Desalination 313 (2013) 44–50

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Desalination

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A hybrid fuzzy multi-criteria decision making approach for desalinationprocess selection

Seyed Ali Ghassemi, Shahnaz Danesh ⁎Department of Civil Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

H I G H L I G H T S

► A hybrid model was developed based on the fuzzy-AHP and TOPSIS methods.► Fuzzy-AHP was used to determine the weights of the criteria and sub-criteria.► TOPSIS method was used to calculate the final ranking of the desalination technologies.► A real world application of the model demonstrated its feasibility and reliability.

⁎ Corresponding author at: FerdowsiUniversity ofMashhRazavi, Iran. Tel.: +98 9153100003; fax: +98 511 8788805

E-mail addresses: seydal2003@gmail.com (S.A. Ghassdanesh@ferdowsi.um.ac.ir (S. Danesh).

0011-9164/$ – see front matter © 2012 Elsevier B.V. Allhttp://dx.doi.org/10.1016/j.desal.2012.12.008

a b s t r a c t

a r t i c l e i n f o

Article history:Received 14 March 2012Received in revised form 27 November 2012Accepted 9 December 2012Available online 5 January 2013

Keywords:Fuzzy-AHPTOPSISDesalinationBrackish waterElectrodialysis

In this paper an integrated two-step model was developed based on the fuzzy-AHP and TOPSIS methods. Theperformance and reliability of themodel were then evaluated in a real world case study concerning the selectionof themost suitable desalination technology for the treatment of brackish groundwater typical of an area locatedin north-east of Iran. The desalination technologies included in this study were reverse osmosis, electrodialysis,ion exchange, multistage flash distillation, multi-effect distillation, and vapor compression. The comparison ofthe technologies was based on various environmental, technical and economical criteria and sub-criteria. Thefuzzy-AHPwas used to analyze the structure of the selection process and to determine theweights of the criteriaand sub-criteria, and the TOPSISmethodwas used to calculate the final ranking of the technologies. The outcomeresults of the two-step model revealed that electrodialysis, with a closeness coefficient value of 0.7547, was themost applicable desalination technology for the study area.Moreover, sensitivity analysis demonstrated that anyvariation in the criteria weights does not affect the outcome of the model.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

In recent years, the scarcity of fresh water resources in countrieslocated in the arid and semi arid regions of the world has becomemore critical due to resource limitations, global warming and the in-crease in water consumption. As such, the use of brackish groundwaterand the application of different technologies to improve their quality forvarious consumptions have gained special attention in water resourcemanagement programs.

At the present, there are many different types of desalination tech-nologies available in the market, each with its own technical specifica-tions and applicability. These technologies can be categorized in threegeneral groups of distillation, membrane-based and ion exchange. Indistillation processes, water is transformed into vapor and then is con-densed into a liquid state. Commercially available technologies of thistype include multistage flash distillation (MSF), multi-effect distillation

ad, Azadi Sq.,Mashhad, Khorasan.semi),

rights reserved.

(MED), and vapor compression (VC) [1]. In contrast, membrane-baseddesalination techniques use different types of membrane to separatedissolved solids fromwater. Themost popularmembrane-based desali-nation technologies are reverse osmosis (RO) and electrodialysis (ED).In ion exchange process (IE) the ions in the solution are exchanged bythe ions of a resin [2].

Because of the advantages and disadvantages associated with eachdesalination technology, the selection of the optimum technique forany specific area is a complicated task due to the diversity of objectivesand constraints that should be considered and satisfied simultaneously.With these types of problems, decision makers cannot go through thestandard single criteria mathematical programming techniques to findthe best option. Moreover, like most other real-life problems, there al-ways exists a lack of sufficient data which will add an extra dimensionof complexity. In such situations where the decision maker confrontsmany criteria and constraints, multi criteria decision making (MCDM)methods canoffer a proper solution, as they provide techniques for com-paring and rankingmany criteria and choices. Another major advantageof most MCDM techniques is their ability to analyze both quantitativeand qualitative criteria together. Many techniques and methodologiesare reported in the literature for MCDM [3]. Among most popular ones

Table 1Triangular fuzzy scale of preferences [26].

Linguistic terms Triangular fuzzyscale

Triangular fuzzyreciprocal scale

Just equal (1, 1, 1) (1, 1, 1)Equally important (1/2, 1, 3/2) (2/3, 1, 2)Weakly important (1, 3/2, 2) (1/2, 2/3, 1)Strongly more important (3/2, 2, 5/2) (2/5, 1/2, 2/3)Very strong more important (2, 5/2, 3) (1/3, 2/5, 1/2)Absolutely more important (5/2, 3, 7/2) (2/7, 1/3, 2/5)

45S.A. Ghassemi, S. Danesh / Desalination 313 (2013) 44–50

are the analytic hierarchy process (AHP) [4], the technique for orderpreference by similarity to an ideal solution (TOPSIS) [5], eliminationand choice corresponding to reality (ELECTRE) [6], preference rank-ing organization method for enrichment of evaluations (PROMETHEE)[7], decision-making trial and evaluation laboratory (DEMATEL) [8],analytic network process (ANP) [9], and Vlsekriterijumska OptimizacijaI Kompromisno Resenje (VIKOR) [10].

In regard to desalination technologies, Hajeeh and Al-Othman[11] used a two-stage AHP process to select the most appropriate al-ternative. Seven criteria were selected and used in order to identifythe most suitable desalination technology from four desalinationplants. Mohsen and Al-Jayyousi [12] also applied a five-step AHPmodel to evaluate various desalination technologies. The criteriaadopted for evaluation were based on technical, economic, and envi-ronmental aspects. Hajeeh [13] presented a hierarchy model basedon the fuzzy set theory to deal with the desalination technologyselection problem. The linguistic values were used to assess the rat-ings and weights for the technology evaluating factors. The selectionprocess was limited to six factors and three commercially availabledesalination technologies including MSF, MED, and RO. Bick andOron [14] developed an AHP-based decision making approach toselect the best post-treatment technology for a specific seawater re-verse osmosis plant. Post-treatment systems were evaluated basedon seven criteria. A sensitivity analysis was performed to examinethe response of alternatives when the relative importance rating ofeach criterion was changed.

In this study, an integrated model consisting of fuzzy-AHP andTOPSISwas established to provide a stepwisemethodology for the selec-tion of the optimum desalination technology among different availabletechnologies. The model was then applied in a case study to demon-strate its applicability in a real world pilot study and prove its reliability.

The fuzzy-AHP has a strong ability to handle the uncertainty and am-biguity present in deciding the priorities of different alternatives in anMCDM situation. Moreover, it allows for approximate values and infer-ences as well as incomplete or ambiguous data (fuzzy data) as opposedto only relying on crisp data (binary yes/no choices) [15]. TOPSIS is anefficient model in handling the sensible attributes and there is no limitin terms of number of criteria, sub-criteria or alternatives. As a result,the integration of AHP-fuzzy and TOPSIS can provide a strong base forthe analysis of complex decision problems [16–20]. Furthermore, theAHP-fuzzy and TOPSIS methods can be easily programmed by using aspreadsheet to automate the decision making process.

The following sections cover respectively: a brief description offuzzy-AHP and TOPSIS, the proposed integrated methodology, theapplication of the model in a real world situation concerned with theselection of the optimal desalination technology, and the conclusions.

2. Fuzzy-AHP method

AHP is an MCDM technique developed by Saaty [4] for evaluatingdifferent alternatives against a set of selected criteria in order to de-termine the best alternative. AHP assumes that criteria can beexpressed in a hierarchical structure. In this model, the criteria arecompared pairwise and the final decision is made based on the resultsof these comparisons [21]. In conventional AHP for pairwise compar-isons of the criteria an arbitrary value (acquired by mainly decisionmakers) is allocated to each criterion. Therefore, due to the highdegree of uncertainty involved in the allocated values, the results can-not be completely reliable [22]. To reduce the degree of uncertaintyand vagueness associated with the conventional AHP, different ver-sions of the fuzzy-AHP methods were developed [23]. In general, inthe fuzzy-AHP models a linguistic approach is applied, in which theoptimism/pessimism conceptual rating attitude of decision-makersis taken into account. Because of the linguistic approach, triangularfuzzy numbers (TFNs) are used to quantify conceptual preferringratings of criteria [24]. The linguistic scale of TFNs can be chosen

according to the extent of uncertainty and ambiguity present in thedecision making problem. In a literature a range of linguistic scales in-cluding 5-point, 6-point and 7-point has been reported [25]. In thisresearch, a 6-point triangular fuzzy scale of preferences was used(Table 1). This scale was proposed by Kahraman et al. [26] and usedfor solving fuzzy decision making problems [27–29].

There are many alternatives as solution methods to perform on thefuzzy-AHP based structured model on MCDM problems [23,30–34].Among the most reliable and simple ones is the Chang [30] extent anal-ysismethodwhich is used in this study. Themethod is used to determinethe extent of an object to be satisfied for the goal. The Chang's [30]meth-od includes several steps which are summarized as follows [21,26].

Assume X={x1, x2, …, xn} be an object set, and G={g1, g2, …, gm}be a goal set. According to the method of extent analysis, each objectis taken and extent analysis is performed for each goal, gi respectively.Therefore, the m extent analysis values for each object can be ob-tained, with the following signs:

M̃1gi;M̃

2gi;…; M̃

mgi ; i ¼ 1;2;…;n

where all the M̃jgi; j ¼ 1;2;…;m are TFNs. A TFN is represented by

three parameters: the least possible value, the most possible value,and the highest possible value, here are represented by l, m and urespectively.

Step 1 The value of the fuzzy synthetic extent with respect to the ithobject is defined as follows:

~Si ¼Xmj¼1

M̃ j

gi⊗Xni¼1

Xmj¼1

~M j

gi

24

35−1

: ð1Þ

To obtain∑mj¼1

~Mjgi, the fuzzy addition operation of them extent anal-

ysis values for a particular matrix is performed as shown inEq. (2):

Xmj¼1

~M j

gi¼

Xmj¼1

lj;Xmj¼1

mj;Xmj¼1

uj

24

35−1

: ð2Þ

And to obtain ∑ni¼1∑

mj¼1

~M jgi the fuzzy addition operation ~Mj

gi (j=1,2, …, m) values are performed as in Eq. (3):

Xni¼1

Xmj¼1

~M j

gi¼

Xni¼1

li;Xni¼1

mi;Xni¼1

ui

!: ð3Þ

The inverse of the vector above is then computed as presentedin Eq. (4):

Xni¼1

Xmj¼1

~M j

gi

24

35−1

¼ 1∑n

i¼1ui

;1

∑ni¼1mi

;1

∑ni¼1li

!: ð4Þ

Fig. 1. The intersection between ~M1 and ~M2.

46 S.A. Ghassemi, S. Danesh / Desalination 313 (2013) 44–50

Step 2 As ~M1 and ~M2 are two TFNs, the degree of possibility of ~M2 ¼l2;m2;u2ð Þ≥ ~M1 ¼ l1;m1;u1ð Þ is defined as:

V ~M2≥ ~M1

� �¼ supy≥x minμ ~M1

xð Þ; minμ ~M2yð Þ

h ið5Þ

and can be equivalently expressed as follows:

V ~M2≥ ~M1

� �¼ μ ~M2

dð Þ ¼1;0;

l1−u2

m2−u2ð Þ− m1−l1ð Þ ;

if m2≥m1if l1≥u2otherwise

8>><>>: ð6Þ

where d is the ordinate of the highest intersection point Dbetween μ ~M1

and μ ~M2, as shown in Fig. 1. To compare ~M1

and ~M2, both values of V ~M2≥ ~M1

� �and V ~M1≥ ~M2

� �should

be calculated.Step 3 The degree of possibility for a convex fuzzy number to be

greater than k convex fuzzy numbers Mi (i=1, 2, …, k) canbe defined by:

V ~M≥ ~M1;~M2;…; ~Mk

� �¼ minV ~M≥ ~Mi

� �ð7Þ

Define criteria and sub criteria for evaluation of desalin

Construct fuzzy pairwise comparison matrices using triang

Calculate fuzzy relative importance weights of

Check the consistency of the matrices

Obtain the evaluation criteria, sub criteria and altern

Determining alternative desalination techno

Evaluate the desalination technologies using TOP

Calculate PIS and NIS, and separation mea

Rank the preference order for desalination technologies and selectin

Fig. 2. Schematic diagram of the proposed mo

where i=1, 2, …, k.Assume that:

d′ Aið Þ ¼ minV ~Si≥~Sk� �

: ð8Þ

For k=1, 2, …; k≠ i.Then the weight vector is given by:

W ′ ¼ d′ A1ð Þ; d′ A2ð Þ;…;d′ Anð Þ� �T ð9Þ

where Ai (i=1,2, …, n) are n elements.Step 4 Via normalization, the normalized weight vectors are defined

as:

W ¼ d A1ð Þ;d A2ð Þ;…;d Anð Þð ÞT ð10Þ

where W is a non-fuzzy number.The issue of consistency of fuzzy pairwise comparison matricesin fuzzy-AHP is another subject that needs to be taken into con-sideration. The consistency of a comparison matrix in conven-tional AHP is measured by the consistency ratio [4]. But theresults of fuzzy synthetic decision are fuzzy numbers, thus, it

ation technologies

ular fuzzy numbers

matrices

atives weights

logies

SIS method

sures

g the optimal technology

Literature review

Expert opinions

Fuzz

y A

HP

TO

PSIS

del for desalination technology selection.

Table 2Desalination technology evaluation criteria, sub-criteria and definition.

Criteria Sub-criteria Definition

Environmental (C1) Brine management (SC1) Handling and disposal of brineAir pollution (SC2) Water vapor as a byproduct of thermal desalination processes

Technical (C2) Operational complexity (SC3) Skill required to operate technologyReliability (SC4) The ability of technology to perform steadily under stated conditionsExpandability (SC5) Ability of technology to accommodate additions to its capacity or capabilitiesAdaptability (SC6) Compatibility of technology with quality of influent waterWater recovery (SC7) Product water relative to the input water flowTreated water quality (SC8) Salinity of product water

Economical (C3) Capital costs (SC9) Purchase of mechanical equipments, installations and other incidental construction workOperating costs (SC10) Wages and the funds spent for the energy, the products, services and maintenance

47S.A. Ghassemi, S. Danesh / Desalination 313 (2013) 44–50

should be converted to real numbers which could be doneby employing any of the defuzzification techniques [35]. Themost common techniques are right value, center of area, andα-cut method [36]. In this research the center of area approachwas used because: a) it is simple and does not need an analyst'spersonal judgment [37], b) the center of area method is themost prevalent and physically most appealing of all thedefuzzification methods [38], and C) it gives the same rankingwith most of the other methods [39].

3. TOPSIS method

TOPSIS is one of the major techniques in dealing with MCDMproblems. It is based upon the concept that the best alternative isthe one that has the shortest distance from the positive ideal solution(PIS) and the longest distance from the negative ideal solution (NIS).The PIS is the solution that maximizes the benefit criteria and min-imizes the cost criteria; whereas the NIS has an opposite logic,i.e., maximizes the cost criteria and minimizes the benefit criteria[40]. The TOPSIS method considers the distances to both PIS and theNIS, simultaneously. Due to its rationality, logic, and computationalsimplicity, TOPSIS has been widely applied in many research areas as-sociated with a selection of various alternatives and their risk analysis[16,41–44].

The application of the TOPSIS model includes the following steps[45]:

Step 1 Decision matrix is normalized by using Eq. (11):

rij ¼wijffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

∑Jj¼1w

2ij

q ; j ¼ 1;2;…; J; i ¼ 1;2;…;n: ð11Þ

Desalination Techn

C2

SC1 SC2

VCIE MED

SC4 SC5SC3

C1

Fig. 3. The decision hierarchy of des

Step 2 The normalized decision matrix is then weighted by multiply-ing the normalized matrix with the weights of the criteria:

vij ¼ w�i rij; j ¼ 1;2;…; J; i ¼ 1;2;…;n: ð12Þ

Step 3 PIS (maximum values) and NIS (minimum values) are deter-mined respectively as:

A� ¼ v�1; v�2;…; v�n

� �; ð13Þ

A− ¼ v−1 ; v−2 ;…; v−nf g: ð14Þ

Step 4 The distance of each alternative from PIS and NIS is calculatedas follows:

d�i ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXnj¼1

vij−v�j� �2

;

vuut j ¼ 1;2; … , J ð15Þ

d−i ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXnj¼1

vij−v−j� �2

;

vuut j ¼ 1;2;…; J: ð16Þ

Step 5 The closeness coefficient of each alternative (CCi) relative toits distance from PIS and NIS is then calculated by using thefollowing equation:

CCi ¼d−i

d�i þ d−i: ð17Þ

Step 6 Finally, the ranking of alternatives is determined by comparingthe CCi values.

ology Selection

C3

SC7

ROEDMSF

SC8SC6 SC9 SC10

alination technology selection.

Table 3The pairwise comparison matrix for criteria.

C1 C2 C3

C1 (1, 1, 1) (0.44, 0.57, 0.8) (0.67, 1, 2)C2 (1.25, 1.75, 2.25) (1, 1, 1) (1, 1.5, 2)C3 (0.5, 1, 1.5) (0.5, 0.67, 1) (1, 1, 1)

Table 4Priority weights of sub-criteria.

Sub-criteria Priority weight Sub-criteria Priority weight

SC1 1.000 SC6 0.271SC2 0.000 SC7 0.184SC3 0.087 SC8 0.192SC4 0.192 SC9 0.500SC5 0.073 SC10 0.500

48 S.A. Ghassemi, S. Danesh / Desalination 313 (2013) 44–50

4. Proposed methodology

The proposedmodel for thewater desalination technology selectionintegrates the fuzzy-AHP and TOPSIS methods and includes three basicstages: (1) identification of the criteria, sub-criteria and alternatives tobe used in developing the decision hierarchy structure, (2) fuzzy-AHPcomputations, and (3) evaluation of the alternatives and determinationof the final ranking by TOPSIS.

In the first stage, alternative desalination technologies, criteriaand sub-criteria of importance, are selected and the decision hierar-chy is structured. The objective is placed in the first level and thecriteria, sub-criteria and alternative desalination technologies areplaced in the second, third and fourth level, respectively. The deci-sion hierarchy should be approved by the decision-making team.

In the next stage, the criteria used in desalination technology selec-tion are assigned weights using fuzzy-AHP. As described in Section 2,linguistic values are used to allocate the criteria weights.

In the third stage, by using the TOPSIS procedure, the desalinationtechnologies are ranked. Ranking is done according to CCi values, in adescending order. The desalination technology which obtains themaximum CCi value is selected as the optimum desalination technol-ogy. The schematic diagram of the proposed model for the desalina-tion technology selection is provided in Fig. 2.

5. Application of the proposed model

The proposedmethodology was applied to an area located in a semiarid region, north-east of Iran, with an annual average precipitationof about 150 mm/yr [46]. The water consumption in this area is sup-plied mainly by groundwater resources. The average total dissolvedsolids content of the water samples taken from a few wells in thestudy area indicated a value of about 2623 mg/lit, categorizing the aqui-fer as a brackish source. Due to the critical limitation of water resourcesin this area, the desalination of brackish water has gained special atten-tion in water resource management to extend water supply for domes-tic consumption. However, as mentioned in the previous sections, with

Table 5Evaluation of alternative desalination technologies with respect to brine management (SC1

Alternatives ED RO IE

ED (1, 1, 1) (5/4, 7/4, 9/4) (3/2, 2, 5/2)RO (4/9, 4/7, 4/5) (1, 1, 1) (1/2, 1, 3/2)IE (2/5, 1/2, 2/3) (2/3, 1, 2) (1, 1, 1)MSF (2/5, 1/2, 2/3) (1/2, 2/3, 1) (2/3, 1, 2)MED (2/5, 1/2, 2/3) (1/2, 2/3, 1) (2/3, 1, 2)VC (4/9, 4/7, 4/5) (1/2, 2/3, 1) (1, 1, 1)

so many different desalination technologies being available in themarket, as well as, the environmental, technical and economical con-straints to be considered, the final decision making for the most suit-able technology, was not an easy task to achieve [47]. Therefore, theproposed methodology was applied to analyze the situation and tosimplify the decision making process, effectively. For this purpose,in the first step, an expert team of fivemembers including three expertsfrom the province's Water and Wastewater Company and the authors,was formed. The experience and viewpoints of these members wereused throughout the entire course of this study, following the proceduredescribed below.

5.1. Identification of criteria

The criteria and sub-criteria of importance for comparison ofdesalination technologies were determined by the expert team mem-bers based on their backgrounds and experiences. The final outcomeof their decision included three criteria and ten sub-criteria whichare summarized in Table 2.

In the next step, available desalination technologies were researchedby the team members and six desalination processes including IE, VC,MED, MSF, ED and RO were chosen to be included in this study. The de-cision hierarchy was then structured using desalination technologies,criteria and sub-criteria, as shown in Fig. 3.

The decision hierarchy included four levels: The overall goal “the se-lection of the optimum desalination process” was considered to be thefirst level of the hierarchy, the criteria and sub-criteria were locatedin the second and third level, respectively, and the alternative desalina-tion technologies were included in the fourth level.

5.2. Weights of criteria

After forming the decision hierarchy structure, the weights of thecriteria were calculated by the fuzzy extent analysis method, describedin Section 2. For this purpose, the expert teammembers were given thetask of forming pairwise comparison matrices by using the linguisticscale given in Table 1. Since it was not possible to make mathematicalcalculations using linguistic terms, each term was given a TFN. In orderto obtain the fuzzy pairwise comparison matrix, the arithmetic meansof the fuzzy scores given by the team members were calculated withthe results summarized in Table 3.

In the next step, the weights of all the criteria were determinedbased on the fuzzy-AHPprocedure. For this purpose, by using the valuesreported in Table 3, the synthesis values with respect to the main goalwere calculated by using Eq. (1) as shown below:

C1 ¼ 2:11;2:57;3:8ð Þ⊗ 112:55

;1

9:49;

17:36

� �¼ 0:168;0:271;0:516ð Þ

C2 ¼ 3:25;4:25;5:25ð Þ⊗ 112:55

;1

9:49;

17:36

� �¼ 0:259;0:448;0:713ð Þ

C3 ¼ 2;2:67;3:5ð Þ⊗ 112:55

;1

9:49;

17:36

� �¼ 0:159;0:281;0:476ð Þ:

) sub-criterion.

MSF MED VC w

(3/2, 2, 5/2) (3/2, 2, 5/2) (5/4, 7/4, 9/4) 0.146(1, 3/2, 2) (1, 3/2, 2) (1, 3/2, 2) 0.055(1/2, 1, 3/2) (1/2, 1, 3/2) (1, 1, 1) 0.101(1, 1, 1) (1, 1, 1) (1, 1, 1) 0.101(1, 1, 1) (1, 1, 1) (1, 1, 1) 0.371(1, 1, 1) (1, 1, 1) (1, 1, 1) 0.226

Table 6Final pairwise comparison of desalination technologies with respect to sub-criteria.

Criteria Sub-criteria IE VC MED MSF ED RO

C1 SC1 0.146 0.055 0.101 0.101 0.371 0.226SC2 0.197 0.126 0.159 0.096 0.197 0.224

C2 SC3 0.259 0.034 0.065 0.058 0.242 0.341SC4 0.131 0.163 0.163 0.126 0.131 0.286SC5 0.166 0.157 0.145 0.155 0.145 0.231SC6 0.165 0.000 0.000 0.000 0.500 0.335SC7 0.236 0.108 0.068 0.107 0.284 0.196SC8 0.000 0.293 0.284 0.293 0.000 0.129

C3 SC9 0.181 0.132 0.067 0.029 0.259 0.331SC10 0.189 0.078 0.136 0.082 0.225 0.290

49S.A. Ghassemi, S. Danesh / Desalination 313 (2013) 44–50

The above fuzzy values were compared by using Eq. (6), and theobtained degree of possibility values were as follows:

V C1≥C2ð Þ ¼ 0:59 V C1≥C3ð Þ ¼ 0:97

V C2≥C1ð Þ ¼ 1 V C2≥C3ð Þ ¼ 1

V C3≥C2ð Þ ¼ 0:57 V C3≥C1ð Þ ¼ 1 :

Then, priority weights were calculated by using Eq. (8):

d′ C1ð Þ ¼ min 0:57;1ð Þ ¼ 0:57d′ C2ð Þ ¼ min 1;1ð Þ ¼ 1d′ C3ð Þ ¼ min 0:59;0:97ð Þ ¼ 0:59:

Priority weights with respect to the main goal form w′=(0.57, 1,0.59) vector which should be normalized. After normalization, thepriority weights were (0.264, 0.463, 0.273). As the results indicate,the technical criterion (C2) was determined to be the most importantcriterion in the desalination technology selection. Consistency ratio ofthe pairwise comparisonmatrixwas calculated to be 0.02 (b0.1). There-fore, the weights were shown to be consistent and as such, they wereused in continuation of the selection process.

The similar calculations were performed for each group of sub-criteria, separately. The comparison tables are not all presented here.But, the calculated priority weights of the sub-criteria are shown inTable 4.

It can be seen that the weight of the air pollution sub-criterion(SC2) is zero. It means that this sub-criterion is not important in theanalysis and can be omitted in further steps of evaluation.

5.3. Evaluation of alternatives and determination of the final rank

At this stage of the decision procedure, the team members wereasked to establish the decision matrix, by pairwise comparison ofthe alternatives with respect to each sub-criterion, separately. Then

Table 7Weighted evaluation matrix of the desalination technologies.

Criteria Sub-criteria IE VC MED MSF ED RO

C1 SC1 0.0385 0.0145 0.0267 0.0267 0.0979 0.0597SC2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

C2 SC3 0.0104 0.0014 0.0026 0.0023 0.0097 0.0137SC4 0.0116 0.0145 0.0145 0.0112 0.0116 0.0254SC5 0.0056 0.0053 0.0049 0.0052 0.0049 0.0078SC6 0.0207 0.0000 0.0000 0.0000 0.0627 0.0420SC7 0.0201 0.0092 0.0058 0.0091 0.0242 0.0167SC8 0.0000 0.0260 0.0252 0.0260 0.0000 0.0115

C3 SC9 0.0247 0.0180 0.0091 0.0040 0.0353 0.0451SC10 0.0258 0.0106 0.0186 0.0112 0.0307 0.0396

using TFNs, based on the evaluation of alternative desalination tech-nologies, the fuzzy evaluation matrix was established.

In the next step, using the same procedure as described in Section 2,the desalination technologies were compared pairwised, with respectto each sub-criterion, and their weights were calculated. Due to theextensiveness of the results, the outcome of the pairwise evaluationof the alternative technologies with respect only to the brine manage-ment sub-criterion (SC1), is shown in Table 5. The final weights of thedesalination technologies with respect to all sub-criteria are presentedin Table 6.

In the next step, using the results presented in Tables 4 and 6, andthe priority weights of the criteria, the weights of desalination technol-ogies were calculated which are shown in Table 7. Finally, by followingthe TOPSIS steps and calculations, the ranking of the desalination tech-nologies was determined. The final ranking results are summarized inTable 8.

Based on the CCi (closeness coefficient) values, the ranking of thedesalination technologies, in descending order (from the most prefer-able technology to the least one), was ED, RO, IE, VC, MED andMSF. Asa result, Electrodialysis (ED) with a CCi value of 0.7547, was the bestdesalination technology for the study area included in this research.

5.4. Sensitivity analysis

Decision makers may need sensitivity analysis to evaluate theeffect of changing the priority weights of the attributes on the rankingof alternatives. To investigate the impact of changing criteria weightson the selection of the best desalination technology, a sensitivityanalysis was performed in this research. For this purpose, the weightsof two decision attributes were changed in three different scenarios,while the weights of the other attributes were kept constant. Inother words, the weight of the first criterion C1 was changed withC2, and C3 sequentially. Moreover, the weights of C2 and C3 were ex-changed while the weight of C1 remained the same. Then the close-ness coefficients (CCi) were calculated by using the TOPSIS method.The results of the sensitivity analysis are shown in Table 9. It shouldbe mentioned that the first row of the table (Main) indicates the re-sults gained for the case study. The graphical representation of thesensitivity analysis is illustrated in Fig. 4.

As the CCi values in Table 9 show, any exchange in the criteriaweights does not affect the results of the model. However, in this re-search, ED obtained the highest CCi value under all the conditionstested. Therefore, ED was selected as the most appropriate technolo-gy for the desalination of brackish water in the study area.

6. Conclusions

In this paper, by using fuzzy-AHP and TOPSIS, an integrated two-step model was established to evaluate and select the optimum desa-lination technology among the processes e.g., IE, VC, MSF, MED, EDand RO. The evaluation was based on various environmental, techni-cal and economical criteria and sub-criteria. The model was then ap-plied to a real world case study (desalination of a brackish watersource with TDS of 2623 mg/lit), and its applicability and reliability

Table 8Final evaluation and ranking of the alternative desalination technologies.

Alternatives di− Ranking di⁎ Ranking CCi Ranking

IE 0.0426 3 0.0720 3 0.3716 3VC 0.0298 4 0.1013 6 0.2272 4MED 0.0285 5 0.0971 4 0.2267 5MSF 0.0278 6 0.1006 5 0.2159 6ED 0.1000 1 0.0325 1 0.7547 1RO 0.0774 2 0.0406 2 0.6558 2

Fig. 4. Model results based on the sensitivity analysis.

Table 9The sensitivity analysis results.

Conditions Weights CCi values

W1 W2 W3 IE VC MED MSF ED RO

1 (Main) 0.264 0.462 0.273 0.3716 0.2272 0.2267 0.2159 0.7547 0.65582 0.273 0.462 0.264 0.3743 0.2300 0.2278 0.2157 0.7519 0.66173 0.264 0.273 0.462 0.4307 0.2177 0.1917 0.1371 0.7780 0.73774 0.462 0.264 0.273 0.3598 0.1427 0.1701 0.1567 0.8504 0.6009

50 S.A. Ghassemi, S. Danesh / Desalination 313 (2013) 44–50

were well demonstrated. Based on the model evaluation, ED with theCCi value of 0.7547 was the most suitable technology for the casestudy in this research. The obtained CCi values for other technologies(RO, IE, VC, MED, and MSF) were 0.6558, 0.3716, 0.2272, 0.2267,0.2159, respectively. Results also showed that membrane-based tech-nologies (ED and RO) have priority over the distillation technologies.The sensitivity analysis indicated that changes made in the criteriaweights do not affect the final output of the model. In general, it canbe concluded that thedeveloped two-stepmodel can be applied reliablyto the decision making situations where there are many options avail-able and the criteria for the final decision are uncertain and ambiguous.

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