

uzzy

roug

h-se

ts A

HP

Phas

e 2 m

ultis

tage

wei

ght

synt

hesis

Phas

e 3 P

ROM

ETH

EE II

Yes

No



Dimension l 1 2 3 4 5 6 7 8 9RI 000 000 058 090 112 124 132 141 145

8 Complexity



RBI 1113957ρtij1113872 1113873 LRL 1113957ρt

ij1113872 1113873URL 1113957ρtij1113872 11138731113960 1113961

1q

1113944

q

k1LRL 1113957ϕkt

ij1113874 11138751q

1113944

q

k1URL 1113957ϕkt

ij1113874 1113875⎡⎣ ⎤⎦

(26)


1113957Λt

RBI 1113957ρt111113872 1113873 RBI 1113957ρt


RBI 1113957ρt211113872 1113873 RBI 1113957ρt


⋮ ⋮ ⋮

RBI 1113957ρtl11113872 1113873 RBI 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(27)


1113957Λt

LRL

LRL 1113957ρt111113872 1113873 LRL 1113957ρt


LRL 1113957ρt211113872 1113873 LRL 1113957ρt


⋮ ⋮ ⋮

LRL 1113957ρtl11113872 1113873 LRL 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(28)

1113957Λt

URL

URL 1113957ρt111113872 1113873 URL 1113957ρt


URL 1113957ρt211113872 1113873 URL 1113957ρt


⋮ ⋮ ⋮URL 1113957ρt


ll1113872 1113873

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(29)


LRL and 1113957Λt





Eig ΛtLRL1113872 1113873 Eig1 Λ

tLRL1113872 1113873Eig2 Λ

tLRL1113872 1113873 Eigl Λ

tLRL1113872 11138731113960 1113961

(30)

Eig ΛtURL1113872 1113873 Eig1 Λ

tURL1113872 1113873Eig2 Λ

tURL1113872 1113873 Eigl Λ

tURL1113872 11138731113960 1113961

(31)



tAver1113872 1113873Eig2 Λ

tAver1113872 1113873 Eigl Λ

tAver1113872 11138731113960 1113961

(32)





Aver)








Complexity 9

SW

Substage

Substage

Substage

Substage

OW3

Substage

OWg

OWSu

bstage

TW

Stage 1

sub

jective w

eigh

t syn

thesis

Stage 2

objectiv

e weigh

t syn

thesis



ANP method

Delphi method

Entropy method

CRITIC method



OW1 OW2SW1

SW3

SW2

SWh









10 Complexity



SW1 sw1

1 sw12 sw1

N1113960 1113961T

SW2 sw2

1 sw22 sw2

N1113960 1113961T


SWh swh

1 swh2 swh

N1113960 1113961T

(33)


1 sw1∘22 sw1∘2


SW1∘2 τ1SW

1+ τ2SW

2 (34)



ξ1∘2 1113944l

i11113944

N

t1τ1sw

1t xit minus τ2sw

2t xit1113872 1113873

2 (35)


and SW2 as follows

min ξ1∘2

st τ1 ge 0 τ2 ge 0 τ1 + τ2 1(36)


τ1 1113936

li1 1113936

Nt1 xit1113872 1113873

2sw2

t sw1t + sw2

t( 1113857

1113936li1 1113936

Nt1 xit1113872 1113873

2sw1

t + sw2t( 1113857

τ2 1 minus τ1

(37)


SW1∘2∘∘h sw1∘2∘∘h

1 sw1∘2∘∘h2 sw1∘2∘∘h

N1113960 1113961T (38)




Overall goal

Index 1

Index 3

Index 2

Index 7

Index 9

Index 8

Index 4

Index 6

Index 5

Dimension 1


Control layer

Network layer


Complexity 11



OW1∘2∘∘g ow1∘2∘∘g

1 ow1∘2∘∘g2 ow1∘2∘∘g

N1113960 1113961T

(39)




(40)






⎧⎨

⎩ (41)



p(i m) 1113944N




Ω+i 1113944

l

m1mneip(i m)

Ωminusi 1113944

l

m1mneip(m i)

(43)






i (44)




12 Complexity


[1113957ϕ11ij ]10times10 1113957Φ21

[1113957ϕ21ij ]10times10 and

1113957Φ31 [1113957ϕ31


1113957Φ11











⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(45)


ij 1113957ϕ21ij 1113957ϕ31


1113957ρ112 1113957ϕ1112

1113957ϕ2112

1113957ϕ31121113882 1113883 OSEOS (10000 12222


12 OS in 1113957ρ112

1113957ϕ1112

1113957ϕ2112


12) [LRL(1113957ϕ1112)

URL(1113957ϕ1112)] [(10000 11481 15714 18889) (10000

12222 18571 23333)] while RBI(1113957ϕ2112)

[LRL(1113957ϕ2112)URL(1113957ϕ21

12)] [(10000 10000 10000 10000)(10000 11481 15714 18889)] and RBI(1113957ϕ31

12)

[LRL(1113957ϕ3112)URL(1113957ϕ31



1113957ϕ2112

1113957ϕ31121113882 1113883 can be obtained

as RBI(1113957ρ112) [(10000 10988 13809 15926) (1000011975 17619 21852)]














Complexity 13




Model 21 SW1+OW1

Model 22 SW1+OW2

Model 23 SW2 +OW2

Model 24 SW2 +OW3

Model 25 SW3 +OW1

Model 26 SW3 +OW3


Model 31 SW1 +OW1

Model 32 SW1 +OW2

Model 33 SW2 +OW2

Model 34 SW2 +OW3

Model 35 SW3 +OW1

Model 36 SW3 +OW3


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 10988 1380915926)

(11037 16779 1869419372)

(06468 17128 1854018657)

(09951 13021 1357217378)

2 (05336 05676 1039713301) (1 1 1 1) (04684 09725 11776

13317)(08246 10541 10761

16594)(05427 08139 09974

13416)

3 (11489 14540 1456115842)

(04953 05825 0856816916) (1 1 1 1) (08178 11612 12975

19428)(10195 10630 15027

19814)

4 (07188 10560 1695217386)

(09026 11191 1423414681)

(07571 09762 1027212090) (1 1 1 1) (05961 11055 11799

13777)

5 (05566 09454 1272814644)

(06137 09540 1273613970)

(14355 14538 1502519150)

(11477 11610 1391314760) (1 1 1 1)

6 (08475 14009 1741017550)

(10563 11164 1723718260)

(07848 10350 1675119214)

(07092 16417 1786119843)

(04996 13061 1402814263)

7 (06408 06771 0743107685)

(11400 12236 1280515275)

(05379 07261 1007412589)

(06112 11761 1496918638)

(06579 07795 0914913757)

8 (05216 06006 0879217264)

(10414 11301 1636616826)

(08778 15035 1549516198)

(06862 08049 1730018657)

(04572 06153 1651119409)

9 (11202 12001 1371513804)

(09248 11256 1142512045)

(10368 12759 1448717079)

(07720 09169 1359914148)

(12160 15583 1657518508)

10 (04973 11939 1225016033)

(07335 08219 1343916985)

(12856 14828 1483115321)

(05005 13199 1487218169)

(06924 10332 1449417761)


Alter 6 7 8 9 10

1 (08231 14384 1498019344)

(07973 08449 1485117588)

(04518 10495 1383418698)

(10328 10413 1067112811)

(10170 10771 1145016334)

2 (05954 06653 0747615292)

(06231 06613 1217515019)

(13189 15298 1768618909)

(04508 13995 1791419844)

(06138 06702 0708014125)

3 (05483 15937 1783718983)

(04979 06576 0725310678)

(05462 09109 0964719929)

(05753 05893 1428216547)

(04660 09057 0974116068)

4 (07969 09776 1357219376)

(06649 12982 1830919369)

(08275 09925 1712118904)

(06747 13023 1348517974)

(05677 06411 0821910728)

5 (12083 12108 1849219144)

(07146 08002 0802911253)

(06222 11302 1852619686)

(06320 07937 1384415524)

(08933 09312 1100123003)

6 (1 1 1 1) (05999 12586 1717217181)

(11534 14559 1690519581)

(08006 10462 1353613637)

(09830 15819 1727819731)

7 (04849 08541 1371317175) (1 1 1 1) (05054 09498 11806

16663)(07472 09787 13915

15946)(05912 07424 08956

13431)

8 (10599 12561 1490715989)

(05189 08263 1135716201) (1 1 1 1) (04803 11356 15093

15413)(12220 13407 17600

18463)

9 (05794 14202 1474515811)

(04763 06373 1349118889)

(04891 11740 1454717554) (1 1 1 1) (05341 07245 09628

14774)

10 (08962 10925 1545719992)

(08964 15462 1581016611)

(09733 13922 1598916593)

(05296 15882 1688418302) (1 1 1 1)

14 Complexity


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 11975 1761921852)

(13959 18678 2560629058)

(08786 22426 2668147228)

(14288 24658 2817839657)

2 (13456 19678 2514228548) (1 1 1 1) (11568 14847 25474

30198)(10122 10903 28725

48158)(08339 08947 15098

26066)

3 (14519 15936 2003424383)

(18749 24067 2843532298) (1 1 1 1) (13095 18756 19465

34211)(08830 27474 28092

41440)

4 (09330 16784 1959125506)

(08341 11678 1246129649)

(09159 28247 2893638990) (1 1 1 1) (09411 22048 23311

23398)

5 (16968 23804 2604048683)

(09998 17316 1919225134)

(12597 13015 1319723604)

(15705 22564 2494625479) (1 1 1 1)

6 (19121 19896 2080927139)

(16729 24921 2578739713)

(15206 17650 2276843007)

(14500 19317 2093727454)

(09090 15973 1608518771)

7 (08938 14201 2197430621)

(10727 18788 2676644705)

(11865 12597 1538946016)

(15736 20361 2419824402)

(09572 10258 1333527689)

8 (09447 14976 2328628905)

(12111 17803 1877535145)

(10618 11577 2241228931)

(09720 19844 2659229915)

(09858 24791 2598127111)

9 (08528 11187 1690118615)

(19187 19237 2598841383)

(15716 27271 2865831107)

(13071 16180 1836026575)

(15352 16308 2337227600)

10 (21417 21589 2790444097)

(08631 15053 1877827503)

(10816 11919 1518729980)

(12190 16116 1813649229)

(12200 13066 1742218604)


Alter 6 7 8 9 10

1 (10856 14359 2278023293)

(08282 15578 2285725171)

(17336 18140 1817440347)

(12599 12930 1567629902)

(21814 24984 2852348855)

2 (19559 19668 2694528364)

(10309 11247 1217418890)

(20821 25939 2733849534)

(17569 18550 1960925630)

(09146 20622 2848638604)

3 (25282 26897 2956229657)

(14502 14629 2198328661)

(09020 14561 1911939980)

(10401 19743 2791342684)

(09066 21276 2269430096)

4 (13612 19131 2452837361)

(11284 13665 1868026496)

(12325 13524 2155327878)

(15721 21685 2676729556)

(10085 12046 1327917180)

5 (12671 15430 1612327801)

(14844 15762 1746528314)

(13677 16992 1901321088)

(14527 15013 1733229330)

(11802 12257 1554719670)

6 (1 1 1 1) (11297 22511 2389429781)

(09836 13593 1751326157)

(13540 14390 1914221576)

(10371 20850 2793944945)

7 (11553 14880 1550817356) (1 1 1 1) (11869 14414 18417

23879)(13343 13919 28183

40151)(17366 20025 23034

35067)

8 (11300 15650 1901020894)

(15903 23132 2419924578) (1 1 1 1) (13946 15279 16276

17335)(13428 20892 24250

35989)

9 (24919 27597 2961132421)

(16795 18655 2658726980)

(15653 20299 2673326790) (1 1 1 1) (10599 27767 29745

30679)

10 (12209 18226 2480726000)

(10587 16723 2024723236)

(10306 10814 2009028380)

(09603 09948 2556447606) (1 1 1 1)


Alter 1 2 3 4 5 6 7 8 9 101 1 15314 16206 14502 13533 14101 12253 11829 11195 124672 08732 1 09696 11815 09277 09341 10056 16240 13692 090033 13962 09456 1 13245 14052 13976 07491 11550 10641 100244 12965 12240 09899 1 10433 12840 14147 13558 12670 078295 10521 10520 16035 12950 1 15459 08802 13835 10907 138236 14157 14310 13540 14816 11058 1 13005 15629 11353 154467 07071 13030 08849 12772 09513 11062 1 10778 11772 090948 09719 13723 13468 12719 11681 13485 10335 1 11417 154179 12668 10891 13683 11145 15616 12089 10983 11979 1 0940810 11048 11561 14336 12495 12373 13923 13778 13899 13436 1

Complexity 15




Alter 1 2 3 4 5 6 7 8 9 101 1 19481 21786 26741 26765 17774 17807 25275 18617 321432 21596 1 20555 25039 15031 23644 13543 32199 20662 241493 18819 25825 1 22090 26034 27819 20116 21619 25455 204334 17712 16605 25614 1 18669 24042 17760 18956 23310 132615 30017 17821 16409 21853 1 18684 19738 17633 19750 149446 22110 27231 25680 20662 14638 1 21489 17024 17196 263857 19067 25757 23581 21032 16022 14725 1 17266 24189 244278 19157 21776 18503 21235 20933 16615 21507 1 15697 239049 13786 27131 25055 18854 20731 28643 22239 22266 1 2358710 29505 17620 17784 25948 15328 20168 17550 17606 23935 1





SW3

SW2SW1

OW3

OW1 OW2

Subs

tage

1-1

Subs

tage

1-2

Subs

tage

2-1

Subs

tage

2-2

TW

Stage 1 Stage 2

Stage 3

SW1∘2 OW1∘2

SW1∘2∘3 OW1∘2∘3


16 Complexity










































Complexity 17





















18 Complexity










Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36





Complexity 19






Table 20 Continued

Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36










Model1

Model41

Model42

Model43

Model44

Model45

Model46

Model51

Model52

Model53

Model54

Model55

Model56













20 Complexity


Model1

Model61

Model62

Model63

Model64

Model65

Model66

Model71

Model72

Model73

Model74

Model75

Model76














Model1

Model81

Model82

Model83

Model84

Model85

Model86

Model91

Model92

Model93

Model94

Model95

Model96













Complexity 21











22 Complexity



6 Conclusions




Data Availability






Acknowledgments


References







Complexity 23





























24 Complexity





D D1 D2 Dn1113864 1113865 (9)









LRL Sw( 1113857 1

Num LRAS Sw( 1113857( 11138571113944

YisinLRAS Sw( )

Y (13)

URL Sw( 1113857 1

Num URAS Sw( 1113857( 11138571113944

YisinURAS Sw( )

Y (14)






(15)


(16)




~fa(x)

a

xβδχα0

1~


Complexity 5


0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

a = 1a = 2a = 3

a = 4a = 5a = 6

a = 7a = 8a = 9


0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

EISIOI

WIEWS

OSSSES




Dimen

sionIn

dex

Targ

et

12

3

1

3 2

4

5

67

8

9


6 Complexity






1113957Φkt

1113957ϕkt

111113957ϕkt


1l

1113957ϕkt

211113957ϕkt


2l

⋮ ⋮ ⋮1113957ϕkt

l11113957ϕkt


ll

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(18)

where 1113957ϕkt



ji 11113957ϕkt






1113957ϕkt

ij αktij χkt

ij δktij βkt

ij1113872 1113873 (19)




Φkt

ϕktl1 ϕkt


ϕkt21 ϕkt


⋮ ⋮ ⋮

ϕktl1 ϕkt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(20)


CIkt

λmax( 1113857kt

minus l

l minus 1 (21)



CRktCIkt

RIkt (22)




Complexity 7

1113957Θt

1113957ρt11 1113957ρt


1113957ρt21 1113957ρt


⋮ ⋮ ⋮

1113957ρtl1 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(23)


1113957ρtij 1113957ϕ1t

ij 1113957ϕ2t

ij 1113957ϕqt

ij1113882 1113883 (24)



RBI 1113957ϕkt

ij1113874 1113875 LRL 1113957ϕkt

ij1113874 1113875URL 1113957ϕkt

ij1113874 11138751113876 1113877

1


ij1113874 11138751113874 11138751113944

Yisin1113957ρt

ij

Yle1113957ϕkt

ij

Y1


ij1113874 11138751113874 11138751113944

Yisin1113957ρt

ij

Yge1113957ϕkt

ij

Y

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(25)











Total synthesis



indexes



Index value matrix



Experts judgement

Phas

e 1 f

uzzy

roug

h-se

ts A

HP

Phas

e 2 m

ultis

tage

wei

ght

synt

hesis

Phas

e 3 P

ROM

ETH

EE II

Yes

No



Dimension l 1 2 3 4 5 6 7 8 9RI 000 000 058 090 112 124 132 141 145

8 Complexity



RBI 1113957ρtij1113872 1113873 LRL 1113957ρt

ij1113872 1113873URL 1113957ρtij1113872 11138731113960 1113961

1q

1113944

q

k1LRL 1113957ϕkt

ij1113874 11138751q

1113944

q

k1URL 1113957ϕkt

ij1113874 1113875⎡⎣ ⎤⎦

(26)


1113957Λt

RBI 1113957ρt111113872 1113873 RBI 1113957ρt


RBI 1113957ρt211113872 1113873 RBI 1113957ρt


⋮ ⋮ ⋮

RBI 1113957ρtl11113872 1113873 RBI 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(27)


1113957Λt

LRL

LRL 1113957ρt111113872 1113873 LRL 1113957ρt


LRL 1113957ρt211113872 1113873 LRL 1113957ρt


⋮ ⋮ ⋮

LRL 1113957ρtl11113872 1113873 LRL 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(28)

1113957Λt

URL

URL 1113957ρt111113872 1113873 URL 1113957ρt


URL 1113957ρt211113872 1113873 URL 1113957ρt


⋮ ⋮ ⋮URL 1113957ρt


ll1113872 1113873

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(29)


LRL and 1113957Λt





Eig ΛtLRL1113872 1113873 Eig1 Λ

tLRL1113872 1113873Eig2 Λ

tLRL1113872 1113873 Eigl Λ

tLRL1113872 11138731113960 1113961

(30)

Eig ΛtURL1113872 1113873 Eig1 Λ

tURL1113872 1113873Eig2 Λ

tURL1113872 1113873 Eigl Λ

tURL1113872 11138731113960 1113961

(31)



tAver1113872 1113873Eig2 Λ

tAver1113872 1113873 Eigl Λ

tAver1113872 11138731113960 1113961

(32)





Aver)








Complexity 9

SW

Substage

Substage

Substage

Substage

OW3

Substage

OWg

OWSu

bstage

TW

Stage 1

sub

jective w

eigh

t syn

thesis

Stage 2

objectiv

e weigh

t syn

thesis



ANP method

Delphi method

Entropy method

CRITIC method



OW1 OW2SW1

SW3

SW2

SWh









10 Complexity



SW1 sw1

1 sw12 sw1

N1113960 1113961T

SW2 sw2

1 sw22 sw2

N1113960 1113961T


SWh swh

1 swh2 swh

N1113960 1113961T

(33)


1 sw1∘22 sw1∘2


SW1∘2 τ1SW

1+ τ2SW

2 (34)



ξ1∘2 1113944l

i11113944

N

t1τ1sw

1t xit minus τ2sw

2t xit1113872 1113873

2 (35)


and SW2 as follows

min ξ1∘2

st τ1 ge 0 τ2 ge 0 τ1 + τ2 1(36)


τ1 1113936

li1 1113936

Nt1 xit1113872 1113873

2sw2

t sw1t + sw2

t( 1113857

1113936li1 1113936

Nt1 xit1113872 1113873

2sw1

t + sw2t( 1113857

τ2 1 minus τ1

(37)


SW1∘2∘∘h sw1∘2∘∘h

1 sw1∘2∘∘h2 sw1∘2∘∘h

N1113960 1113961T (38)




Overall goal

Index 1

Index 3

Index 2

Index 7

Index 9

Index 8

Index 4

Index 6

Index 5

Dimension 1


Control layer

Network layer


Complexity 11



OW1∘2∘∘g ow1∘2∘∘g

1 ow1∘2∘∘g2 ow1∘2∘∘g

N1113960 1113961T

(39)




(40)






⎧⎨

⎩ (41)



p(i m) 1113944N




Ω+i 1113944

l

m1mneip(i m)

Ωminusi 1113944

l

m1mneip(m i)

(43)






i (44)




12 Complexity


[1113957ϕ11ij ]10times10 1113957Φ21

[1113957ϕ21ij ]10times10 and

1113957Φ31 [1113957ϕ31


1113957Φ11











⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(45)


ij 1113957ϕ21ij 1113957ϕ31


1113957ρ112 1113957ϕ1112

1113957ϕ2112

1113957ϕ31121113882 1113883 OSEOS (10000 12222


12 OS in 1113957ρ112

1113957ϕ1112

1113957ϕ2112


12) [LRL(1113957ϕ1112)

URL(1113957ϕ1112)] [(10000 11481 15714 18889) (10000

12222 18571 23333)] while RBI(1113957ϕ2112)

[LRL(1113957ϕ2112)URL(1113957ϕ21

12)] [(10000 10000 10000 10000)(10000 11481 15714 18889)] and RBI(1113957ϕ31

12)

[LRL(1113957ϕ3112)URL(1113957ϕ31



1113957ϕ2112

1113957ϕ31121113882 1113883 can be obtained

as RBI(1113957ρ112) [(10000 10988 13809 15926) (1000011975 17619 21852)]














Complexity 13




Model 21 SW1+OW1

Model 22 SW1+OW2

Model 23 SW2 +OW2

Model 24 SW2 +OW3

Model 25 SW3 +OW1

Model 26 SW3 +OW3


Model 31 SW1 +OW1

Model 32 SW1 +OW2

Model 33 SW2 +OW2

Model 34 SW2 +OW3

Model 35 SW3 +OW1

Model 36 SW3 +OW3


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 10988 1380915926)

(11037 16779 1869419372)

(06468 17128 1854018657)

(09951 13021 1357217378)

2 (05336 05676 1039713301) (1 1 1 1) (04684 09725 11776

13317)(08246 10541 10761

16594)(05427 08139 09974

13416)

3 (11489 14540 1456115842)

(04953 05825 0856816916) (1 1 1 1) (08178 11612 12975

19428)(10195 10630 15027

19814)

4 (07188 10560 1695217386)

(09026 11191 1423414681)

(07571 09762 1027212090) (1 1 1 1) (05961 11055 11799

13777)

5 (05566 09454 1272814644)

(06137 09540 1273613970)

(14355 14538 1502519150)

(11477 11610 1391314760) (1 1 1 1)

6 (08475 14009 1741017550)

(10563 11164 1723718260)

(07848 10350 1675119214)

(07092 16417 1786119843)

(04996 13061 1402814263)

7 (06408 06771 0743107685)

(11400 12236 1280515275)

(05379 07261 1007412589)

(06112 11761 1496918638)

(06579 07795 0914913757)

8 (05216 06006 0879217264)

(10414 11301 1636616826)

(08778 15035 1549516198)

(06862 08049 1730018657)

(04572 06153 1651119409)

9 (11202 12001 1371513804)

(09248 11256 1142512045)

(10368 12759 1448717079)

(07720 09169 1359914148)

(12160 15583 1657518508)

10 (04973 11939 1225016033)

(07335 08219 1343916985)

(12856 14828 1483115321)

(05005 13199 1487218169)

(06924 10332 1449417761)


Alter 6 7 8 9 10

1 (08231 14384 1498019344)

(07973 08449 1485117588)

(04518 10495 1383418698)

(10328 10413 1067112811)

(10170 10771 1145016334)

2 (05954 06653 0747615292)

(06231 06613 1217515019)

(13189 15298 1768618909)

(04508 13995 1791419844)

(06138 06702 0708014125)

3 (05483 15937 1783718983)

(04979 06576 0725310678)

(05462 09109 0964719929)

(05753 05893 1428216547)

(04660 09057 0974116068)

4 (07969 09776 1357219376)

(06649 12982 1830919369)

(08275 09925 1712118904)

(06747 13023 1348517974)

(05677 06411 0821910728)

5 (12083 12108 1849219144)

(07146 08002 0802911253)

(06222 11302 1852619686)

(06320 07937 1384415524)

(08933 09312 1100123003)

6 (1 1 1 1) (05999 12586 1717217181)

(11534 14559 1690519581)

(08006 10462 1353613637)

(09830 15819 1727819731)

7 (04849 08541 1371317175) (1 1 1 1) (05054 09498 11806

16663)(07472 09787 13915

15946)(05912 07424 08956

13431)

8 (10599 12561 1490715989)

(05189 08263 1135716201) (1 1 1 1) (04803 11356 15093

15413)(12220 13407 17600

18463)

9 (05794 14202 1474515811)

(04763 06373 1349118889)

(04891 11740 1454717554) (1 1 1 1) (05341 07245 09628

14774)

10 (08962 10925 1545719992)

(08964 15462 1581016611)

(09733 13922 1598916593)

(05296 15882 1688418302) (1 1 1 1)

14 Complexity


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 11975 1761921852)

(13959 18678 2560629058)

(08786 22426 2668147228)

(14288 24658 2817839657)

2 (13456 19678 2514228548) (1 1 1 1) (11568 14847 25474

30198)(10122 10903 28725

48158)(08339 08947 15098

26066)

3 (14519 15936 2003424383)

(18749 24067 2843532298) (1 1 1 1) (13095 18756 19465

34211)(08830 27474 28092

41440)

4 (09330 16784 1959125506)

(08341 11678 1246129649)

(09159 28247 2893638990) (1 1 1 1) (09411 22048 23311

23398)

5 (16968 23804 2604048683)

(09998 17316 1919225134)

(12597 13015 1319723604)

(15705 22564 2494625479) (1 1 1 1)

6 (19121 19896 2080927139)

(16729 24921 2578739713)

(15206 17650 2276843007)

(14500 19317 2093727454)

(09090 15973 1608518771)

7 (08938 14201 2197430621)

(10727 18788 2676644705)

(11865 12597 1538946016)

(15736 20361 2419824402)

(09572 10258 1333527689)

8 (09447 14976 2328628905)

(12111 17803 1877535145)

(10618 11577 2241228931)

(09720 19844 2659229915)

(09858 24791 2598127111)

9 (08528 11187 1690118615)

(19187 19237 2598841383)

(15716 27271 2865831107)

(13071 16180 1836026575)

(15352 16308 2337227600)

10 (21417 21589 2790444097)

(08631 15053 1877827503)

(10816 11919 1518729980)

(12190 16116 1813649229)

(12200 13066 1742218604)


Alter 6 7 8 9 10

1 (10856 14359 2278023293)

(08282 15578 2285725171)

(17336 18140 1817440347)

(12599 12930 1567629902)

(21814 24984 2852348855)

2 (19559 19668 2694528364)

(10309 11247 1217418890)

(20821 25939 2733849534)

(17569 18550 1960925630)

(09146 20622 2848638604)

3 (25282 26897 2956229657)

(14502 14629 2198328661)

(09020 14561 1911939980)

(10401 19743 2791342684)

(09066 21276 2269430096)

4 (13612 19131 2452837361)

(11284 13665 1868026496)

(12325 13524 2155327878)

(15721 21685 2676729556)

(10085 12046 1327917180)

5 (12671 15430 1612327801)

(14844 15762 1746528314)

(13677 16992 1901321088)

(14527 15013 1733229330)

(11802 12257 1554719670)

6 (1 1 1 1) (11297 22511 2389429781)

(09836 13593 1751326157)

(13540 14390 1914221576)

(10371 20850 2793944945)

7 (11553 14880 1550817356) (1 1 1 1) (11869 14414 18417

23879)(13343 13919 28183

40151)(17366 20025 23034

35067)

8 (11300 15650 1901020894)

(15903 23132 2419924578) (1 1 1 1) (13946 15279 16276

17335)(13428 20892 24250

35989)

9 (24919 27597 2961132421)

(16795 18655 2658726980)

(15653 20299 2673326790) (1 1 1 1) (10599 27767 29745

30679)

10 (12209 18226 2480726000)

(10587 16723 2024723236)

(10306 10814 2009028380)

(09603 09948 2556447606) (1 1 1 1)


Alter 1 2 3 4 5 6 7 8 9 101 1 15314 16206 14502 13533 14101 12253 11829 11195 124672 08732 1 09696 11815 09277 09341 10056 16240 13692 090033 13962 09456 1 13245 14052 13976 07491 11550 10641 100244 12965 12240 09899 1 10433 12840 14147 13558 12670 078295 10521 10520 16035 12950 1 15459 08802 13835 10907 138236 14157 14310 13540 14816 11058 1 13005 15629 11353 154467 07071 13030 08849 12772 09513 11062 1 10778 11772 090948 09719 13723 13468 12719 11681 13485 10335 1 11417 154179 12668 10891 13683 11145 15616 12089 10983 11979 1 0940810 11048 11561 14336 12495 12373 13923 13778 13899 13436 1

Complexity 15




Alter 1 2 3 4 5 6 7 8 9 101 1 19481 21786 26741 26765 17774 17807 25275 18617 321432 21596 1 20555 25039 15031 23644 13543 32199 20662 241493 18819 25825 1 22090 26034 27819 20116 21619 25455 204334 17712 16605 25614 1 18669 24042 17760 18956 23310 132615 30017 17821 16409 21853 1 18684 19738 17633 19750 149446 22110 27231 25680 20662 14638 1 21489 17024 17196 263857 19067 25757 23581 21032 16022 14725 1 17266 24189 244278 19157 21776 18503 21235 20933 16615 21507 1 15697 239049 13786 27131 25055 18854 20731 28643 22239 22266 1 2358710 29505 17620 17784 25948 15328 20168 17550 17606 23935 1





SW3

SW2SW1

OW3

OW1 OW2

Subs

tage

1-1

Subs

tage

1-2

Subs

tage

2-1

Subs

tage

2-2

TW

Stage 1 Stage 2

Stage 3

SW1∘2 OW1∘2

SW1∘2∘3 OW1∘2∘3


16 Complexity










































Complexity 17





















18 Complexity










Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36





Complexity 19






Table 20 Continued

Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36










Model1

Model41

Model42

Model43

Model44

Model45

Model46

Model51

Model52

Model53

Model54

Model55

Model56













20 Complexity


Model1

Model61

Model62

Model63

Model64

Model65

Model66

Model71

Model72

Model73

Model74

Model75

Model76














Model1

Model81

Model82

Model83

Model84

Model85

Model86

Model91

Model92

Model93

Model94

Model95

Model96













Complexity 21











22 Complexity



6 Conclusions




Data Availability






Acknowledgments


References







Complexity 23





























24 Complexity


0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

a = 1a = 2a = 3

a = 4a = 5a = 6

a = 7a = 8a = 9


0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

EISIOI

WIEWS

OSSSES




Dimen

sionIn

dex

Targ

et

12

3

1

3 2

4

5

67

8

9


6 Complexity






1113957Φkt

1113957ϕkt

111113957ϕkt


1l

1113957ϕkt

211113957ϕkt


2l

⋮ ⋮ ⋮1113957ϕkt

l11113957ϕkt


ll

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(18)

where 1113957ϕkt



ji 11113957ϕkt






1113957ϕkt

ij αktij χkt

ij δktij βkt

ij1113872 1113873 (19)




Φkt

ϕktl1 ϕkt


ϕkt21 ϕkt


⋮ ⋮ ⋮

ϕktl1 ϕkt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(20)


CIkt

λmax( 1113857kt

minus l

l minus 1 (21)



CRktCIkt

RIkt (22)




Complexity 7

1113957Θt

1113957ρt11 1113957ρt


1113957ρt21 1113957ρt


⋮ ⋮ ⋮

1113957ρtl1 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(23)


1113957ρtij 1113957ϕ1t

ij 1113957ϕ2t

ij 1113957ϕqt

ij1113882 1113883 (24)



RBI 1113957ϕkt

ij1113874 1113875 LRL 1113957ϕkt

ij1113874 1113875URL 1113957ϕkt

ij1113874 11138751113876 1113877

1


ij1113874 11138751113874 11138751113944

Yisin1113957ρt

ij

Yle1113957ϕkt

ij

Y1


ij1113874 11138751113874 11138751113944

Yisin1113957ρt

ij

Yge1113957ϕkt

ij

Y

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(25)











Total synthesis



indexes



Index value matrix



Experts judgement

Phas

e 1 f

uzzy

roug

h-se

ts A

HP

Phas

e 2 m

ultis

tage

wei

ght

synt

hesis

Phas

e 3 P

ROM

ETH

EE II

Yes

No



Dimension l 1 2 3 4 5 6 7 8 9RI 000 000 058 090 112 124 132 141 145

8 Complexity



RBI 1113957ρtij1113872 1113873 LRL 1113957ρt

ij1113872 1113873URL 1113957ρtij1113872 11138731113960 1113961

1q

1113944

q

k1LRL 1113957ϕkt

ij1113874 11138751q

1113944

q

k1URL 1113957ϕkt

ij1113874 1113875⎡⎣ ⎤⎦

(26)


1113957Λt

RBI 1113957ρt111113872 1113873 RBI 1113957ρt


RBI 1113957ρt211113872 1113873 RBI 1113957ρt


⋮ ⋮ ⋮

RBI 1113957ρtl11113872 1113873 RBI 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(27)


1113957Λt

LRL

LRL 1113957ρt111113872 1113873 LRL 1113957ρt


LRL 1113957ρt211113872 1113873 LRL 1113957ρt


⋮ ⋮ ⋮

LRL 1113957ρtl11113872 1113873 LRL 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(28)

1113957Λt

URL

URL 1113957ρt111113872 1113873 URL 1113957ρt


URL 1113957ρt211113872 1113873 URL 1113957ρt


⋮ ⋮ ⋮URL 1113957ρt


ll1113872 1113873

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(29)


LRL and 1113957Λt





Eig ΛtLRL1113872 1113873 Eig1 Λ

tLRL1113872 1113873Eig2 Λ

tLRL1113872 1113873 Eigl Λ

tLRL1113872 11138731113960 1113961

(30)

Eig ΛtURL1113872 1113873 Eig1 Λ

tURL1113872 1113873Eig2 Λ

tURL1113872 1113873 Eigl Λ

tURL1113872 11138731113960 1113961

(31)



tAver1113872 1113873Eig2 Λ

tAver1113872 1113873 Eigl Λ

tAver1113872 11138731113960 1113961

(32)





Aver)








Complexity 9

SW

Substage

Substage

Substage

Substage

OW3

Substage

OWg

OWSu

bstage

TW

Stage 1

sub

jective w

eigh

t syn

thesis

Stage 2

objectiv

e weigh

t syn

thesis



ANP method

Delphi method

Entropy method

CRITIC method



OW1 OW2SW1

SW3

SW2

SWh









10 Complexity



SW1 sw1

1 sw12 sw1

N1113960 1113961T

SW2 sw2

1 sw22 sw2

N1113960 1113961T


SWh swh

1 swh2 swh

N1113960 1113961T

(33)


1 sw1∘22 sw1∘2


SW1∘2 τ1SW

1+ τ2SW

2 (34)



ξ1∘2 1113944l

i11113944

N

t1τ1sw

1t xit minus τ2sw

2t xit1113872 1113873

2 (35)


and SW2 as follows

min ξ1∘2

st τ1 ge 0 τ2 ge 0 τ1 + τ2 1(36)


τ1 1113936

li1 1113936

Nt1 xit1113872 1113873

2sw2

t sw1t + sw2

t( 1113857

1113936li1 1113936

Nt1 xit1113872 1113873

2sw1

t + sw2t( 1113857

τ2 1 minus τ1

(37)


SW1∘2∘∘h sw1∘2∘∘h

1 sw1∘2∘∘h2 sw1∘2∘∘h

N1113960 1113961T (38)




Overall goal

Index 1

Index 3

Index 2

Index 7

Index 9

Index 8

Index 4

Index 6

Index 5

Dimension 1


Control layer

Network layer


Complexity 11



OW1∘2∘∘g ow1∘2∘∘g

1 ow1∘2∘∘g2 ow1∘2∘∘g

N1113960 1113961T

(39)




(40)






⎧⎨

⎩ (41)



p(i m) 1113944N




Ω+i 1113944

l

m1mneip(i m)

Ωminusi 1113944

l

m1mneip(m i)

(43)






i (44)




12 Complexity


[1113957ϕ11ij ]10times10 1113957Φ21

[1113957ϕ21ij ]10times10 and

1113957Φ31 [1113957ϕ31


1113957Φ11











⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(45)


ij 1113957ϕ21ij 1113957ϕ31


1113957ρ112 1113957ϕ1112

1113957ϕ2112

1113957ϕ31121113882 1113883 OSEOS (10000 12222


12 OS in 1113957ρ112

1113957ϕ1112

1113957ϕ2112


12) [LRL(1113957ϕ1112)

URL(1113957ϕ1112)] [(10000 11481 15714 18889) (10000

12222 18571 23333)] while RBI(1113957ϕ2112)

[LRL(1113957ϕ2112)URL(1113957ϕ21

12)] [(10000 10000 10000 10000)(10000 11481 15714 18889)] and RBI(1113957ϕ31

12)

[LRL(1113957ϕ3112)URL(1113957ϕ31



1113957ϕ2112

1113957ϕ31121113882 1113883 can be obtained

as RBI(1113957ρ112) [(10000 10988 13809 15926) (1000011975 17619 21852)]














Complexity 13




Model 21 SW1+OW1

Model 22 SW1+OW2

Model 23 SW2 +OW2

Model 24 SW2 +OW3

Model 25 SW3 +OW1

Model 26 SW3 +OW3


Model 31 SW1 +OW1

Model 32 SW1 +OW2

Model 33 SW2 +OW2

Model 34 SW2 +OW3

Model 35 SW3 +OW1

Model 36 SW3 +OW3


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 10988 1380915926)

(11037 16779 1869419372)

(06468 17128 1854018657)

(09951 13021 1357217378)

2 (05336 05676 1039713301) (1 1 1 1) (04684 09725 11776

13317)(08246 10541 10761

16594)(05427 08139 09974

13416)

3 (11489 14540 1456115842)

(04953 05825 0856816916) (1 1 1 1) (08178 11612 12975

19428)(10195 10630 15027

19814)

4 (07188 10560 1695217386)

(09026 11191 1423414681)

(07571 09762 1027212090) (1 1 1 1) (05961 11055 11799

13777)

5 (05566 09454 1272814644)

(06137 09540 1273613970)

(14355 14538 1502519150)

(11477 11610 1391314760) (1 1 1 1)

6 (08475 14009 1741017550)

(10563 11164 1723718260)

(07848 10350 1675119214)

(07092 16417 1786119843)

(04996 13061 1402814263)

7 (06408 06771 0743107685)

(11400 12236 1280515275)

(05379 07261 1007412589)

(06112 11761 1496918638)

(06579 07795 0914913757)

8 (05216 06006 0879217264)

(10414 11301 1636616826)

(08778 15035 1549516198)

(06862 08049 1730018657)

(04572 06153 1651119409)

9 (11202 12001 1371513804)

(09248 11256 1142512045)

(10368 12759 1448717079)

(07720 09169 1359914148)

(12160 15583 1657518508)

10 (04973 11939 1225016033)

(07335 08219 1343916985)

(12856 14828 1483115321)

(05005 13199 1487218169)

(06924 10332 1449417761)


Alter 6 7 8 9 10

1 (08231 14384 1498019344)

(07973 08449 1485117588)

(04518 10495 1383418698)

(10328 10413 1067112811)

(10170 10771 1145016334)

2 (05954 06653 0747615292)

(06231 06613 1217515019)

(13189 15298 1768618909)

(04508 13995 1791419844)

(06138 06702 0708014125)

3 (05483 15937 1783718983)

(04979 06576 0725310678)

(05462 09109 0964719929)

(05753 05893 1428216547)

(04660 09057 0974116068)

4 (07969 09776 1357219376)

(06649 12982 1830919369)

(08275 09925 1712118904)

(06747 13023 1348517974)

(05677 06411 0821910728)

5 (12083 12108 1849219144)

(07146 08002 0802911253)

(06222 11302 1852619686)

(06320 07937 1384415524)

(08933 09312 1100123003)

6 (1 1 1 1) (05999 12586 1717217181)

(11534 14559 1690519581)

(08006 10462 1353613637)

(09830 15819 1727819731)

7 (04849 08541 1371317175) (1 1 1 1) (05054 09498 11806

16663)(07472 09787 13915

15946)(05912 07424 08956

13431)

8 (10599 12561 1490715989)

(05189 08263 1135716201) (1 1 1 1) (04803 11356 15093

15413)(12220 13407 17600

18463)

9 (05794 14202 1474515811)

(04763 06373 1349118889)

(04891 11740 1454717554) (1 1 1 1) (05341 07245 09628

14774)

10 (08962 10925 1545719992)

(08964 15462 1581016611)

(09733 13922 1598916593)

(05296 15882 1688418302) (1 1 1 1)

14 Complexity


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 11975 1761921852)

(13959 18678 2560629058)

(08786 22426 2668147228)

(14288 24658 2817839657)

2 (13456 19678 2514228548) (1 1 1 1) (11568 14847 25474

30198)(10122 10903 28725

48158)(08339 08947 15098

26066)

3 (14519 15936 2003424383)

(18749 24067 2843532298) (1 1 1 1) (13095 18756 19465

34211)(08830 27474 28092

41440)

4 (09330 16784 1959125506)

(08341 11678 1246129649)

(09159 28247 2893638990) (1 1 1 1) (09411 22048 23311

23398)

5 (16968 23804 2604048683)

(09998 17316 1919225134)

(12597 13015 1319723604)

(15705 22564 2494625479) (1 1 1 1)

6 (19121 19896 2080927139)

(16729 24921 2578739713)

(15206 17650 2276843007)

(14500 19317 2093727454)

(09090 15973 1608518771)

7 (08938 14201 2197430621)

(10727 18788 2676644705)

(11865 12597 1538946016)

(15736 20361 2419824402)

(09572 10258 1333527689)

8 (09447 14976 2328628905)

(12111 17803 1877535145)

(10618 11577 2241228931)

(09720 19844 2659229915)

(09858 24791 2598127111)

9 (08528 11187 1690118615)

(19187 19237 2598841383)

(15716 27271 2865831107)

(13071 16180 1836026575)

(15352 16308 2337227600)

10 (21417 21589 2790444097)

(08631 15053 1877827503)

(10816 11919 1518729980)

(12190 16116 1813649229)

(12200 13066 1742218604)


Alter 6 7 8 9 10

1 (10856 14359 2278023293)

(08282 15578 2285725171)

(17336 18140 1817440347)

(12599 12930 1567629902)

(21814 24984 2852348855)

2 (19559 19668 2694528364)

(10309 11247 1217418890)

(20821 25939 2733849534)

(17569 18550 1960925630)

(09146 20622 2848638604)

3 (25282 26897 2956229657)

(14502 14629 2198328661)

(09020 14561 1911939980)

(10401 19743 2791342684)

(09066 21276 2269430096)

4 (13612 19131 2452837361)

(11284 13665 1868026496)

(12325 13524 2155327878)

(15721 21685 2676729556)

(10085 12046 1327917180)

5 (12671 15430 1612327801)

(14844 15762 1746528314)

(13677 16992 1901321088)

(14527 15013 1733229330)

(11802 12257 1554719670)

6 (1 1 1 1) (11297 22511 2389429781)

(09836 13593 1751326157)

(13540 14390 1914221576)

(10371 20850 2793944945)

7 (11553 14880 1550817356) (1 1 1 1) (11869 14414 18417

23879)(13343 13919 28183

40151)(17366 20025 23034

35067)

8 (11300 15650 1901020894)

(15903 23132 2419924578) (1 1 1 1) (13946 15279 16276

17335)(13428 20892 24250

35989)

9 (24919 27597 2961132421)

(16795 18655 2658726980)

(15653 20299 2673326790) (1 1 1 1) (10599 27767 29745

30679)

10 (12209 18226 2480726000)

(10587 16723 2024723236)

(10306 10814 2009028380)

(09603 09948 2556447606) (1 1 1 1)


Alter 1 2 3 4 5 6 7 8 9 101 1 15314 16206 14502 13533 14101 12253 11829 11195 124672 08732 1 09696 11815 09277 09341 10056 16240 13692 090033 13962 09456 1 13245 14052 13976 07491 11550 10641 100244 12965 12240 09899 1 10433 12840 14147 13558 12670 078295 10521 10520 16035 12950 1 15459 08802 13835 10907 138236 14157 14310 13540 14816 11058 1 13005 15629 11353 154467 07071 13030 08849 12772 09513 11062 1 10778 11772 090948 09719 13723 13468 12719 11681 13485 10335 1 11417 154179 12668 10891 13683 11145 15616 12089 10983 11979 1 0940810 11048 11561 14336 12495 12373 13923 13778 13899 13436 1

Complexity 15




Alter 1 2 3 4 5 6 7 8 9 101 1 19481 21786 26741 26765 17774 17807 25275 18617 321432 21596 1 20555 25039 15031 23644 13543 32199 20662 241493 18819 25825 1 22090 26034 27819 20116 21619 25455 204334 17712 16605 25614 1 18669 24042 17760 18956 23310 132615 30017 17821 16409 21853 1 18684 19738 17633 19750 149446 22110 27231 25680 20662 14638 1 21489 17024 17196 263857 19067 25757 23581 21032 16022 14725 1 17266 24189 244278 19157 21776 18503 21235 20933 16615 21507 1 15697 239049 13786 27131 25055 18854 20731 28643 22239 22266 1 2358710 29505 17620 17784 25948 15328 20168 17550 17606 23935 1





SW3

SW2SW1

OW3

OW1 OW2

Subs

tage

1-1

Subs

tage

1-2

Subs

tage

2-1

Subs

tage

2-2

TW

Stage 1 Stage 2

Stage 3

SW1∘2 OW1∘2

SW1∘2∘3 OW1∘2∘3


16 Complexity










































Complexity 17





















18 Complexity










Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36





Complexity 19






Table 20 Continued

Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36










Model1

Model41

Model42

Model43

Model44

Model45

Model46

Model51

Model52

Model53

Model54

Model55

Model56













20 Complexity


Model1

Model61

Model62

Model63

Model64

Model65

Model66

Model71

Model72

Model73

Model74

Model75

Model76














Model1

Model81

Model82

Model83

Model84

Model85

Model86

Model91

Model92

Model93

Model94

Model95

Model96













Complexity 21











22 Complexity



6 Conclusions




Data Availability






Acknowledgments


References







Complexity 23





























24 Complexity






1113957Φkt

1113957ϕkt

111113957ϕkt


1l

1113957ϕkt

211113957ϕkt


2l

⋮ ⋮ ⋮1113957ϕkt

l11113957ϕkt


ll

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(18)

where 1113957ϕkt



ji 11113957ϕkt






1113957ϕkt

ij αktij χkt

ij δktij βkt

ij1113872 1113873 (19)




Φkt

ϕktl1 ϕkt


ϕkt21 ϕkt


⋮ ⋮ ⋮

ϕktl1 ϕkt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(20)


CIkt

λmax( 1113857kt

minus l

l minus 1 (21)



CRktCIkt

RIkt (22)




Complexity 7

1113957Θt

1113957ρt11 1113957ρt


1113957ρt21 1113957ρt


⋮ ⋮ ⋮

1113957ρtl1 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(23)


1113957ρtij 1113957ϕ1t

ij 1113957ϕ2t

ij 1113957ϕqt

ij1113882 1113883 (24)



RBI 1113957ϕkt

ij1113874 1113875 LRL 1113957ϕkt

ij1113874 1113875URL 1113957ϕkt

ij1113874 11138751113876 1113877

1


ij1113874 11138751113874 11138751113944

Yisin1113957ρt

ij

Yle1113957ϕkt

ij

Y1


ij1113874 11138751113874 11138751113944

Yisin1113957ρt

ij

Yge1113957ϕkt

ij

Y

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(25)











Total synthesis



indexes



Index value matrix



Experts judgement

Phas

e 1 f

uzzy

roug

h-se

ts A

HP

Phas

e 2 m

ultis

tage

wei

ght

synt

hesis

Phas

e 3 P

ROM

ETH

EE II

Yes

No



Dimension l 1 2 3 4 5 6 7 8 9RI 000 000 058 090 112 124 132 141 145

8 Complexity



RBI 1113957ρtij1113872 1113873 LRL 1113957ρt

ij1113872 1113873URL 1113957ρtij1113872 11138731113960 1113961

1q

1113944

q

k1LRL 1113957ϕkt

ij1113874 11138751q

1113944

q

k1URL 1113957ϕkt

ij1113874 1113875⎡⎣ ⎤⎦

(26)


1113957Λt

RBI 1113957ρt111113872 1113873 RBI 1113957ρt


RBI 1113957ρt211113872 1113873 RBI 1113957ρt


⋮ ⋮ ⋮

RBI 1113957ρtl11113872 1113873 RBI 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(27)


1113957Λt

LRL

LRL 1113957ρt111113872 1113873 LRL 1113957ρt


LRL 1113957ρt211113872 1113873 LRL 1113957ρt


⋮ ⋮ ⋮

LRL 1113957ρtl11113872 1113873 LRL 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(28)

1113957Λt

URL

URL 1113957ρt111113872 1113873 URL 1113957ρt


URL 1113957ρt211113872 1113873 URL 1113957ρt


⋮ ⋮ ⋮URL 1113957ρt


ll1113872 1113873

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(29)


LRL and 1113957Λt





Eig ΛtLRL1113872 1113873 Eig1 Λ

tLRL1113872 1113873Eig2 Λ

tLRL1113872 1113873 Eigl Λ

tLRL1113872 11138731113960 1113961

(30)

Eig ΛtURL1113872 1113873 Eig1 Λ

tURL1113872 1113873Eig2 Λ

tURL1113872 1113873 Eigl Λ

tURL1113872 11138731113960 1113961

(31)



tAver1113872 1113873Eig2 Λ

tAver1113872 1113873 Eigl Λ

tAver1113872 11138731113960 1113961

(32)





Aver)








Complexity 9

SW

Substage

Substage

Substage

Substage

OW3

Substage

OWg

OWSu

bstage

TW

Stage 1

sub

jective w

eigh

t syn

thesis

Stage 2

objectiv

e weigh

t syn

thesis



ANP method

Delphi method

Entropy method

CRITIC method



OW1 OW2SW1

SW3

SW2

SWh









10 Complexity



SW1 sw1

1 sw12 sw1

N1113960 1113961T

SW2 sw2

1 sw22 sw2

N1113960 1113961T


SWh swh

1 swh2 swh

N1113960 1113961T

(33)


1 sw1∘22 sw1∘2


SW1∘2 τ1SW

1+ τ2SW

2 (34)



ξ1∘2 1113944l

i11113944

N

t1τ1sw

1t xit minus τ2sw

2t xit1113872 1113873

2 (35)


and SW2 as follows

min ξ1∘2

st τ1 ge 0 τ2 ge 0 τ1 + τ2 1(36)


τ1 1113936

li1 1113936

Nt1 xit1113872 1113873

2sw2

t sw1t + sw2

t( 1113857

1113936li1 1113936

Nt1 xit1113872 1113873

2sw1

t + sw2t( 1113857

τ2 1 minus τ1

(37)


SW1∘2∘∘h sw1∘2∘∘h

1 sw1∘2∘∘h2 sw1∘2∘∘h

N1113960 1113961T (38)




Overall goal

Index 1

Index 3

Index 2

Index 7

Index 9

Index 8

Index 4

Index 6

Index 5

Dimension 1


Control layer

Network layer


Complexity 11



OW1∘2∘∘g ow1∘2∘∘g

1 ow1∘2∘∘g2 ow1∘2∘∘g

N1113960 1113961T

(39)




(40)






⎧⎨

⎩ (41)



p(i m) 1113944N




Ω+i 1113944

l

m1mneip(i m)

Ωminusi 1113944

l

m1mneip(m i)

(43)






i (44)




12 Complexity


[1113957ϕ11ij ]10times10 1113957Φ21

[1113957ϕ21ij ]10times10 and

1113957Φ31 [1113957ϕ31


1113957Φ11











⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(45)


ij 1113957ϕ21ij 1113957ϕ31


1113957ρ112 1113957ϕ1112

1113957ϕ2112

1113957ϕ31121113882 1113883 OSEOS (10000 12222


12 OS in 1113957ρ112

1113957ϕ1112

1113957ϕ2112


12) [LRL(1113957ϕ1112)

URL(1113957ϕ1112)] [(10000 11481 15714 18889) (10000

12222 18571 23333)] while RBI(1113957ϕ2112)

[LRL(1113957ϕ2112)URL(1113957ϕ21

12)] [(10000 10000 10000 10000)(10000 11481 15714 18889)] and RBI(1113957ϕ31

12)

[LRL(1113957ϕ3112)URL(1113957ϕ31



1113957ϕ2112

1113957ϕ31121113882 1113883 can be obtained

as RBI(1113957ρ112) [(10000 10988 13809 15926) (1000011975 17619 21852)]














Complexity 13




Model 21 SW1+OW1

Model 22 SW1+OW2

Model 23 SW2 +OW2

Model 24 SW2 +OW3

Model 25 SW3 +OW1

Model 26 SW3 +OW3


Model 31 SW1 +OW1

Model 32 SW1 +OW2

Model 33 SW2 +OW2

Model 34 SW2 +OW3

Model 35 SW3 +OW1

Model 36 SW3 +OW3


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 10988 1380915926)

(11037 16779 1869419372)

(06468 17128 1854018657)

(09951 13021 1357217378)

2 (05336 05676 1039713301) (1 1 1 1) (04684 09725 11776

13317)(08246 10541 10761

16594)(05427 08139 09974

13416)

3 (11489 14540 1456115842)

(04953 05825 0856816916) (1 1 1 1) (08178 11612 12975

19428)(10195 10630 15027

19814)

4 (07188 10560 1695217386)

(09026 11191 1423414681)

(07571 09762 1027212090) (1 1 1 1) (05961 11055 11799

13777)

5 (05566 09454 1272814644)

(06137 09540 1273613970)

(14355 14538 1502519150)

(11477 11610 1391314760) (1 1 1 1)

6 (08475 14009 1741017550)

(10563 11164 1723718260)

(07848 10350 1675119214)

(07092 16417 1786119843)

(04996 13061 1402814263)

7 (06408 06771 0743107685)

(11400 12236 1280515275)

(05379 07261 1007412589)

(06112 11761 1496918638)

(06579 07795 0914913757)

8 (05216 06006 0879217264)

(10414 11301 1636616826)

(08778 15035 1549516198)

(06862 08049 1730018657)

(04572 06153 1651119409)

9 (11202 12001 1371513804)

(09248 11256 1142512045)

(10368 12759 1448717079)

(07720 09169 1359914148)

(12160 15583 1657518508)

10 (04973 11939 1225016033)

(07335 08219 1343916985)

(12856 14828 1483115321)

(05005 13199 1487218169)

(06924 10332 1449417761)


Alter 6 7 8 9 10

1 (08231 14384 1498019344)

(07973 08449 1485117588)

(04518 10495 1383418698)

(10328 10413 1067112811)

(10170 10771 1145016334)

2 (05954 06653 0747615292)

(06231 06613 1217515019)

(13189 15298 1768618909)

(04508 13995 1791419844)

(06138 06702 0708014125)

3 (05483 15937 1783718983)

(04979 06576 0725310678)

(05462 09109 0964719929)

(05753 05893 1428216547)

(04660 09057 0974116068)

4 (07969 09776 1357219376)

(06649 12982 1830919369)

(08275 09925 1712118904)

(06747 13023 1348517974)

(05677 06411 0821910728)

5 (12083 12108 1849219144)

(07146 08002 0802911253)

(06222 11302 1852619686)

(06320 07937 1384415524)

(08933 09312 1100123003)

6 (1 1 1 1) (05999 12586 1717217181)

(11534 14559 1690519581)

(08006 10462 1353613637)

(09830 15819 1727819731)

7 (04849 08541 1371317175) (1 1 1 1) (05054 09498 11806

16663)(07472 09787 13915

15946)(05912 07424 08956

13431)

8 (10599 12561 1490715989)

(05189 08263 1135716201) (1 1 1 1) (04803 11356 15093

15413)(12220 13407 17600

18463)

9 (05794 14202 1474515811)

(04763 06373 1349118889)

(04891 11740 1454717554) (1 1 1 1) (05341 07245 09628

14774)

10 (08962 10925 1545719992)

(08964 15462 1581016611)

(09733 13922 1598916593)

(05296 15882 1688418302) (1 1 1 1)

14 Complexity


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 11975 1761921852)

(13959 18678 2560629058)

(08786 22426 2668147228)

(14288 24658 2817839657)

2 (13456 19678 2514228548) (1 1 1 1) (11568 14847 25474

30198)(10122 10903 28725

48158)(08339 08947 15098

26066)

3 (14519 15936 2003424383)

(18749 24067 2843532298) (1 1 1 1) (13095 18756 19465

34211)(08830 27474 28092

41440)

4 (09330 16784 1959125506)

(08341 11678 1246129649)

(09159 28247 2893638990) (1 1 1 1) (09411 22048 23311

23398)

5 (16968 23804 2604048683)

(09998 17316 1919225134)

(12597 13015 1319723604)

(15705 22564 2494625479) (1 1 1 1)

6 (19121 19896 2080927139)

(16729 24921 2578739713)

(15206 17650 2276843007)

(14500 19317 2093727454)

(09090 15973 1608518771)

7 (08938 14201 2197430621)

(10727 18788 2676644705)

(11865 12597 1538946016)

(15736 20361 2419824402)

(09572 10258 1333527689)

8 (09447 14976 2328628905)

(12111 17803 1877535145)

(10618 11577 2241228931)

(09720 19844 2659229915)

(09858 24791 2598127111)

9 (08528 11187 1690118615)

(19187 19237 2598841383)

(15716 27271 2865831107)

(13071 16180 1836026575)

(15352 16308 2337227600)

10 (21417 21589 2790444097)

(08631 15053 1877827503)

(10816 11919 1518729980)

(12190 16116 1813649229)

(12200 13066 1742218604)


Alter 6 7 8 9 10

1 (10856 14359 2278023293)

(08282 15578 2285725171)

(17336 18140 1817440347)

(12599 12930 1567629902)

(21814 24984 2852348855)

2 (19559 19668 2694528364)

(10309 11247 1217418890)

(20821 25939 2733849534)

(17569 18550 1960925630)

(09146 20622 2848638604)

3 (25282 26897 2956229657)

(14502 14629 2198328661)

(09020 14561 1911939980)

(10401 19743 2791342684)

(09066 21276 2269430096)

4 (13612 19131 2452837361)

(11284 13665 1868026496)

(12325 13524 2155327878)

(15721 21685 2676729556)

(10085 12046 1327917180)

5 (12671 15430 1612327801)

(14844 15762 1746528314)

(13677 16992 1901321088)

(14527 15013 1733229330)

(11802 12257 1554719670)

6 (1 1 1 1) (11297 22511 2389429781)

(09836 13593 1751326157)

(13540 14390 1914221576)

(10371 20850 2793944945)

7 (11553 14880 1550817356) (1 1 1 1) (11869 14414 18417

23879)(13343 13919 28183

40151)(17366 20025 23034

35067)

8 (11300 15650 1901020894)

(15903 23132 2419924578) (1 1 1 1) (13946 15279 16276

17335)(13428 20892 24250

35989)

9 (24919 27597 2961132421)

(16795 18655 2658726980)

(15653 20299 2673326790) (1 1 1 1) (10599 27767 29745

30679)

10 (12209 18226 2480726000)

(10587 16723 2024723236)

(10306 10814 2009028380)

(09603 09948 2556447606) (1 1 1 1)


Alter 1 2 3 4 5 6 7 8 9 101 1 15314 16206 14502 13533 14101 12253 11829 11195 124672 08732 1 09696 11815 09277 09341 10056 16240 13692 090033 13962 09456 1 13245 14052 13976 07491 11550 10641 100244 12965 12240 09899 1 10433 12840 14147 13558 12670 078295 10521 10520 16035 12950 1 15459 08802 13835 10907 138236 14157 14310 13540 14816 11058 1 13005 15629 11353 154467 07071 13030 08849 12772 09513 11062 1 10778 11772 090948 09719 13723 13468 12719 11681 13485 10335 1 11417 154179 12668 10891 13683 11145 15616 12089 10983 11979 1 0940810 11048 11561 14336 12495 12373 13923 13778 13899 13436 1

Complexity 15




Alter 1 2 3 4 5 6 7 8 9 101 1 19481 21786 26741 26765 17774 17807 25275 18617 321432 21596 1 20555 25039 15031 23644 13543 32199 20662 241493 18819 25825 1 22090 26034 27819 20116 21619 25455 204334 17712 16605 25614 1 18669 24042 17760 18956 23310 132615 30017 17821 16409 21853 1 18684 19738 17633 19750 149446 22110 27231 25680 20662 14638 1 21489 17024 17196 263857 19067 25757 23581 21032 16022 14725 1 17266 24189 244278 19157 21776 18503 21235 20933 16615 21507 1 15697 239049 13786 27131 25055 18854 20731 28643 22239 22266 1 2358710 29505 17620 17784 25948 15328 20168 17550 17606 23935 1





SW3

SW2SW1

OW3

OW1 OW2

Subs

tage

1-1

Subs

tage

1-2

Subs

tage

2-1

Subs

tage

2-2

TW

Stage 1 Stage 2

Stage 3

SW1∘2 OW1∘2

SW1∘2∘3 OW1∘2∘3


16 Complexity










































Complexity 17





















18 Complexity










Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36





Complexity 19






Table 20 Continued

Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36










Model1

Model41

Model42

Model43

Model44

Model45

Model46

Model51

Model52

Model53

Model54

Model55

Model56













20 Complexity


Model1

Model61

Model62

Model63

Model64

Model65

Model66

Model71

Model72

Model73

Model74

Model75

Model76














Model1

Model81

Model82

Model83

Model84

Model85

Model86

Model91

Model92

Model93

Model94

Model95

Model96













Complexity 21











22 Complexity



6 Conclusions




Data Availability






Acknowledgments


References







Complexity 23





























24 Complexity

1113957Θt

1113957ρt11 1113957ρt


1113957ρt21 1113957ρt


⋮ ⋮ ⋮

1113957ρtl1 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(23)


1113957ρtij 1113957ϕ1t

ij 1113957ϕ2t

ij 1113957ϕqt

ij1113882 1113883 (24)



RBI 1113957ϕkt

ij1113874 1113875 LRL 1113957ϕkt

ij1113874 1113875URL 1113957ϕkt

ij1113874 11138751113876 1113877

1


ij1113874 11138751113874 11138751113944

Yisin1113957ρt

ij

Yle1113957ϕkt

ij

Y1


ij1113874 11138751113874 11138751113944

Yisin1113957ρt

ij

Yge1113957ϕkt

ij

Y

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(25)











Total synthesis



indexes



Index value matrix



Experts judgement

Phas

e 1 f

uzzy

roug

h-se

ts A

HP

Phas

e 2 m

ultis

tage

wei

ght

synt

hesis

Phas

e 3 P

ROM

ETH

EE II

Yes

No



Dimension l 1 2 3 4 5 6 7 8 9RI 000 000 058 090 112 124 132 141 145

8 Complexity



RBI 1113957ρtij1113872 1113873 LRL 1113957ρt

ij1113872 1113873URL 1113957ρtij1113872 11138731113960 1113961

1q

1113944

q

k1LRL 1113957ϕkt

ij1113874 11138751q

1113944

q

k1URL 1113957ϕkt

ij1113874 1113875⎡⎣ ⎤⎦

(26)


1113957Λt

RBI 1113957ρt111113872 1113873 RBI 1113957ρt


RBI 1113957ρt211113872 1113873 RBI 1113957ρt


⋮ ⋮ ⋮

RBI 1113957ρtl11113872 1113873 RBI 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(27)


1113957Λt

LRL

LRL 1113957ρt111113872 1113873 LRL 1113957ρt


LRL 1113957ρt211113872 1113873 LRL 1113957ρt


⋮ ⋮ ⋮

LRL 1113957ρtl11113872 1113873 LRL 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(28)

1113957Λt

URL

URL 1113957ρt111113872 1113873 URL 1113957ρt


URL 1113957ρt211113872 1113873 URL 1113957ρt


⋮ ⋮ ⋮URL 1113957ρt


ll1113872 1113873

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(29)


LRL and 1113957Λt





Eig ΛtLRL1113872 1113873 Eig1 Λ

tLRL1113872 1113873Eig2 Λ

tLRL1113872 1113873 Eigl Λ

tLRL1113872 11138731113960 1113961

(30)

Eig ΛtURL1113872 1113873 Eig1 Λ

tURL1113872 1113873Eig2 Λ

tURL1113872 1113873 Eigl Λ

tURL1113872 11138731113960 1113961

(31)



tAver1113872 1113873Eig2 Λ

tAver1113872 1113873 Eigl Λ

tAver1113872 11138731113960 1113961

(32)





Aver)








Complexity 9

SW

Substage

Substage

Substage

Substage

OW3

Substage

OWg

OWSu

bstage

TW

Stage 1

sub

jective w

eigh

t syn

thesis

Stage 2

objectiv

e weigh

t syn

thesis



ANP method

Delphi method

Entropy method

CRITIC method



OW1 OW2SW1

SW3

SW2

SWh









10 Complexity



SW1 sw1

1 sw12 sw1

N1113960 1113961T

SW2 sw2

1 sw22 sw2

N1113960 1113961T


SWh swh

1 swh2 swh

N1113960 1113961T

(33)


1 sw1∘22 sw1∘2


SW1∘2 τ1SW

1+ τ2SW

2 (34)



ξ1∘2 1113944l

i11113944

N

t1τ1sw

1t xit minus τ2sw

2t xit1113872 1113873

2 (35)


and SW2 as follows

min ξ1∘2

st τ1 ge 0 τ2 ge 0 τ1 + τ2 1(36)


τ1 1113936

li1 1113936

Nt1 xit1113872 1113873

2sw2

t sw1t + sw2

t( 1113857

1113936li1 1113936

Nt1 xit1113872 1113873

2sw1

t + sw2t( 1113857

τ2 1 minus τ1

(37)


SW1∘2∘∘h sw1∘2∘∘h

1 sw1∘2∘∘h2 sw1∘2∘∘h

N1113960 1113961T (38)




Overall goal

Index 1

Index 3

Index 2

Index 7

Index 9

Index 8

Index 4

Index 6

Index 5

Dimension 1


Control layer

Network layer


Complexity 11



OW1∘2∘∘g ow1∘2∘∘g

1 ow1∘2∘∘g2 ow1∘2∘∘g

N1113960 1113961T

(39)




(40)






⎧⎨

⎩ (41)



p(i m) 1113944N




Ω+i 1113944

l

m1mneip(i m)

Ωminusi 1113944

l

m1mneip(m i)

(43)






i (44)




12 Complexity


[1113957ϕ11ij ]10times10 1113957Φ21

[1113957ϕ21ij ]10times10 and

1113957Φ31 [1113957ϕ31


1113957Φ11











⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(45)


ij 1113957ϕ21ij 1113957ϕ31


1113957ρ112 1113957ϕ1112

1113957ϕ2112

1113957ϕ31121113882 1113883 OSEOS (10000 12222


12 OS in 1113957ρ112

1113957ϕ1112

1113957ϕ2112


12) [LRL(1113957ϕ1112)

URL(1113957ϕ1112)] [(10000 11481 15714 18889) (10000

12222 18571 23333)] while RBI(1113957ϕ2112)

[LRL(1113957ϕ2112)URL(1113957ϕ21

12)] [(10000 10000 10000 10000)(10000 11481 15714 18889)] and RBI(1113957ϕ31

12)

[LRL(1113957ϕ3112)URL(1113957ϕ31



1113957ϕ2112

1113957ϕ31121113882 1113883 can be obtained

as RBI(1113957ρ112) [(10000 10988 13809 15926) (1000011975 17619 21852)]














Complexity 13




Model 21 SW1+OW1

Model 22 SW1+OW2

Model 23 SW2 +OW2

Model 24 SW2 +OW3

Model 25 SW3 +OW1

Model 26 SW3 +OW3


Model 31 SW1 +OW1

Model 32 SW1 +OW2

Model 33 SW2 +OW2

Model 34 SW2 +OW3

Model 35 SW3 +OW1

Model 36 SW3 +OW3


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 10988 1380915926)

(11037 16779 1869419372)

(06468 17128 1854018657)

(09951 13021 1357217378)

2 (05336 05676 1039713301) (1 1 1 1) (04684 09725 11776

13317)(08246 10541 10761

16594)(05427 08139 09974

13416)

3 (11489 14540 1456115842)

(04953 05825 0856816916) (1 1 1 1) (08178 11612 12975

19428)(10195 10630 15027

19814)

4 (07188 10560 1695217386)

(09026 11191 1423414681)

(07571 09762 1027212090) (1 1 1 1) (05961 11055 11799

13777)

5 (05566 09454 1272814644)

(06137 09540 1273613970)

(14355 14538 1502519150)

(11477 11610 1391314760) (1 1 1 1)

6 (08475 14009 1741017550)

(10563 11164 1723718260)

(07848 10350 1675119214)

(07092 16417 1786119843)

(04996 13061 1402814263)

7 (06408 06771 0743107685)

(11400 12236 1280515275)

(05379 07261 1007412589)

(06112 11761 1496918638)

(06579 07795 0914913757)

8 (05216 06006 0879217264)

(10414 11301 1636616826)

(08778 15035 1549516198)

(06862 08049 1730018657)

(04572 06153 1651119409)

9 (11202 12001 1371513804)

(09248 11256 1142512045)

(10368 12759 1448717079)

(07720 09169 1359914148)

(12160 15583 1657518508)

10 (04973 11939 1225016033)

(07335 08219 1343916985)

(12856 14828 1483115321)

(05005 13199 1487218169)

(06924 10332 1449417761)


Alter 6 7 8 9 10

1 (08231 14384 1498019344)

(07973 08449 1485117588)

(04518 10495 1383418698)

(10328 10413 1067112811)

(10170 10771 1145016334)

2 (05954 06653 0747615292)

(06231 06613 1217515019)

(13189 15298 1768618909)

(04508 13995 1791419844)

(06138 06702 0708014125)

3 (05483 15937 1783718983)

(04979 06576 0725310678)

(05462 09109 0964719929)

(05753 05893 1428216547)

(04660 09057 0974116068)

4 (07969 09776 1357219376)

(06649 12982 1830919369)

(08275 09925 1712118904)

(06747 13023 1348517974)

(05677 06411 0821910728)

5 (12083 12108 1849219144)

(07146 08002 0802911253)

(06222 11302 1852619686)

(06320 07937 1384415524)

(08933 09312 1100123003)

6 (1 1 1 1) (05999 12586 1717217181)

(11534 14559 1690519581)

(08006 10462 1353613637)

(09830 15819 1727819731)

7 (04849 08541 1371317175) (1 1 1 1) (05054 09498 11806

16663)(07472 09787 13915

15946)(05912 07424 08956

13431)

8 (10599 12561 1490715989)

(05189 08263 1135716201) (1 1 1 1) (04803 11356 15093

15413)(12220 13407 17600

18463)

9 (05794 14202 1474515811)

(04763 06373 1349118889)

(04891 11740 1454717554) (1 1 1 1) (05341 07245 09628

14774)

10 (08962 10925 1545719992)

(08964 15462 1581016611)

(09733 13922 1598916593)

(05296 15882 1688418302) (1 1 1 1)

14 Complexity


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 11975 1761921852)

(13959 18678 2560629058)

(08786 22426 2668147228)

(14288 24658 2817839657)

2 (13456 19678 2514228548) (1 1 1 1) (11568 14847 25474

30198)(10122 10903 28725

48158)(08339 08947 15098

26066)

3 (14519 15936 2003424383)

(18749 24067 2843532298) (1 1 1 1) (13095 18756 19465

34211)(08830 27474 28092

41440)

4 (09330 16784 1959125506)

(08341 11678 1246129649)

(09159 28247 2893638990) (1 1 1 1) (09411 22048 23311

23398)

5 (16968 23804 2604048683)

(09998 17316 1919225134)

(12597 13015 1319723604)

(15705 22564 2494625479) (1 1 1 1)

6 (19121 19896 2080927139)

(16729 24921 2578739713)

(15206 17650 2276843007)

(14500 19317 2093727454)

(09090 15973 1608518771)

7 (08938 14201 2197430621)

(10727 18788 2676644705)

(11865 12597 1538946016)

(15736 20361 2419824402)

(09572 10258 1333527689)

8 (09447 14976 2328628905)

(12111 17803 1877535145)

(10618 11577 2241228931)

(09720 19844 2659229915)

(09858 24791 2598127111)

9 (08528 11187 1690118615)

(19187 19237 2598841383)

(15716 27271 2865831107)

(13071 16180 1836026575)

(15352 16308 2337227600)

10 (21417 21589 2790444097)

(08631 15053 1877827503)

(10816 11919 1518729980)

(12190 16116 1813649229)

(12200 13066 1742218604)


Alter 6 7 8 9 10

1 (10856 14359 2278023293)

(08282 15578 2285725171)

(17336 18140 1817440347)

(12599 12930 1567629902)

(21814 24984 2852348855)

2 (19559 19668 2694528364)

(10309 11247 1217418890)

(20821 25939 2733849534)

(17569 18550 1960925630)

(09146 20622 2848638604)

3 (25282 26897 2956229657)

(14502 14629 2198328661)

(09020 14561 1911939980)

(10401 19743 2791342684)

(09066 21276 2269430096)

4 (13612 19131 2452837361)

(11284 13665 1868026496)

(12325 13524 2155327878)

(15721 21685 2676729556)

(10085 12046 1327917180)

5 (12671 15430 1612327801)

(14844 15762 1746528314)

(13677 16992 1901321088)

(14527 15013 1733229330)

(11802 12257 1554719670)

6 (1 1 1 1) (11297 22511 2389429781)

(09836 13593 1751326157)

(13540 14390 1914221576)

(10371 20850 2793944945)

7 (11553 14880 1550817356) (1 1 1 1) (11869 14414 18417

23879)(13343 13919 28183

40151)(17366 20025 23034

35067)

8 (11300 15650 1901020894)

(15903 23132 2419924578) (1 1 1 1) (13946 15279 16276

17335)(13428 20892 24250

35989)

9 (24919 27597 2961132421)

(16795 18655 2658726980)

(15653 20299 2673326790) (1 1 1 1) (10599 27767 29745

30679)

10 (12209 18226 2480726000)

(10587 16723 2024723236)

(10306 10814 2009028380)

(09603 09948 2556447606) (1 1 1 1)


Alter 1 2 3 4 5 6 7 8 9 101 1 15314 16206 14502 13533 14101 12253 11829 11195 124672 08732 1 09696 11815 09277 09341 10056 16240 13692 090033 13962 09456 1 13245 14052 13976 07491 11550 10641 100244 12965 12240 09899 1 10433 12840 14147 13558 12670 078295 10521 10520 16035 12950 1 15459 08802 13835 10907 138236 14157 14310 13540 14816 11058 1 13005 15629 11353 154467 07071 13030 08849 12772 09513 11062 1 10778 11772 090948 09719 13723 13468 12719 11681 13485 10335 1 11417 154179 12668 10891 13683 11145 15616 12089 10983 11979 1 0940810 11048 11561 14336 12495 12373 13923 13778 13899 13436 1

Complexity 15




Alter 1 2 3 4 5 6 7 8 9 101 1 19481 21786 26741 26765 17774 17807 25275 18617 321432 21596 1 20555 25039 15031 23644 13543 32199 20662 241493 18819 25825 1 22090 26034 27819 20116 21619 25455 204334 17712 16605 25614 1 18669 24042 17760 18956 23310 132615 30017 17821 16409 21853 1 18684 19738 17633 19750 149446 22110 27231 25680 20662 14638 1 21489 17024 17196 263857 19067 25757 23581 21032 16022 14725 1 17266 24189 244278 19157 21776 18503 21235 20933 16615 21507 1 15697 239049 13786 27131 25055 18854 20731 28643 22239 22266 1 2358710 29505 17620 17784 25948 15328 20168 17550 17606 23935 1





SW3

SW2SW1

OW3

OW1 OW2

Subs

tage

1-1

Subs

tage

1-2

Subs

tage

2-1

Subs

tage

2-2

TW

Stage 1 Stage 2

Stage 3

SW1∘2 OW1∘2

SW1∘2∘3 OW1∘2∘3


16 Complexity










































Complexity 17





















18 Complexity










Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36





Complexity 19






Table 20 Continued

Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36










Model1

Model41

Model42

Model43

Model44

Model45

Model46

Model51

Model52

Model53

Model54

Model55

Model56













20 Complexity


Model1

Model61

Model62

Model63

Model64

Model65

Model66

Model71

Model72

Model73

Model74

Model75

Model76














Model1

Model81

Model82

Model83

Model84

Model85

Model86

Model91

Model92

Model93

Model94

Model95

Model96













Complexity 21











22 Complexity



6 Conclusions




Data Availability






Acknowledgments


References







Complexity 23





























24 Complexity



RBI 1113957ρtij1113872 1113873 LRL 1113957ρt

ij1113872 1113873URL 1113957ρtij1113872 11138731113960 1113961

1q

1113944

q

k1LRL 1113957ϕkt

ij1113874 11138751q

1113944

q

k1URL 1113957ϕkt

ij1113874 1113875⎡⎣ ⎤⎦

(26)


1113957Λt

RBI 1113957ρt111113872 1113873 RBI 1113957ρt


RBI 1113957ρt211113872 1113873 RBI 1113957ρt


⋮ ⋮ ⋮

RBI 1113957ρtl11113872 1113873 RBI 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(27)


1113957Λt

LRL

LRL 1113957ρt111113872 1113873 LRL 1113957ρt


LRL 1113957ρt211113872 1113873 LRL 1113957ρt


⋮ ⋮ ⋮

LRL 1113957ρtl11113872 1113873 LRL 1113957ρt


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(28)

1113957Λt

URL

URL 1113957ρt111113872 1113873 URL 1113957ρt


URL 1113957ρt211113872 1113873 URL 1113957ρt


⋮ ⋮ ⋮URL 1113957ρt


ll1113872 1113873

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(29)


LRL and 1113957Λt





Eig ΛtLRL1113872 1113873 Eig1 Λ

tLRL1113872 1113873Eig2 Λ

tLRL1113872 1113873 Eigl Λ

tLRL1113872 11138731113960 1113961

(30)

Eig ΛtURL1113872 1113873 Eig1 Λ

tURL1113872 1113873Eig2 Λ

tURL1113872 1113873 Eigl Λ

tURL1113872 11138731113960 1113961

(31)



tAver1113872 1113873Eig2 Λ

tAver1113872 1113873 Eigl Λ

tAver1113872 11138731113960 1113961

(32)





Aver)








Complexity 9

SW

Substage

Substage

Substage

Substage

OW3

Substage

OWg

OWSu

bstage

TW

Stage 1

sub

jective w

eigh

t syn

thesis

Stage 2

objectiv

e weigh

t syn

thesis



ANP method

Delphi method

Entropy method

CRITIC method



OW1 OW2SW1

SW3

SW2

SWh









10 Complexity



SW1 sw1

1 sw12 sw1

N1113960 1113961T

SW2 sw2

1 sw22 sw2

N1113960 1113961T


SWh swh

1 swh2 swh

N1113960 1113961T

(33)


1 sw1∘22 sw1∘2


SW1∘2 τ1SW

1+ τ2SW

2 (34)



ξ1∘2 1113944l

i11113944

N

t1τ1sw

1t xit minus τ2sw

2t xit1113872 1113873

2 (35)


and SW2 as follows

min ξ1∘2

st τ1 ge 0 τ2 ge 0 τ1 + τ2 1(36)


τ1 1113936

li1 1113936

Nt1 xit1113872 1113873

2sw2

t sw1t + sw2

t( 1113857

1113936li1 1113936

Nt1 xit1113872 1113873

2sw1

t + sw2t( 1113857

τ2 1 minus τ1

(37)


SW1∘2∘∘h sw1∘2∘∘h

1 sw1∘2∘∘h2 sw1∘2∘∘h

N1113960 1113961T (38)




Overall goal

Index 1

Index 3

Index 2

Index 7

Index 9

Index 8

Index 4

Index 6

Index 5

Dimension 1


Control layer

Network layer


Complexity 11



OW1∘2∘∘g ow1∘2∘∘g

1 ow1∘2∘∘g2 ow1∘2∘∘g

N1113960 1113961T

(39)




(40)






⎧⎨

⎩ (41)



p(i m) 1113944N




Ω+i 1113944

l

m1mneip(i m)

Ωminusi 1113944

l

m1mneip(m i)

(43)






i (44)




12 Complexity


[1113957ϕ11ij ]10times10 1113957Φ21

[1113957ϕ21ij ]10times10 and

1113957Φ31 [1113957ϕ31


1113957Φ11











⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(45)


ij 1113957ϕ21ij 1113957ϕ31


1113957ρ112 1113957ϕ1112

1113957ϕ2112

1113957ϕ31121113882 1113883 OSEOS (10000 12222


12 OS in 1113957ρ112

1113957ϕ1112

1113957ϕ2112


12) [LRL(1113957ϕ1112)

URL(1113957ϕ1112)] [(10000 11481 15714 18889) (10000

12222 18571 23333)] while RBI(1113957ϕ2112)

[LRL(1113957ϕ2112)URL(1113957ϕ21

12)] [(10000 10000 10000 10000)(10000 11481 15714 18889)] and RBI(1113957ϕ31

12)

[LRL(1113957ϕ3112)URL(1113957ϕ31



1113957ϕ2112

1113957ϕ31121113882 1113883 can be obtained

as RBI(1113957ρ112) [(10000 10988 13809 15926) (1000011975 17619 21852)]














Complexity 13




Model 21 SW1+OW1

Model 22 SW1+OW2

Model 23 SW2 +OW2

Model 24 SW2 +OW3

Model 25 SW3 +OW1

Model 26 SW3 +OW3


Model 31 SW1 +OW1

Model 32 SW1 +OW2

Model 33 SW2 +OW2

Model 34 SW2 +OW3

Model 35 SW3 +OW1

Model 36 SW3 +OW3


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 10988 1380915926)

(11037 16779 1869419372)

(06468 17128 1854018657)

(09951 13021 1357217378)

2 (05336 05676 1039713301) (1 1 1 1) (04684 09725 11776

13317)(08246 10541 10761

16594)(05427 08139 09974

13416)

3 (11489 14540 1456115842)

(04953 05825 0856816916) (1 1 1 1) (08178 11612 12975

19428)(10195 10630 15027

19814)

4 (07188 10560 1695217386)

(09026 11191 1423414681)

(07571 09762 1027212090) (1 1 1 1) (05961 11055 11799

13777)

5 (05566 09454 1272814644)

(06137 09540 1273613970)

(14355 14538 1502519150)

(11477 11610 1391314760) (1 1 1 1)

6 (08475 14009 1741017550)

(10563 11164 1723718260)

(07848 10350 1675119214)

(07092 16417 1786119843)

(04996 13061 1402814263)

7 (06408 06771 0743107685)

(11400 12236 1280515275)

(05379 07261 1007412589)

(06112 11761 1496918638)

(06579 07795 0914913757)

8 (05216 06006 0879217264)

(10414 11301 1636616826)

(08778 15035 1549516198)

(06862 08049 1730018657)

(04572 06153 1651119409)

9 (11202 12001 1371513804)

(09248 11256 1142512045)

(10368 12759 1448717079)

(07720 09169 1359914148)

(12160 15583 1657518508)

10 (04973 11939 1225016033)

(07335 08219 1343916985)

(12856 14828 1483115321)

(05005 13199 1487218169)

(06924 10332 1449417761)


Alter 6 7 8 9 10

1 (08231 14384 1498019344)

(07973 08449 1485117588)

(04518 10495 1383418698)

(10328 10413 1067112811)

(10170 10771 1145016334)

2 (05954 06653 0747615292)

(06231 06613 1217515019)

(13189 15298 1768618909)

(04508 13995 1791419844)

(06138 06702 0708014125)

3 (05483 15937 1783718983)

(04979 06576 0725310678)

(05462 09109 0964719929)

(05753 05893 1428216547)

(04660 09057 0974116068)

4 (07969 09776 1357219376)

(06649 12982 1830919369)

(08275 09925 1712118904)

(06747 13023 1348517974)

(05677 06411 0821910728)

5 (12083 12108 1849219144)

(07146 08002 0802911253)

(06222 11302 1852619686)

(06320 07937 1384415524)

(08933 09312 1100123003)

6 (1 1 1 1) (05999 12586 1717217181)

(11534 14559 1690519581)

(08006 10462 1353613637)

(09830 15819 1727819731)

7 (04849 08541 1371317175) (1 1 1 1) (05054 09498 11806

16663)(07472 09787 13915

15946)(05912 07424 08956

13431)

8 (10599 12561 1490715989)

(05189 08263 1135716201) (1 1 1 1) (04803 11356 15093

15413)(12220 13407 17600

18463)

9 (05794 14202 1474515811)

(04763 06373 1349118889)

(04891 11740 1454717554) (1 1 1 1) (05341 07245 09628

14774)

10 (08962 10925 1545719992)

(08964 15462 1581016611)

(09733 13922 1598916593)

(05296 15882 1688418302) (1 1 1 1)

14 Complexity


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 11975 1761921852)

(13959 18678 2560629058)

(08786 22426 2668147228)

(14288 24658 2817839657)

2 (13456 19678 2514228548) (1 1 1 1) (11568 14847 25474

30198)(10122 10903 28725

48158)(08339 08947 15098

26066)

3 (14519 15936 2003424383)

(18749 24067 2843532298) (1 1 1 1) (13095 18756 19465

34211)(08830 27474 28092

41440)

4 (09330 16784 1959125506)

(08341 11678 1246129649)

(09159 28247 2893638990) (1 1 1 1) (09411 22048 23311

23398)

5 (16968 23804 2604048683)

(09998 17316 1919225134)

(12597 13015 1319723604)

(15705 22564 2494625479) (1 1 1 1)

6 (19121 19896 2080927139)

(16729 24921 2578739713)

(15206 17650 2276843007)

(14500 19317 2093727454)

(09090 15973 1608518771)

7 (08938 14201 2197430621)

(10727 18788 2676644705)

(11865 12597 1538946016)

(15736 20361 2419824402)

(09572 10258 1333527689)

8 (09447 14976 2328628905)

(12111 17803 1877535145)

(10618 11577 2241228931)

(09720 19844 2659229915)

(09858 24791 2598127111)

9 (08528 11187 1690118615)

(19187 19237 2598841383)

(15716 27271 2865831107)

(13071 16180 1836026575)

(15352 16308 2337227600)

10 (21417 21589 2790444097)

(08631 15053 1877827503)

(10816 11919 1518729980)

(12190 16116 1813649229)

(12200 13066 1742218604)


Alter 6 7 8 9 10

1 (10856 14359 2278023293)

(08282 15578 2285725171)

(17336 18140 1817440347)

(12599 12930 1567629902)

(21814 24984 2852348855)

2 (19559 19668 2694528364)

(10309 11247 1217418890)

(20821 25939 2733849534)

(17569 18550 1960925630)

(09146 20622 2848638604)

3 (25282 26897 2956229657)

(14502 14629 2198328661)

(09020 14561 1911939980)

(10401 19743 2791342684)

(09066 21276 2269430096)

4 (13612 19131 2452837361)

(11284 13665 1868026496)

(12325 13524 2155327878)

(15721 21685 2676729556)

(10085 12046 1327917180)

5 (12671 15430 1612327801)

(14844 15762 1746528314)

(13677 16992 1901321088)

(14527 15013 1733229330)

(11802 12257 1554719670)

6 (1 1 1 1) (11297 22511 2389429781)

(09836 13593 1751326157)

(13540 14390 1914221576)

(10371 20850 2793944945)

7 (11553 14880 1550817356) (1 1 1 1) (11869 14414 18417

23879)(13343 13919 28183

40151)(17366 20025 23034

35067)

8 (11300 15650 1901020894)

(15903 23132 2419924578) (1 1 1 1) (13946 15279 16276

17335)(13428 20892 24250

35989)

9 (24919 27597 2961132421)

(16795 18655 2658726980)

(15653 20299 2673326790) (1 1 1 1) (10599 27767 29745

30679)

10 (12209 18226 2480726000)

(10587 16723 2024723236)

(10306 10814 2009028380)

(09603 09948 2556447606) (1 1 1 1)


Alter 1 2 3 4 5 6 7 8 9 101 1 15314 16206 14502 13533 14101 12253 11829 11195 124672 08732 1 09696 11815 09277 09341 10056 16240 13692 090033 13962 09456 1 13245 14052 13976 07491 11550 10641 100244 12965 12240 09899 1 10433 12840 14147 13558 12670 078295 10521 10520 16035 12950 1 15459 08802 13835 10907 138236 14157 14310 13540 14816 11058 1 13005 15629 11353 154467 07071 13030 08849 12772 09513 11062 1 10778 11772 090948 09719 13723 13468 12719 11681 13485 10335 1 11417 154179 12668 10891 13683 11145 15616 12089 10983 11979 1 0940810 11048 11561 14336 12495 12373 13923 13778 13899 13436 1

Complexity 15




Alter 1 2 3 4 5 6 7 8 9 101 1 19481 21786 26741 26765 17774 17807 25275 18617 321432 21596 1 20555 25039 15031 23644 13543 32199 20662 241493 18819 25825 1 22090 26034 27819 20116 21619 25455 204334 17712 16605 25614 1 18669 24042 17760 18956 23310 132615 30017 17821 16409 21853 1 18684 19738 17633 19750 149446 22110 27231 25680 20662 14638 1 21489 17024 17196 263857 19067 25757 23581 21032 16022 14725 1 17266 24189 244278 19157 21776 18503 21235 20933 16615 21507 1 15697 239049 13786 27131 25055 18854 20731 28643 22239 22266 1 2358710 29505 17620 17784 25948 15328 20168 17550 17606 23935 1





SW3

SW2SW1

OW3

OW1 OW2

Subs

tage

1-1

Subs

tage

1-2

Subs

tage

2-1

Subs

tage

2-2

TW

Stage 1 Stage 2

Stage 3

SW1∘2 OW1∘2

SW1∘2∘3 OW1∘2∘3


16 Complexity










































Complexity 17





















18 Complexity










Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36





Complexity 19






Table 20 Continued

Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36










Model1

Model41

Model42

Model43

Model44

Model45

Model46

Model51

Model52

Model53

Model54

Model55

Model56













20 Complexity


Model1

Model61

Model62

Model63

Model64

Model65

Model66

Model71

Model72

Model73

Model74

Model75

Model76














Model1

Model81

Model82

Model83

Model84

Model85

Model86

Model91

Model92

Model93

Model94

Model95

Model96













Complexity 21











22 Complexity



6 Conclusions




Data Availability






Acknowledgments


References







Complexity 23





























24 Complexity

SW

Substage

Substage

Substage

Substage

OW3

Substage

OWg

OWSu

bstage

TW

Stage 1

sub

jective w

eigh

t syn

thesis

Stage 2

objectiv

e weigh

t syn

thesis



ANP method

Delphi method

Entropy method

CRITIC method



OW1 OW2SW1

SW3

SW2

SWh









10 Complexity



SW1 sw1

1 sw12 sw1

N1113960 1113961T

SW2 sw2

1 sw22 sw2

N1113960 1113961T


SWh swh

1 swh2 swh

N1113960 1113961T

(33)


1 sw1∘22 sw1∘2


SW1∘2 τ1SW

1+ τ2SW

2 (34)



ξ1∘2 1113944l

i11113944

N

t1τ1sw

1t xit minus τ2sw

2t xit1113872 1113873

2 (35)


and SW2 as follows

min ξ1∘2

st τ1 ge 0 τ2 ge 0 τ1 + τ2 1(36)


τ1 1113936

li1 1113936

Nt1 xit1113872 1113873

2sw2

t sw1t + sw2

t( 1113857

1113936li1 1113936

Nt1 xit1113872 1113873

2sw1

t + sw2t( 1113857

τ2 1 minus τ1

(37)


SW1∘2∘∘h sw1∘2∘∘h

1 sw1∘2∘∘h2 sw1∘2∘∘h

N1113960 1113961T (38)




Overall goal

Index 1

Index 3

Index 2

Index 7

Index 9

Index 8

Index 4

Index 6

Index 5

Dimension 1


Control layer

Network layer


Complexity 11



OW1∘2∘∘g ow1∘2∘∘g

1 ow1∘2∘∘g2 ow1∘2∘∘g

N1113960 1113961T

(39)




(40)






⎧⎨

⎩ (41)



p(i m) 1113944N




Ω+i 1113944

l

m1mneip(i m)

Ωminusi 1113944

l

m1mneip(m i)

(43)






i (44)




12 Complexity


[1113957ϕ11ij ]10times10 1113957Φ21

[1113957ϕ21ij ]10times10 and

1113957Φ31 [1113957ϕ31


1113957Φ11











⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(45)


ij 1113957ϕ21ij 1113957ϕ31


1113957ρ112 1113957ϕ1112

1113957ϕ2112

1113957ϕ31121113882 1113883 OSEOS (10000 12222


12 OS in 1113957ρ112

1113957ϕ1112

1113957ϕ2112


12) [LRL(1113957ϕ1112)

URL(1113957ϕ1112)] [(10000 11481 15714 18889) (10000

12222 18571 23333)] while RBI(1113957ϕ2112)

[LRL(1113957ϕ2112)URL(1113957ϕ21

12)] [(10000 10000 10000 10000)(10000 11481 15714 18889)] and RBI(1113957ϕ31

12)

[LRL(1113957ϕ3112)URL(1113957ϕ31



1113957ϕ2112

1113957ϕ31121113882 1113883 can be obtained

as RBI(1113957ρ112) [(10000 10988 13809 15926) (1000011975 17619 21852)]














Complexity 13




Model 21 SW1+OW1

Model 22 SW1+OW2

Model 23 SW2 +OW2

Model 24 SW2 +OW3

Model 25 SW3 +OW1

Model 26 SW3 +OW3


Model 31 SW1 +OW1

Model 32 SW1 +OW2

Model 33 SW2 +OW2

Model 34 SW2 +OW3

Model 35 SW3 +OW1

Model 36 SW3 +OW3


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 10988 1380915926)

(11037 16779 1869419372)

(06468 17128 1854018657)

(09951 13021 1357217378)

2 (05336 05676 1039713301) (1 1 1 1) (04684 09725 11776

13317)(08246 10541 10761

16594)(05427 08139 09974

13416)

3 (11489 14540 1456115842)

(04953 05825 0856816916) (1 1 1 1) (08178 11612 12975

19428)(10195 10630 15027

19814)

4 (07188 10560 1695217386)

(09026 11191 1423414681)

(07571 09762 1027212090) (1 1 1 1) (05961 11055 11799

13777)

5 (05566 09454 1272814644)

(06137 09540 1273613970)

(14355 14538 1502519150)

(11477 11610 1391314760) (1 1 1 1)

6 (08475 14009 1741017550)

(10563 11164 1723718260)

(07848 10350 1675119214)

(07092 16417 1786119843)

(04996 13061 1402814263)

7 (06408 06771 0743107685)

(11400 12236 1280515275)

(05379 07261 1007412589)

(06112 11761 1496918638)

(06579 07795 0914913757)

8 (05216 06006 0879217264)

(10414 11301 1636616826)

(08778 15035 1549516198)

(06862 08049 1730018657)

(04572 06153 1651119409)

9 (11202 12001 1371513804)

(09248 11256 1142512045)

(10368 12759 1448717079)

(07720 09169 1359914148)

(12160 15583 1657518508)

10 (04973 11939 1225016033)

(07335 08219 1343916985)

(12856 14828 1483115321)

(05005 13199 1487218169)

(06924 10332 1449417761)


Alter 6 7 8 9 10

1 (08231 14384 1498019344)

(07973 08449 1485117588)

(04518 10495 1383418698)

(10328 10413 1067112811)

(10170 10771 1145016334)

2 (05954 06653 0747615292)

(06231 06613 1217515019)

(13189 15298 1768618909)

(04508 13995 1791419844)

(06138 06702 0708014125)

3 (05483 15937 1783718983)

(04979 06576 0725310678)

(05462 09109 0964719929)

(05753 05893 1428216547)

(04660 09057 0974116068)

4 (07969 09776 1357219376)

(06649 12982 1830919369)

(08275 09925 1712118904)

(06747 13023 1348517974)

(05677 06411 0821910728)

5 (12083 12108 1849219144)

(07146 08002 0802911253)

(06222 11302 1852619686)

(06320 07937 1384415524)

(08933 09312 1100123003)

6 (1 1 1 1) (05999 12586 1717217181)

(11534 14559 1690519581)

(08006 10462 1353613637)

(09830 15819 1727819731)

7 (04849 08541 1371317175) (1 1 1 1) (05054 09498 11806

16663)(07472 09787 13915

15946)(05912 07424 08956

13431)

8 (10599 12561 1490715989)

(05189 08263 1135716201) (1 1 1 1) (04803 11356 15093

15413)(12220 13407 17600

18463)

9 (05794 14202 1474515811)

(04763 06373 1349118889)

(04891 11740 1454717554) (1 1 1 1) (05341 07245 09628

14774)

10 (08962 10925 1545719992)

(08964 15462 1581016611)

(09733 13922 1598916593)

(05296 15882 1688418302) (1 1 1 1)

14 Complexity


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 11975 1761921852)

(13959 18678 2560629058)

(08786 22426 2668147228)

(14288 24658 2817839657)

2 (13456 19678 2514228548) (1 1 1 1) (11568 14847 25474

30198)(10122 10903 28725

48158)(08339 08947 15098

26066)

3 (14519 15936 2003424383)

(18749 24067 2843532298) (1 1 1 1) (13095 18756 19465

34211)(08830 27474 28092

41440)

4 (09330 16784 1959125506)

(08341 11678 1246129649)

(09159 28247 2893638990) (1 1 1 1) (09411 22048 23311

23398)

5 (16968 23804 2604048683)

(09998 17316 1919225134)

(12597 13015 1319723604)

(15705 22564 2494625479) (1 1 1 1)

6 (19121 19896 2080927139)

(16729 24921 2578739713)

(15206 17650 2276843007)

(14500 19317 2093727454)

(09090 15973 1608518771)

7 (08938 14201 2197430621)

(10727 18788 2676644705)

(11865 12597 1538946016)

(15736 20361 2419824402)

(09572 10258 1333527689)

8 (09447 14976 2328628905)

(12111 17803 1877535145)

(10618 11577 2241228931)

(09720 19844 2659229915)

(09858 24791 2598127111)

9 (08528 11187 1690118615)

(19187 19237 2598841383)

(15716 27271 2865831107)

(13071 16180 1836026575)

(15352 16308 2337227600)

10 (21417 21589 2790444097)

(08631 15053 1877827503)

(10816 11919 1518729980)

(12190 16116 1813649229)

(12200 13066 1742218604)


Alter 6 7 8 9 10

1 (10856 14359 2278023293)

(08282 15578 2285725171)

(17336 18140 1817440347)

(12599 12930 1567629902)

(21814 24984 2852348855)

2 (19559 19668 2694528364)

(10309 11247 1217418890)

(20821 25939 2733849534)

(17569 18550 1960925630)

(09146 20622 2848638604)

3 (25282 26897 2956229657)

(14502 14629 2198328661)

(09020 14561 1911939980)

(10401 19743 2791342684)

(09066 21276 2269430096)

4 (13612 19131 2452837361)

(11284 13665 1868026496)

(12325 13524 2155327878)

(15721 21685 2676729556)

(10085 12046 1327917180)

5 (12671 15430 1612327801)

(14844 15762 1746528314)

(13677 16992 1901321088)

(14527 15013 1733229330)

(11802 12257 1554719670)

6 (1 1 1 1) (11297 22511 2389429781)

(09836 13593 1751326157)

(13540 14390 1914221576)

(10371 20850 2793944945)

7 (11553 14880 1550817356) (1 1 1 1) (11869 14414 18417

23879)(13343 13919 28183

40151)(17366 20025 23034

35067)

8 (11300 15650 1901020894)

(15903 23132 2419924578) (1 1 1 1) (13946 15279 16276

17335)(13428 20892 24250

35989)

9 (24919 27597 2961132421)

(16795 18655 2658726980)

(15653 20299 2673326790) (1 1 1 1) (10599 27767 29745

30679)

10 (12209 18226 2480726000)

(10587 16723 2024723236)

(10306 10814 2009028380)

(09603 09948 2556447606) (1 1 1 1)


Alter 1 2 3 4 5 6 7 8 9 101 1 15314 16206 14502 13533 14101 12253 11829 11195 124672 08732 1 09696 11815 09277 09341 10056 16240 13692 090033 13962 09456 1 13245 14052 13976 07491 11550 10641 100244 12965 12240 09899 1 10433 12840 14147 13558 12670 078295 10521 10520 16035 12950 1 15459 08802 13835 10907 138236 14157 14310 13540 14816 11058 1 13005 15629 11353 154467 07071 13030 08849 12772 09513 11062 1 10778 11772 090948 09719 13723 13468 12719 11681 13485 10335 1 11417 154179 12668 10891 13683 11145 15616 12089 10983 11979 1 0940810 11048 11561 14336 12495 12373 13923 13778 13899 13436 1

Complexity 15




Alter 1 2 3 4 5 6 7 8 9 101 1 19481 21786 26741 26765 17774 17807 25275 18617 321432 21596 1 20555 25039 15031 23644 13543 32199 20662 241493 18819 25825 1 22090 26034 27819 20116 21619 25455 204334 17712 16605 25614 1 18669 24042 17760 18956 23310 132615 30017 17821 16409 21853 1 18684 19738 17633 19750 149446 22110 27231 25680 20662 14638 1 21489 17024 17196 263857 19067 25757 23581 21032 16022 14725 1 17266 24189 244278 19157 21776 18503 21235 20933 16615 21507 1 15697 239049 13786 27131 25055 18854 20731 28643 22239 22266 1 2358710 29505 17620 17784 25948 15328 20168 17550 17606 23935 1





SW3

SW2SW1

OW3

OW1 OW2

Subs

tage

1-1

Subs

tage

1-2

Subs

tage

2-1

Subs

tage

2-2

TW

Stage 1 Stage 2

Stage 3

SW1∘2 OW1∘2

SW1∘2∘3 OW1∘2∘3


16 Complexity










































Complexity 17





















18 Complexity










Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36





Complexity 19






Table 20 Continued

Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36










Model1

Model41

Model42

Model43

Model44

Model45

Model46

Model51

Model52

Model53

Model54

Model55

Model56













20 Complexity


Model1

Model61

Model62

Model63

Model64

Model65

Model66

Model71

Model72

Model73

Model74

Model75

Model76














Model1

Model81

Model82

Model83

Model84

Model85

Model86

Model91

Model92

Model93

Model94

Model95

Model96













Complexity 21











22 Complexity



6 Conclusions




Data Availability






Acknowledgments


References







Complexity 23





























24 Complexity



SW1 sw1

1 sw12 sw1

N1113960 1113961T

SW2 sw2

1 sw22 sw2

N1113960 1113961T


SWh swh

1 swh2 swh

N1113960 1113961T

(33)


1 sw1∘22 sw1∘2


SW1∘2 τ1SW

1+ τ2SW

2 (34)



ξ1∘2 1113944l

i11113944

N

t1τ1sw

1t xit minus τ2sw

2t xit1113872 1113873

2 (35)


and SW2 as follows

min ξ1∘2

st τ1 ge 0 τ2 ge 0 τ1 + τ2 1(36)


τ1 1113936

li1 1113936

Nt1 xit1113872 1113873

2sw2

t sw1t + sw2

t( 1113857

1113936li1 1113936

Nt1 xit1113872 1113873

2sw1

t + sw2t( 1113857

τ2 1 minus τ1

(37)


SW1∘2∘∘h sw1∘2∘∘h

1 sw1∘2∘∘h2 sw1∘2∘∘h

N1113960 1113961T (38)




Overall goal

Index 1

Index 3

Index 2

Index 7

Index 9

Index 8

Index 4

Index 6

Index 5

Dimension 1


Control layer

Network layer


Complexity 11



OW1∘2∘∘g ow1∘2∘∘g

1 ow1∘2∘∘g2 ow1∘2∘∘g

N1113960 1113961T

(39)




(40)






⎧⎨

⎩ (41)



p(i m) 1113944N




Ω+i 1113944

l

m1mneip(i m)

Ωminusi 1113944

l

m1mneip(m i)

(43)






i (44)




12 Complexity


[1113957ϕ11ij ]10times10 1113957Φ21

[1113957ϕ21ij ]10times10 and

1113957Φ31 [1113957ϕ31


1113957Φ11











⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(45)


ij 1113957ϕ21ij 1113957ϕ31


1113957ρ112 1113957ϕ1112

1113957ϕ2112

1113957ϕ31121113882 1113883 OSEOS (10000 12222


12 OS in 1113957ρ112

1113957ϕ1112

1113957ϕ2112


12) [LRL(1113957ϕ1112)

URL(1113957ϕ1112)] [(10000 11481 15714 18889) (10000

12222 18571 23333)] while RBI(1113957ϕ2112)

[LRL(1113957ϕ2112)URL(1113957ϕ21

12)] [(10000 10000 10000 10000)(10000 11481 15714 18889)] and RBI(1113957ϕ31

12)

[LRL(1113957ϕ3112)URL(1113957ϕ31



1113957ϕ2112

1113957ϕ31121113882 1113883 can be obtained

as RBI(1113957ρ112) [(10000 10988 13809 15926) (1000011975 17619 21852)]














Complexity 13




Model 21 SW1+OW1

Model 22 SW1+OW2

Model 23 SW2 +OW2

Model 24 SW2 +OW3

Model 25 SW3 +OW1

Model 26 SW3 +OW3


Model 31 SW1 +OW1

Model 32 SW1 +OW2

Model 33 SW2 +OW2

Model 34 SW2 +OW3

Model 35 SW3 +OW1

Model 36 SW3 +OW3


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 10988 1380915926)

(11037 16779 1869419372)

(06468 17128 1854018657)

(09951 13021 1357217378)

2 (05336 05676 1039713301) (1 1 1 1) (04684 09725 11776

13317)(08246 10541 10761

16594)(05427 08139 09974

13416)

3 (11489 14540 1456115842)

(04953 05825 0856816916) (1 1 1 1) (08178 11612 12975

19428)(10195 10630 15027

19814)

4 (07188 10560 1695217386)

(09026 11191 1423414681)

(07571 09762 1027212090) (1 1 1 1) (05961 11055 11799

13777)

5 (05566 09454 1272814644)

(06137 09540 1273613970)

(14355 14538 1502519150)

(11477 11610 1391314760) (1 1 1 1)

6 (08475 14009 1741017550)

(10563 11164 1723718260)

(07848 10350 1675119214)

(07092 16417 1786119843)

(04996 13061 1402814263)

7 (06408 06771 0743107685)

(11400 12236 1280515275)

(05379 07261 1007412589)

(06112 11761 1496918638)

(06579 07795 0914913757)

8 (05216 06006 0879217264)

(10414 11301 1636616826)

(08778 15035 1549516198)

(06862 08049 1730018657)

(04572 06153 1651119409)

9 (11202 12001 1371513804)

(09248 11256 1142512045)

(10368 12759 1448717079)

(07720 09169 1359914148)

(12160 15583 1657518508)

10 (04973 11939 1225016033)

(07335 08219 1343916985)

(12856 14828 1483115321)

(05005 13199 1487218169)

(06924 10332 1449417761)


Alter 6 7 8 9 10

1 (08231 14384 1498019344)

(07973 08449 1485117588)

(04518 10495 1383418698)

(10328 10413 1067112811)

(10170 10771 1145016334)

2 (05954 06653 0747615292)

(06231 06613 1217515019)

(13189 15298 1768618909)

(04508 13995 1791419844)

(06138 06702 0708014125)

3 (05483 15937 1783718983)

(04979 06576 0725310678)

(05462 09109 0964719929)

(05753 05893 1428216547)

(04660 09057 0974116068)

4 (07969 09776 1357219376)

(06649 12982 1830919369)

(08275 09925 1712118904)

(06747 13023 1348517974)

(05677 06411 0821910728)

5 (12083 12108 1849219144)

(07146 08002 0802911253)

(06222 11302 1852619686)

(06320 07937 1384415524)

(08933 09312 1100123003)

6 (1 1 1 1) (05999 12586 1717217181)

(11534 14559 1690519581)

(08006 10462 1353613637)

(09830 15819 1727819731)

7 (04849 08541 1371317175) (1 1 1 1) (05054 09498 11806

16663)(07472 09787 13915

15946)(05912 07424 08956

13431)

8 (10599 12561 1490715989)

(05189 08263 1135716201) (1 1 1 1) (04803 11356 15093

15413)(12220 13407 17600

18463)

9 (05794 14202 1474515811)

(04763 06373 1349118889)

(04891 11740 1454717554) (1 1 1 1) (05341 07245 09628

14774)

10 (08962 10925 1545719992)

(08964 15462 1581016611)

(09733 13922 1598916593)

(05296 15882 1688418302) (1 1 1 1)

14 Complexity


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 11975 1761921852)

(13959 18678 2560629058)

(08786 22426 2668147228)

(14288 24658 2817839657)

2 (13456 19678 2514228548) (1 1 1 1) (11568 14847 25474

30198)(10122 10903 28725

48158)(08339 08947 15098

26066)

3 (14519 15936 2003424383)

(18749 24067 2843532298) (1 1 1 1) (13095 18756 19465

34211)(08830 27474 28092

41440)

4 (09330 16784 1959125506)

(08341 11678 1246129649)

(09159 28247 2893638990) (1 1 1 1) (09411 22048 23311

23398)

5 (16968 23804 2604048683)

(09998 17316 1919225134)

(12597 13015 1319723604)

(15705 22564 2494625479) (1 1 1 1)

6 (19121 19896 2080927139)

(16729 24921 2578739713)

(15206 17650 2276843007)

(14500 19317 2093727454)

(09090 15973 1608518771)

7 (08938 14201 2197430621)

(10727 18788 2676644705)

(11865 12597 1538946016)

(15736 20361 2419824402)

(09572 10258 1333527689)

8 (09447 14976 2328628905)

(12111 17803 1877535145)

(10618 11577 2241228931)

(09720 19844 2659229915)

(09858 24791 2598127111)

9 (08528 11187 1690118615)

(19187 19237 2598841383)

(15716 27271 2865831107)

(13071 16180 1836026575)

(15352 16308 2337227600)

10 (21417 21589 2790444097)

(08631 15053 1877827503)

(10816 11919 1518729980)

(12190 16116 1813649229)

(12200 13066 1742218604)


Alter 6 7 8 9 10

1 (10856 14359 2278023293)

(08282 15578 2285725171)

(17336 18140 1817440347)

(12599 12930 1567629902)

(21814 24984 2852348855)

2 (19559 19668 2694528364)

(10309 11247 1217418890)

(20821 25939 2733849534)

(17569 18550 1960925630)

(09146 20622 2848638604)

3 (25282 26897 2956229657)

(14502 14629 2198328661)

(09020 14561 1911939980)

(10401 19743 2791342684)

(09066 21276 2269430096)

4 (13612 19131 2452837361)

(11284 13665 1868026496)

(12325 13524 2155327878)

(15721 21685 2676729556)

(10085 12046 1327917180)

5 (12671 15430 1612327801)

(14844 15762 1746528314)

(13677 16992 1901321088)

(14527 15013 1733229330)

(11802 12257 1554719670)

6 (1 1 1 1) (11297 22511 2389429781)

(09836 13593 1751326157)

(13540 14390 1914221576)

(10371 20850 2793944945)

7 (11553 14880 1550817356) (1 1 1 1) (11869 14414 18417

23879)(13343 13919 28183

40151)(17366 20025 23034

35067)

8 (11300 15650 1901020894)

(15903 23132 2419924578) (1 1 1 1) (13946 15279 16276

17335)(13428 20892 24250

35989)

9 (24919 27597 2961132421)

(16795 18655 2658726980)

(15653 20299 2673326790) (1 1 1 1) (10599 27767 29745

30679)

10 (12209 18226 2480726000)

(10587 16723 2024723236)

(10306 10814 2009028380)

(09603 09948 2556447606) (1 1 1 1)


Alter 1 2 3 4 5 6 7 8 9 101 1 15314 16206 14502 13533 14101 12253 11829 11195 124672 08732 1 09696 11815 09277 09341 10056 16240 13692 090033 13962 09456 1 13245 14052 13976 07491 11550 10641 100244 12965 12240 09899 1 10433 12840 14147 13558 12670 078295 10521 10520 16035 12950 1 15459 08802 13835 10907 138236 14157 14310 13540 14816 11058 1 13005 15629 11353 154467 07071 13030 08849 12772 09513 11062 1 10778 11772 090948 09719 13723 13468 12719 11681 13485 10335 1 11417 154179 12668 10891 13683 11145 15616 12089 10983 11979 1 0940810 11048 11561 14336 12495 12373 13923 13778 13899 13436 1

Complexity 15




Alter 1 2 3 4 5 6 7 8 9 101 1 19481 21786 26741 26765 17774 17807 25275 18617 321432 21596 1 20555 25039 15031 23644 13543 32199 20662 241493 18819 25825 1 22090 26034 27819 20116 21619 25455 204334 17712 16605 25614 1 18669 24042 17760 18956 23310 132615 30017 17821 16409 21853 1 18684 19738 17633 19750 149446 22110 27231 25680 20662 14638 1 21489 17024 17196 263857 19067 25757 23581 21032 16022 14725 1 17266 24189 244278 19157 21776 18503 21235 20933 16615 21507 1 15697 239049 13786 27131 25055 18854 20731 28643 22239 22266 1 2358710 29505 17620 17784 25948 15328 20168 17550 17606 23935 1





SW3

SW2SW1

OW3

OW1 OW2

Subs

tage

1-1

Subs

tage

1-2

Subs

tage

2-1

Subs

tage

2-2

TW

Stage 1 Stage 2

Stage 3

SW1∘2 OW1∘2

SW1∘2∘3 OW1∘2∘3


16 Complexity










































Complexity 17





















18 Complexity










Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36





Complexity 19






Table 20 Continued

Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36










Model1

Model41

Model42

Model43

Model44

Model45

Model46

Model51

Model52

Model53

Model54

Model55

Model56













20 Complexity


Model1

Model61

Model62

Model63

Model64

Model65

Model66

Model71

Model72

Model73

Model74

Model75

Model76














Model1

Model81

Model82

Model83

Model84

Model85

Model86

Model91

Model92

Model93

Model94

Model95

Model96













Complexity 21











22 Complexity



6 Conclusions




Data Availability






Acknowledgments


References







Complexity 23





























24 Complexity



OW1∘2∘∘g ow1∘2∘∘g

1 ow1∘2∘∘g2 ow1∘2∘∘g

N1113960 1113961T

(39)




(40)






⎧⎨

⎩ (41)



p(i m) 1113944N




Ω+i 1113944

l

m1mneip(i m)

Ωminusi 1113944

l

m1mneip(m i)

(43)






i (44)




12 Complexity


[1113957ϕ11ij ]10times10 1113957Φ21

[1113957ϕ21ij ]10times10 and

1113957Φ31 [1113957ϕ31


1113957Φ11











⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(45)


ij 1113957ϕ21ij 1113957ϕ31


1113957ρ112 1113957ϕ1112

1113957ϕ2112

1113957ϕ31121113882 1113883 OSEOS (10000 12222


12 OS in 1113957ρ112

1113957ϕ1112

1113957ϕ2112


12) [LRL(1113957ϕ1112)

URL(1113957ϕ1112)] [(10000 11481 15714 18889) (10000

12222 18571 23333)] while RBI(1113957ϕ2112)

[LRL(1113957ϕ2112)URL(1113957ϕ21

12)] [(10000 10000 10000 10000)(10000 11481 15714 18889)] and RBI(1113957ϕ31

12)

[LRL(1113957ϕ3112)URL(1113957ϕ31



1113957ϕ2112

1113957ϕ31121113882 1113883 can be obtained

as RBI(1113957ρ112) [(10000 10988 13809 15926) (1000011975 17619 21852)]














Complexity 13




Model 21 SW1+OW1

Model 22 SW1+OW2

Model 23 SW2 +OW2

Model 24 SW2 +OW3

Model 25 SW3 +OW1

Model 26 SW3 +OW3


Model 31 SW1 +OW1

Model 32 SW1 +OW2

Model 33 SW2 +OW2

Model 34 SW2 +OW3

Model 35 SW3 +OW1

Model 36 SW3 +OW3


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 10988 1380915926)

(11037 16779 1869419372)

(06468 17128 1854018657)

(09951 13021 1357217378)

2 (05336 05676 1039713301) (1 1 1 1) (04684 09725 11776

13317)(08246 10541 10761

16594)(05427 08139 09974

13416)

3 (11489 14540 1456115842)

(04953 05825 0856816916) (1 1 1 1) (08178 11612 12975

19428)(10195 10630 15027

19814)

4 (07188 10560 1695217386)

(09026 11191 1423414681)

(07571 09762 1027212090) (1 1 1 1) (05961 11055 11799

13777)

5 (05566 09454 1272814644)

(06137 09540 1273613970)

(14355 14538 1502519150)

(11477 11610 1391314760) (1 1 1 1)

6 (08475 14009 1741017550)

(10563 11164 1723718260)

(07848 10350 1675119214)

(07092 16417 1786119843)

(04996 13061 1402814263)

7 (06408 06771 0743107685)

(11400 12236 1280515275)

(05379 07261 1007412589)

(06112 11761 1496918638)

(06579 07795 0914913757)

8 (05216 06006 0879217264)

(10414 11301 1636616826)

(08778 15035 1549516198)

(06862 08049 1730018657)

(04572 06153 1651119409)

9 (11202 12001 1371513804)

(09248 11256 1142512045)

(10368 12759 1448717079)

(07720 09169 1359914148)

(12160 15583 1657518508)

10 (04973 11939 1225016033)

(07335 08219 1343916985)

(12856 14828 1483115321)

(05005 13199 1487218169)

(06924 10332 1449417761)


Alter 6 7 8 9 10

1 (08231 14384 1498019344)

(07973 08449 1485117588)

(04518 10495 1383418698)

(10328 10413 1067112811)

(10170 10771 1145016334)

2 (05954 06653 0747615292)

(06231 06613 1217515019)

(13189 15298 1768618909)

(04508 13995 1791419844)

(06138 06702 0708014125)

3 (05483 15937 1783718983)

(04979 06576 0725310678)

(05462 09109 0964719929)

(05753 05893 1428216547)

(04660 09057 0974116068)

4 (07969 09776 1357219376)

(06649 12982 1830919369)

(08275 09925 1712118904)

(06747 13023 1348517974)

(05677 06411 0821910728)

5 (12083 12108 1849219144)

(07146 08002 0802911253)

(06222 11302 1852619686)

(06320 07937 1384415524)

(08933 09312 1100123003)

6 (1 1 1 1) (05999 12586 1717217181)

(11534 14559 1690519581)

(08006 10462 1353613637)

(09830 15819 1727819731)

7 (04849 08541 1371317175) (1 1 1 1) (05054 09498 11806

16663)(07472 09787 13915

15946)(05912 07424 08956

13431)

8 (10599 12561 1490715989)

(05189 08263 1135716201) (1 1 1 1) (04803 11356 15093

15413)(12220 13407 17600

18463)

9 (05794 14202 1474515811)

(04763 06373 1349118889)

(04891 11740 1454717554) (1 1 1 1) (05341 07245 09628

14774)

10 (08962 10925 1545719992)

(08964 15462 1581016611)

(09733 13922 1598916593)

(05296 15882 1688418302) (1 1 1 1)

14 Complexity


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 11975 1761921852)

(13959 18678 2560629058)

(08786 22426 2668147228)

(14288 24658 2817839657)

2 (13456 19678 2514228548) (1 1 1 1) (11568 14847 25474

30198)(10122 10903 28725

48158)(08339 08947 15098

26066)

3 (14519 15936 2003424383)

(18749 24067 2843532298) (1 1 1 1) (13095 18756 19465

34211)(08830 27474 28092

41440)

4 (09330 16784 1959125506)

(08341 11678 1246129649)

(09159 28247 2893638990) (1 1 1 1) (09411 22048 23311

23398)

5 (16968 23804 2604048683)

(09998 17316 1919225134)

(12597 13015 1319723604)

(15705 22564 2494625479) (1 1 1 1)

6 (19121 19896 2080927139)

(16729 24921 2578739713)

(15206 17650 2276843007)

(14500 19317 2093727454)

(09090 15973 1608518771)

7 (08938 14201 2197430621)

(10727 18788 2676644705)

(11865 12597 1538946016)

(15736 20361 2419824402)

(09572 10258 1333527689)

8 (09447 14976 2328628905)

(12111 17803 1877535145)

(10618 11577 2241228931)

(09720 19844 2659229915)

(09858 24791 2598127111)

9 (08528 11187 1690118615)

(19187 19237 2598841383)

(15716 27271 2865831107)

(13071 16180 1836026575)

(15352 16308 2337227600)

10 (21417 21589 2790444097)

(08631 15053 1877827503)

(10816 11919 1518729980)

(12190 16116 1813649229)

(12200 13066 1742218604)


Alter 6 7 8 9 10

1 (10856 14359 2278023293)

(08282 15578 2285725171)

(17336 18140 1817440347)

(12599 12930 1567629902)

(21814 24984 2852348855)

2 (19559 19668 2694528364)

(10309 11247 1217418890)

(20821 25939 2733849534)

(17569 18550 1960925630)

(09146 20622 2848638604)

3 (25282 26897 2956229657)

(14502 14629 2198328661)

(09020 14561 1911939980)

(10401 19743 2791342684)

(09066 21276 2269430096)

4 (13612 19131 2452837361)

(11284 13665 1868026496)

(12325 13524 2155327878)

(15721 21685 2676729556)

(10085 12046 1327917180)

5 (12671 15430 1612327801)

(14844 15762 1746528314)

(13677 16992 1901321088)

(14527 15013 1733229330)

(11802 12257 1554719670)

6 (1 1 1 1) (11297 22511 2389429781)

(09836 13593 1751326157)

(13540 14390 1914221576)

(10371 20850 2793944945)

7 (11553 14880 1550817356) (1 1 1 1) (11869 14414 18417

23879)(13343 13919 28183

40151)(17366 20025 23034

35067)

8 (11300 15650 1901020894)

(15903 23132 2419924578) (1 1 1 1) (13946 15279 16276

17335)(13428 20892 24250

35989)

9 (24919 27597 2961132421)

(16795 18655 2658726980)

(15653 20299 2673326790) (1 1 1 1) (10599 27767 29745

30679)

10 (12209 18226 2480726000)

(10587 16723 2024723236)

(10306 10814 2009028380)

(09603 09948 2556447606) (1 1 1 1)


Alter 1 2 3 4 5 6 7 8 9 101 1 15314 16206 14502 13533 14101 12253 11829 11195 124672 08732 1 09696 11815 09277 09341 10056 16240 13692 090033 13962 09456 1 13245 14052 13976 07491 11550 10641 100244 12965 12240 09899 1 10433 12840 14147 13558 12670 078295 10521 10520 16035 12950 1 15459 08802 13835 10907 138236 14157 14310 13540 14816 11058 1 13005 15629 11353 154467 07071 13030 08849 12772 09513 11062 1 10778 11772 090948 09719 13723 13468 12719 11681 13485 10335 1 11417 154179 12668 10891 13683 11145 15616 12089 10983 11979 1 0940810 11048 11561 14336 12495 12373 13923 13778 13899 13436 1

Complexity 15




Alter 1 2 3 4 5 6 7 8 9 101 1 19481 21786 26741 26765 17774 17807 25275 18617 321432 21596 1 20555 25039 15031 23644 13543 32199 20662 241493 18819 25825 1 22090 26034 27819 20116 21619 25455 204334 17712 16605 25614 1 18669 24042 17760 18956 23310 132615 30017 17821 16409 21853 1 18684 19738 17633 19750 149446 22110 27231 25680 20662 14638 1 21489 17024 17196 263857 19067 25757 23581 21032 16022 14725 1 17266 24189 244278 19157 21776 18503 21235 20933 16615 21507 1 15697 239049 13786 27131 25055 18854 20731 28643 22239 22266 1 2358710 29505 17620 17784 25948 15328 20168 17550 17606 23935 1





SW3

SW2SW1

OW3

OW1 OW2

Subs

tage

1-1

Subs

tage

1-2

Subs

tage

2-1

Subs

tage

2-2

TW

Stage 1 Stage 2

Stage 3

SW1∘2 OW1∘2

SW1∘2∘3 OW1∘2∘3


16 Complexity










































Complexity 17





















18 Complexity










Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36





Complexity 19






Table 20 Continued

Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36










Model1

Model41

Model42

Model43

Model44

Model45

Model46

Model51

Model52

Model53

Model54

Model55

Model56













20 Complexity


Model1

Model61

Model62

Model63

Model64

Model65

Model66

Model71

Model72

Model73

Model74

Model75

Model76














Model1

Model81

Model82

Model83

Model84

Model85

Model86

Model91

Model92

Model93

Model94

Model95

Model96













Complexity 21











22 Complexity



6 Conclusions




Data Availability






Acknowledgments


References







Complexity 23





























24 Complexity


[1113957ϕ11ij ]10times10 1113957Φ21

[1113957ϕ21ij ]10times10 and

1113957Φ31 [1113957ϕ31


1113957Φ11











⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(45)


ij 1113957ϕ21ij 1113957ϕ31


1113957ρ112 1113957ϕ1112

1113957ϕ2112

1113957ϕ31121113882 1113883 OSEOS (10000 12222


12 OS in 1113957ρ112

1113957ϕ1112

1113957ϕ2112


12) [LRL(1113957ϕ1112)

URL(1113957ϕ1112)] [(10000 11481 15714 18889) (10000

12222 18571 23333)] while RBI(1113957ϕ2112)

[LRL(1113957ϕ2112)URL(1113957ϕ21

12)] [(10000 10000 10000 10000)(10000 11481 15714 18889)] and RBI(1113957ϕ31

12)

[LRL(1113957ϕ3112)URL(1113957ϕ31



1113957ϕ2112

1113957ϕ31121113882 1113883 can be obtained

as RBI(1113957ρ112) [(10000 10988 13809 15926) (1000011975 17619 21852)]














Complexity 13




Model 21 SW1+OW1

Model 22 SW1+OW2

Model 23 SW2 +OW2

Model 24 SW2 +OW3

Model 25 SW3 +OW1

Model 26 SW3 +OW3


Model 31 SW1 +OW1

Model 32 SW1 +OW2

Model 33 SW2 +OW2

Model 34 SW2 +OW3

Model 35 SW3 +OW1

Model 36 SW3 +OW3


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 10988 1380915926)

(11037 16779 1869419372)

(06468 17128 1854018657)

(09951 13021 1357217378)

2 (05336 05676 1039713301) (1 1 1 1) (04684 09725 11776

13317)(08246 10541 10761

16594)(05427 08139 09974

13416)

3 (11489 14540 1456115842)

(04953 05825 0856816916) (1 1 1 1) (08178 11612 12975

19428)(10195 10630 15027

19814)

4 (07188 10560 1695217386)

(09026 11191 1423414681)

(07571 09762 1027212090) (1 1 1 1) (05961 11055 11799

13777)

5 (05566 09454 1272814644)

(06137 09540 1273613970)

(14355 14538 1502519150)

(11477 11610 1391314760) (1 1 1 1)

6 (08475 14009 1741017550)

(10563 11164 1723718260)

(07848 10350 1675119214)

(07092 16417 1786119843)

(04996 13061 1402814263)

7 (06408 06771 0743107685)

(11400 12236 1280515275)

(05379 07261 1007412589)

(06112 11761 1496918638)

(06579 07795 0914913757)

8 (05216 06006 0879217264)

(10414 11301 1636616826)

(08778 15035 1549516198)

(06862 08049 1730018657)

(04572 06153 1651119409)

9 (11202 12001 1371513804)

(09248 11256 1142512045)

(10368 12759 1448717079)

(07720 09169 1359914148)

(12160 15583 1657518508)

10 (04973 11939 1225016033)

(07335 08219 1343916985)

(12856 14828 1483115321)

(05005 13199 1487218169)

(06924 10332 1449417761)


Alter 6 7 8 9 10

1 (08231 14384 1498019344)

(07973 08449 1485117588)

(04518 10495 1383418698)

(10328 10413 1067112811)

(10170 10771 1145016334)

2 (05954 06653 0747615292)

(06231 06613 1217515019)

(13189 15298 1768618909)

(04508 13995 1791419844)

(06138 06702 0708014125)

3 (05483 15937 1783718983)

(04979 06576 0725310678)

(05462 09109 0964719929)

(05753 05893 1428216547)

(04660 09057 0974116068)

4 (07969 09776 1357219376)

(06649 12982 1830919369)

(08275 09925 1712118904)

(06747 13023 1348517974)

(05677 06411 0821910728)

5 (12083 12108 1849219144)

(07146 08002 0802911253)

(06222 11302 1852619686)

(06320 07937 1384415524)

(08933 09312 1100123003)

6 (1 1 1 1) (05999 12586 1717217181)

(11534 14559 1690519581)

(08006 10462 1353613637)

(09830 15819 1727819731)

7 (04849 08541 1371317175) (1 1 1 1) (05054 09498 11806

16663)(07472 09787 13915

15946)(05912 07424 08956

13431)

8 (10599 12561 1490715989)

(05189 08263 1135716201) (1 1 1 1) (04803 11356 15093

15413)(12220 13407 17600

18463)

9 (05794 14202 1474515811)

(04763 06373 1349118889)

(04891 11740 1454717554) (1 1 1 1) (05341 07245 09628

14774)

10 (08962 10925 1545719992)

(08964 15462 1581016611)

(09733 13922 1598916593)

(05296 15882 1688418302) (1 1 1 1)

14 Complexity


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 11975 1761921852)

(13959 18678 2560629058)

(08786 22426 2668147228)

(14288 24658 2817839657)

2 (13456 19678 2514228548) (1 1 1 1) (11568 14847 25474

30198)(10122 10903 28725

48158)(08339 08947 15098

26066)

3 (14519 15936 2003424383)

(18749 24067 2843532298) (1 1 1 1) (13095 18756 19465

34211)(08830 27474 28092

41440)

4 (09330 16784 1959125506)

(08341 11678 1246129649)

(09159 28247 2893638990) (1 1 1 1) (09411 22048 23311

23398)

5 (16968 23804 2604048683)

(09998 17316 1919225134)

(12597 13015 1319723604)

(15705 22564 2494625479) (1 1 1 1)

6 (19121 19896 2080927139)

(16729 24921 2578739713)

(15206 17650 2276843007)

(14500 19317 2093727454)

(09090 15973 1608518771)

7 (08938 14201 2197430621)

(10727 18788 2676644705)

(11865 12597 1538946016)

(15736 20361 2419824402)

(09572 10258 1333527689)

8 (09447 14976 2328628905)

(12111 17803 1877535145)

(10618 11577 2241228931)

(09720 19844 2659229915)

(09858 24791 2598127111)

9 (08528 11187 1690118615)

(19187 19237 2598841383)

(15716 27271 2865831107)

(13071 16180 1836026575)

(15352 16308 2337227600)

10 (21417 21589 2790444097)

(08631 15053 1877827503)

(10816 11919 1518729980)

(12190 16116 1813649229)

(12200 13066 1742218604)


Alter 6 7 8 9 10

1 (10856 14359 2278023293)

(08282 15578 2285725171)

(17336 18140 1817440347)

(12599 12930 1567629902)

(21814 24984 2852348855)

2 (19559 19668 2694528364)

(10309 11247 1217418890)

(20821 25939 2733849534)

(17569 18550 1960925630)

(09146 20622 2848638604)

3 (25282 26897 2956229657)

(14502 14629 2198328661)

(09020 14561 1911939980)

(10401 19743 2791342684)

(09066 21276 2269430096)

4 (13612 19131 2452837361)

(11284 13665 1868026496)

(12325 13524 2155327878)

(15721 21685 2676729556)

(10085 12046 1327917180)

5 (12671 15430 1612327801)

(14844 15762 1746528314)

(13677 16992 1901321088)

(14527 15013 1733229330)

(11802 12257 1554719670)

6 (1 1 1 1) (11297 22511 2389429781)

(09836 13593 1751326157)

(13540 14390 1914221576)

(10371 20850 2793944945)

7 (11553 14880 1550817356) (1 1 1 1) (11869 14414 18417

23879)(13343 13919 28183

40151)(17366 20025 23034

35067)

8 (11300 15650 1901020894)

(15903 23132 2419924578) (1 1 1 1) (13946 15279 16276

17335)(13428 20892 24250

35989)

9 (24919 27597 2961132421)

(16795 18655 2658726980)

(15653 20299 2673326790) (1 1 1 1) (10599 27767 29745

30679)

10 (12209 18226 2480726000)

(10587 16723 2024723236)

(10306 10814 2009028380)

(09603 09948 2556447606) (1 1 1 1)


Alter 1 2 3 4 5 6 7 8 9 101 1 15314 16206 14502 13533 14101 12253 11829 11195 124672 08732 1 09696 11815 09277 09341 10056 16240 13692 090033 13962 09456 1 13245 14052 13976 07491 11550 10641 100244 12965 12240 09899 1 10433 12840 14147 13558 12670 078295 10521 10520 16035 12950 1 15459 08802 13835 10907 138236 14157 14310 13540 14816 11058 1 13005 15629 11353 154467 07071 13030 08849 12772 09513 11062 1 10778 11772 090948 09719 13723 13468 12719 11681 13485 10335 1 11417 154179 12668 10891 13683 11145 15616 12089 10983 11979 1 0940810 11048 11561 14336 12495 12373 13923 13778 13899 13436 1

Complexity 15




Alter 1 2 3 4 5 6 7 8 9 101 1 19481 21786 26741 26765 17774 17807 25275 18617 321432 21596 1 20555 25039 15031 23644 13543 32199 20662 241493 18819 25825 1 22090 26034 27819 20116 21619 25455 204334 17712 16605 25614 1 18669 24042 17760 18956 23310 132615 30017 17821 16409 21853 1 18684 19738 17633 19750 149446 22110 27231 25680 20662 14638 1 21489 17024 17196 263857 19067 25757 23581 21032 16022 14725 1 17266 24189 244278 19157 21776 18503 21235 20933 16615 21507 1 15697 239049 13786 27131 25055 18854 20731 28643 22239 22266 1 2358710 29505 17620 17784 25948 15328 20168 17550 17606 23935 1





SW3

SW2SW1

OW3

OW1 OW2

Subs

tage

1-1

Subs

tage

1-2

Subs

tage

2-1

Subs

tage

2-2

TW

Stage 1 Stage 2

Stage 3

SW1∘2 OW1∘2

SW1∘2∘3 OW1∘2∘3


16 Complexity










































Complexity 17





















18 Complexity










Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36





Complexity 19






Table 20 Continued

Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36










Model1

Model41

Model42

Model43

Model44

Model45

Model46

Model51

Model52

Model53

Model54

Model55

Model56













20 Complexity


Model1

Model61

Model62

Model63

Model64

Model65

Model66

Model71

Model72

Model73

Model74

Model75

Model76














Model1

Model81

Model82

Model83

Model84

Model85

Model86

Model91

Model92

Model93

Model94

Model95

Model96













Complexity 21











22 Complexity



6 Conclusions




Data Availability






Acknowledgments


References







Complexity 23





























24 Complexity




Model 21 SW1+OW1

Model 22 SW1+OW2

Model 23 SW2 +OW2

Model 24 SW2 +OW3

Model 25 SW3 +OW1

Model 26 SW3 +OW3


Model 31 SW1 +OW1

Model 32 SW1 +OW2

Model 33 SW2 +OW2

Model 34 SW2 +OW3

Model 35 SW3 +OW1

Model 36 SW3 +OW3


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 10988 1380915926)

(11037 16779 1869419372)

(06468 17128 1854018657)

(09951 13021 1357217378)

2 (05336 05676 1039713301) (1 1 1 1) (04684 09725 11776

13317)(08246 10541 10761

16594)(05427 08139 09974

13416)

3 (11489 14540 1456115842)

(04953 05825 0856816916) (1 1 1 1) (08178 11612 12975

19428)(10195 10630 15027

19814)

4 (07188 10560 1695217386)

(09026 11191 1423414681)

(07571 09762 1027212090) (1 1 1 1) (05961 11055 11799

13777)

5 (05566 09454 1272814644)

(06137 09540 1273613970)

(14355 14538 1502519150)

(11477 11610 1391314760) (1 1 1 1)

6 (08475 14009 1741017550)

(10563 11164 1723718260)

(07848 10350 1675119214)

(07092 16417 1786119843)

(04996 13061 1402814263)

7 (06408 06771 0743107685)

(11400 12236 1280515275)

(05379 07261 1007412589)

(06112 11761 1496918638)

(06579 07795 0914913757)

8 (05216 06006 0879217264)

(10414 11301 1636616826)

(08778 15035 1549516198)

(06862 08049 1730018657)

(04572 06153 1651119409)

9 (11202 12001 1371513804)

(09248 11256 1142512045)

(10368 12759 1448717079)

(07720 09169 1359914148)

(12160 15583 1657518508)

10 (04973 11939 1225016033)

(07335 08219 1343916985)

(12856 14828 1483115321)

(05005 13199 1487218169)

(06924 10332 1449417761)


Alter 6 7 8 9 10

1 (08231 14384 1498019344)

(07973 08449 1485117588)

(04518 10495 1383418698)

(10328 10413 1067112811)

(10170 10771 1145016334)

2 (05954 06653 0747615292)

(06231 06613 1217515019)

(13189 15298 1768618909)

(04508 13995 1791419844)

(06138 06702 0708014125)

3 (05483 15937 1783718983)

(04979 06576 0725310678)

(05462 09109 0964719929)

(05753 05893 1428216547)

(04660 09057 0974116068)

4 (07969 09776 1357219376)

(06649 12982 1830919369)

(08275 09925 1712118904)

(06747 13023 1348517974)

(05677 06411 0821910728)

5 (12083 12108 1849219144)

(07146 08002 0802911253)

(06222 11302 1852619686)

(06320 07937 1384415524)

(08933 09312 1100123003)

6 (1 1 1 1) (05999 12586 1717217181)

(11534 14559 1690519581)

(08006 10462 1353613637)

(09830 15819 1727819731)

7 (04849 08541 1371317175) (1 1 1 1) (05054 09498 11806

16663)(07472 09787 13915

15946)(05912 07424 08956

13431)

8 (10599 12561 1490715989)

(05189 08263 1135716201) (1 1 1 1) (04803 11356 15093

15413)(12220 13407 17600

18463)

9 (05794 14202 1474515811)

(04763 06373 1349118889)

(04891 11740 1454717554) (1 1 1 1) (05341 07245 09628

14774)

10 (08962 10925 1545719992)

(08964 15462 1581016611)

(09733 13922 1598916593)

(05296 15882 1688418302) (1 1 1 1)

14 Complexity


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 11975 1761921852)

(13959 18678 2560629058)

(08786 22426 2668147228)

(14288 24658 2817839657)

2 (13456 19678 2514228548) (1 1 1 1) (11568 14847 25474

30198)(10122 10903 28725

48158)(08339 08947 15098

26066)

3 (14519 15936 2003424383)

(18749 24067 2843532298) (1 1 1 1) (13095 18756 19465

34211)(08830 27474 28092

41440)

4 (09330 16784 1959125506)

(08341 11678 1246129649)

(09159 28247 2893638990) (1 1 1 1) (09411 22048 23311

23398)

5 (16968 23804 2604048683)

(09998 17316 1919225134)

(12597 13015 1319723604)

(15705 22564 2494625479) (1 1 1 1)

6 (19121 19896 2080927139)

(16729 24921 2578739713)

(15206 17650 2276843007)

(14500 19317 2093727454)

(09090 15973 1608518771)

7 (08938 14201 2197430621)

(10727 18788 2676644705)

(11865 12597 1538946016)

(15736 20361 2419824402)

(09572 10258 1333527689)

8 (09447 14976 2328628905)

(12111 17803 1877535145)

(10618 11577 2241228931)

(09720 19844 2659229915)

(09858 24791 2598127111)

9 (08528 11187 1690118615)

(19187 19237 2598841383)

(15716 27271 2865831107)

(13071 16180 1836026575)

(15352 16308 2337227600)

10 (21417 21589 2790444097)

(08631 15053 1877827503)

(10816 11919 1518729980)

(12190 16116 1813649229)

(12200 13066 1742218604)


Alter 6 7 8 9 10

1 (10856 14359 2278023293)

(08282 15578 2285725171)

(17336 18140 1817440347)

(12599 12930 1567629902)

(21814 24984 2852348855)

2 (19559 19668 2694528364)

(10309 11247 1217418890)

(20821 25939 2733849534)

(17569 18550 1960925630)

(09146 20622 2848638604)

3 (25282 26897 2956229657)

(14502 14629 2198328661)

(09020 14561 1911939980)

(10401 19743 2791342684)

(09066 21276 2269430096)

4 (13612 19131 2452837361)

(11284 13665 1868026496)

(12325 13524 2155327878)

(15721 21685 2676729556)

(10085 12046 1327917180)

5 (12671 15430 1612327801)

(14844 15762 1746528314)

(13677 16992 1901321088)

(14527 15013 1733229330)

(11802 12257 1554719670)

6 (1 1 1 1) (11297 22511 2389429781)

(09836 13593 1751326157)

(13540 14390 1914221576)

(10371 20850 2793944945)

7 (11553 14880 1550817356) (1 1 1 1) (11869 14414 18417

23879)(13343 13919 28183

40151)(17366 20025 23034

35067)

8 (11300 15650 1901020894)

(15903 23132 2419924578) (1 1 1 1) (13946 15279 16276

17335)(13428 20892 24250

35989)

9 (24919 27597 2961132421)

(16795 18655 2658726980)

(15653 20299 2673326790) (1 1 1 1) (10599 27767 29745

30679)

10 (12209 18226 2480726000)

(10587 16723 2024723236)

(10306 10814 2009028380)

(09603 09948 2556447606) (1 1 1 1)


Alter 1 2 3 4 5 6 7 8 9 101 1 15314 16206 14502 13533 14101 12253 11829 11195 124672 08732 1 09696 11815 09277 09341 10056 16240 13692 090033 13962 09456 1 13245 14052 13976 07491 11550 10641 100244 12965 12240 09899 1 10433 12840 14147 13558 12670 078295 10521 10520 16035 12950 1 15459 08802 13835 10907 138236 14157 14310 13540 14816 11058 1 13005 15629 11353 154467 07071 13030 08849 12772 09513 11062 1 10778 11772 090948 09719 13723 13468 12719 11681 13485 10335 1 11417 154179 12668 10891 13683 11145 15616 12089 10983 11979 1 0940810 11048 11561 14336 12495 12373 13923 13778 13899 13436 1

Complexity 15




Alter 1 2 3 4 5 6 7 8 9 101 1 19481 21786 26741 26765 17774 17807 25275 18617 321432 21596 1 20555 25039 15031 23644 13543 32199 20662 241493 18819 25825 1 22090 26034 27819 20116 21619 25455 204334 17712 16605 25614 1 18669 24042 17760 18956 23310 132615 30017 17821 16409 21853 1 18684 19738 17633 19750 149446 22110 27231 25680 20662 14638 1 21489 17024 17196 263857 19067 25757 23581 21032 16022 14725 1 17266 24189 244278 19157 21776 18503 21235 20933 16615 21507 1 15697 239049 13786 27131 25055 18854 20731 28643 22239 22266 1 2358710 29505 17620 17784 25948 15328 20168 17550 17606 23935 1





SW3

SW2SW1

OW3

OW1 OW2

Subs

tage

1-1

Subs

tage

1-2

Subs

tage

2-1

Subs

tage

2-2

TW

Stage 1 Stage 2

Stage 3

SW1∘2 OW1∘2

SW1∘2∘3 OW1∘2∘3


16 Complexity










































Complexity 17





















18 Complexity










Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36





Complexity 19






Table 20 Continued

Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36










Model1

Model41

Model42

Model43

Model44

Model45

Model46

Model51

Model52

Model53

Model54

Model55

Model56













20 Complexity


Model1

Model61

Model62

Model63

Model64

Model65

Model66

Model71

Model72

Model73

Model74

Model75

Model76














Model1

Model81

Model82

Model83

Model84

Model85

Model86

Model91

Model92

Model93

Model94

Model95

Model96













Complexity 21











22 Complexity



6 Conclusions




Data Availability






Acknowledgments


References







Complexity 23





























24 Complexity


Alter 1 2 3 4 5

1 (1 1 1 1) (10000 11975 1761921852)

(13959 18678 2560629058)

(08786 22426 2668147228)

(14288 24658 2817839657)

2 (13456 19678 2514228548) (1 1 1 1) (11568 14847 25474

30198)(10122 10903 28725

48158)(08339 08947 15098

26066)

3 (14519 15936 2003424383)

(18749 24067 2843532298) (1 1 1 1) (13095 18756 19465

34211)(08830 27474 28092

41440)

4 (09330 16784 1959125506)

(08341 11678 1246129649)

(09159 28247 2893638990) (1 1 1 1) (09411 22048 23311

23398)

5 (16968 23804 2604048683)

(09998 17316 1919225134)

(12597 13015 1319723604)

(15705 22564 2494625479) (1 1 1 1)

6 (19121 19896 2080927139)

(16729 24921 2578739713)

(15206 17650 2276843007)

(14500 19317 2093727454)

(09090 15973 1608518771)

7 (08938 14201 2197430621)

(10727 18788 2676644705)

(11865 12597 1538946016)

(15736 20361 2419824402)

(09572 10258 1333527689)

8 (09447 14976 2328628905)

(12111 17803 1877535145)

(10618 11577 2241228931)

(09720 19844 2659229915)

(09858 24791 2598127111)

9 (08528 11187 1690118615)

(19187 19237 2598841383)

(15716 27271 2865831107)

(13071 16180 1836026575)

(15352 16308 2337227600)

10 (21417 21589 2790444097)

(08631 15053 1877827503)

(10816 11919 1518729980)

(12190 16116 1813649229)

(12200 13066 1742218604)


Alter 6 7 8 9 10

1 (10856 14359 2278023293)

(08282 15578 2285725171)

(17336 18140 1817440347)

(12599 12930 1567629902)

(21814 24984 2852348855)

2 (19559 19668 2694528364)

(10309 11247 1217418890)

(20821 25939 2733849534)

(17569 18550 1960925630)

(09146 20622 2848638604)

3 (25282 26897 2956229657)

(14502 14629 2198328661)

(09020 14561 1911939980)

(10401 19743 2791342684)

(09066 21276 2269430096)

4 (13612 19131 2452837361)

(11284 13665 1868026496)

(12325 13524 2155327878)

(15721 21685 2676729556)

(10085 12046 1327917180)

5 (12671 15430 1612327801)

(14844 15762 1746528314)

(13677 16992 1901321088)

(14527 15013 1733229330)

(11802 12257 1554719670)

6 (1 1 1 1) (11297 22511 2389429781)

(09836 13593 1751326157)

(13540 14390 1914221576)

(10371 20850 2793944945)

7 (11553 14880 1550817356) (1 1 1 1) (11869 14414 18417

23879)(13343 13919 28183

40151)(17366 20025 23034

35067)

8 (11300 15650 1901020894)

(15903 23132 2419924578) (1 1 1 1) (13946 15279 16276

17335)(13428 20892 24250

35989)

9 (24919 27597 2961132421)

(16795 18655 2658726980)

(15653 20299 2673326790) (1 1 1 1) (10599 27767 29745

30679)

10 (12209 18226 2480726000)

(10587 16723 2024723236)

(10306 10814 2009028380)

(09603 09948 2556447606) (1 1 1 1)


Alter 1 2 3 4 5 6 7 8 9 101 1 15314 16206 14502 13533 14101 12253 11829 11195 124672 08732 1 09696 11815 09277 09341 10056 16240 13692 090033 13962 09456 1 13245 14052 13976 07491 11550 10641 100244 12965 12240 09899 1 10433 12840 14147 13558 12670 078295 10521 10520 16035 12950 1 15459 08802 13835 10907 138236 14157 14310 13540 14816 11058 1 13005 15629 11353 154467 07071 13030 08849 12772 09513 11062 1 10778 11772 090948 09719 13723 13468 12719 11681 13485 10335 1 11417 154179 12668 10891 13683 11145 15616 12089 10983 11979 1 0940810 11048 11561 14336 12495 12373 13923 13778 13899 13436 1

Complexity 15




Alter 1 2 3 4 5 6 7 8 9 101 1 19481 21786 26741 26765 17774 17807 25275 18617 321432 21596 1 20555 25039 15031 23644 13543 32199 20662 241493 18819 25825 1 22090 26034 27819 20116 21619 25455 204334 17712 16605 25614 1 18669 24042 17760 18956 23310 132615 30017 17821 16409 21853 1 18684 19738 17633 19750 149446 22110 27231 25680 20662 14638 1 21489 17024 17196 263857 19067 25757 23581 21032 16022 14725 1 17266 24189 244278 19157 21776 18503 21235 20933 16615 21507 1 15697 239049 13786 27131 25055 18854 20731 28643 22239 22266 1 2358710 29505 17620 17784 25948 15328 20168 17550 17606 23935 1





SW3

SW2SW1

OW3

OW1 OW2

Subs

tage

1-1

Subs

tage

1-2

Subs

tage

2-1

Subs

tage

2-2

TW

Stage 1 Stage 2

Stage 3

SW1∘2 OW1∘2

SW1∘2∘3 OW1∘2∘3


16 Complexity










































Complexity 17





















18 Complexity










Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36





Complexity 19






Table 20 Continued

Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36










Model1

Model41

Model42

Model43

Model44

Model45

Model46

Model51

Model52

Model53

Model54

Model55

Model56













20 Complexity


Model1

Model61

Model62

Model63

Model64

Model65

Model66

Model71

Model72

Model73

Model74

Model75

Model76














Model1

Model81

Model82

Model83

Model84

Model85

Model86

Model91

Model92

Model93

Model94

Model95

Model96













Complexity 21











22 Complexity



6 Conclusions




Data Availability






Acknowledgments


References







Complexity 23





























24 Complexity




Alter 1 2 3 4 5 6 7 8 9 101 1 19481 21786 26741 26765 17774 17807 25275 18617 321432 21596 1 20555 25039 15031 23644 13543 32199 20662 241493 18819 25825 1 22090 26034 27819 20116 21619 25455 204334 17712 16605 25614 1 18669 24042 17760 18956 23310 132615 30017 17821 16409 21853 1 18684 19738 17633 19750 149446 22110 27231 25680 20662 14638 1 21489 17024 17196 263857 19067 25757 23581 21032 16022 14725 1 17266 24189 244278 19157 21776 18503 21235 20933 16615 21507 1 15697 239049 13786 27131 25055 18854 20731 28643 22239 22266 1 2358710 29505 17620 17784 25948 15328 20168 17550 17606 23935 1





SW3

SW2SW1

OW3

OW1 OW2

Subs

tage

1-1

Subs

tage

1-2

Subs

tage

2-1

Subs

tage

2-2

TW

Stage 1 Stage 2

Stage 3

SW1∘2 OW1∘2

SW1∘2∘3 OW1∘2∘3


16 Complexity










































Complexity 17





















18 Complexity










Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36





Complexity 19






Table 20 Continued

Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36










Model1

Model41

Model42

Model43

Model44

Model45

Model46

Model51

Model52

Model53

Model54

Model55

Model56













20 Complexity


Model1

Model61

Model62

Model63

Model64

Model65

Model66

Model71

Model72

Model73

Model74

Model75

Model76














Model1

Model81

Model82

Model83

Model84

Model85

Model86

Model91

Model92

Model93

Model94

Model95

Model96













Complexity 21











22 Complexity



6 Conclusions




Data Availability






Acknowledgments


References







Complexity 23





























24 Complexity










































Complexity 17





















18 Complexity










Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36





Complexity 19






Table 20 Continued

Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36










Model1

Model41

Model42

Model43

Model44

Model45

Model46

Model51

Model52

Model53

Model54

Model55

Model56













20 Complexity


Model1

Model61

Model62

Model63

Model64

Model65

Model66

Model71

Model72

Model73

Model74

Model75

Model76














Model1

Model81

Model82

Model83

Model84

Model85

Model86

Model91

Model92

Model93

Model94

Model95

Model96













Complexity 21











22 Complexity



6 Conclusions




Data Availability






Acknowledgments


References







Complexity 23





























24 Complexity





















18 Complexity










Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36





Complexity 19






Table 20 Continued

Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36










Model1

Model41

Model42

Model43

Model44

Model45

Model46

Model51

Model52

Model53

Model54

Model55

Model56













20 Complexity


Model1

Model61

Model62

Model63

Model64

Model65

Model66

Model71

Model72

Model73

Model74

Model75

Model76














Model1

Model81

Model82

Model83

Model84

Model85

Model86

Model91

Model92

Model93

Model94

Model95

Model96













Complexity 21











22 Complexity



6 Conclusions




Data Availability






Acknowledgments


References







Complexity 23





























24 Complexity










Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36





Complexity 19






Table 20 Continued

Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36










Model1

Model41

Model42

Model43

Model44

Model45

Model46

Model51

Model52

Model53

Model54

Model55

Model56













20 Complexity


Model1

Model61

Model62

Model63

Model64

Model65

Model66

Model71

Model72

Model73

Model74

Model75

Model76














Model1

Model81

Model82

Model83

Model84

Model85

Model86

Model91

Model92

Model93

Model94

Model95

Model96













Complexity 21











22 Complexity



6 Conclusions




Data Availability






Acknowledgments


References







Complexity 23





























24 Complexity






Table 20 Continued

Model1

Model21

Model22

Model23

Model24

Model25

Model26

Model31

Model32

Model33

Model34

Model35

Model36










Model1

Model41

Model42

Model43

Model44

Model45

Model46

Model51

Model52

Model53

Model54

Model55

Model56













20 Complexity


Model1

Model61

Model62

Model63

Model64

Model65

Model66

Model71

Model72

Model73

Model74

Model75

Model76














Model1

Model81

Model82

Model83

Model84

Model85

Model86

Model91

Model92

Model93

Model94

Model95

Model96













Complexity 21











22 Complexity



6 Conclusions




Data Availability






Acknowledgments


References







Complexity 23





























24 Complexity


Model1

Model61

Model62

Model63

Model64

Model65

Model66

Model71

Model72

Model73

Model74

Model75

Model76














Model1

Model81

Model82

Model83

Model84

Model85

Model86

Model91

Model92

Model93

Model94

Model95

Model96













Complexity 21











22 Complexity



6 Conclusions




Data Availability






Acknowledgments


References







Complexity 23





























24 Complexity











22 Complexity



6 Conclusions




Data Availability






Acknowledgments


References







Complexity 23





























24 Complexity



6 Conclusions




Data Availability






Acknowledgments


References







Complexity 23





























24 Complexity





























24 Complexity

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