Application of Fuzzy Multiple

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Mineral Resources Engineering, Vol. 11, No. 1 (2002) 5972c Imperial College Press

APPLICATION OF FUZZY MULTIPLE ATTRIBUTE DECISION

MAKING IN MINING OPERATIONS

AYHAN KESIMAL

Karadeniz Technical University, Mining Engineering Department

61080, Trabzon, Turkey

ATAC BASCETIN

Istanbul University, Mining Engineering Department Avcilar

34850, Istanbul, Turkey

This paper presents a fuzzy multiple attribute decision making as an innovative toolfor criteria aggregation in mining decision problems. So far, various types of formula-tions or solution methods have been proposed with mining systems, but most of themexclusively considered linear functions as objective functions. Real world study is deci-sion making under subjective constraints of different importance, after using uncertain

data (linguistic variables), where compromises between competing criteria are allowed.It seems however that this technique is still very little known in mining. It is one of theaims of this case study to disseminate this technology in many mining fields.

The paper is divided into four sections. The first section provides an overview ofthe underlying concepts and theories of multiple attribute decision making in a fuzzyenvironment and the scope of this type of search. The second section introduces fewapplications of fuzzy set theory to mining industry problems reported in the literature.Some of these applications are briefly reviewed. The third section presents two casestudies which illustrate the application of the system for equipment selection in sur-face mining and method selection in underground mining in a fuzzy environment, andhighlight the flexible nature of the approach. Details of alternative systems and their cri-terion of each operation are given. And finally the fourth section presents the concluding

remarks.

1. Introduction

Over nearly the past three decades, fuzzy logic has been advanced as a formal

means to deal with implicit imprecision in a wide range of problems, e.g. in in-

dustrial control, military operations, economics, engineering, medicine, reliability,

and pattern recognition and classification. Among many existing references see,

e.g. Maiers et al.,15 Kandel,10 Klir et al.,13 Prade,19 Dubois et al.,7 Bandopadhyay

et al.,1

Bandopadhyay,2,3

Gershon et al.

,8

Herzog et al.

,9

Bascetin et al.

5,6

andBascetin4 for relevant applications in these and other fields. In practice, fuzzy logic

synthesizes different solution alternatives each of which need not be right or wrong


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60 A. Kesimal & A. Bascetin

Decision making may be characterised as a process of choosing or selecting

sufficiently good alternative(s), to attain, from a set of alternatives, to attain a

goal or goals. Much decision making involves uncertainty. Hence, one of the mostimportant aspects for a useful decision aid is to provide the ability to handle impre-

cise and vague information, such as large profits, fast speed and cheap price.

A decision model should cover process for identifying, measuring and combining

criteria and alternatives to build a conceptual model for decisions and evaluations

in fuzzy environments. Mine planning engineers often use of their intuition and

experiences in decision making. Mostly linguistic variables (the weather is rain-

ing, soil is wet, etc.) become in question and decision-makers may not know how

these variables are computed. Since the advent of the fuzzy set theory, these un-

certainties are easily evaluated in decision making process. By the development ofcomputer technology and programming of colloquial language with expert systems

have considerably reduced decision makers burden.

2. Fuzzy Set Theory

Researchers and practitioners of equipment and method selection face diverse op-

erational issues such as the complexity of interactive influences, inaccuracy of mea-

sures, uncertainty of environmental forces, and subjectivity of the decision making

process. Acquiring the information necessary for equipment and method selection iselaborate, to say the least, and once obtained is liable to be ambiguous, inconsistent,

incomplete, or deficient in quality. In addition, decision makers must often apply

rules of thumb or incorporate their personal intuition and judgment when deriving

performance measures based on indefinite linguistic concepts, e.g. high, low,

strong, weak, stable, and deteriorating. For example, if haulage level is

low and then truck haulage can be used (the opportunity will be high). If coal

seam is about 2.0 meters in thickness and has weak hanging wall condition then

longwall method with filling can be good choice in alternatives. This terminology

is a natural phenomenon caused by imperfectly defined problem attributes.Fuzzy sets25 have vague boundaries and are therefore well suited for discussing

such concepts as linguistic terms (such as very or somewhat) or natural phe-

nomena (temperatures). Fuzzy set theory has developed as an alternative to ordi-

nary (crisp) set theory and is used to describe fuzzy sets. To clear the difference

between these two sets, let explain with an example. Supposed that a set K has

various cycle times of one shovel loading same size trucks between 20 and 28 sec-

onds. An optimum loading cycle time is considered to be 24 to 25 seconds in this

mine site. Kset is firstly evaluated by crisp and subsequently by fuzzy set.

Figure 1(a) shows crisp set of cycle time in the 24 to 25 seconds range. In this

set, 24 seconds is 100 percent a member while 23 seconds is not in the set at all;

there is no in-between. The boundaries are definite and a particular loading cycle


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Application of Fuzzy Multiple Attribute Decision 61

20 21 22 23 24 25 26 27 28

Loading cycle time (seconds)

%membership

100

50

0

(a)

20 21 22 23 24 25 26 27 28

Loading cycle time (seconds)

%membership

100

50

0

(b)

Fig. 1. Crisp (a) and fuzzy set (b).

degree. Figure 1(b) shows 25 seconds is 100 percent a member of the set of loading

cycle time, whereas 22 seconds is only 50 percent a member of the set.

Additionally, the nature of fuzzy sets allows something to be a member in more

than one fuzzy set. For example, a 3-year-old haulage truck might be 20 percent a

member of the set of young trucks and 45 percent a member of the set of middle-

aged trucks.

Driving the set membership function for a fuzzy set is through the use in fuzzylogic or fuzzy decision making. The problem of constructing meaningful member-

ship functions has a lot of additional research work that will have to be done on

it to achieve full satisfaction. There are a number of empirical ways to establish

membership functions for fuzzy sets. Measuring of these is beyond the scope of this

article. However, for more information, see Li et al.14 and Klir et al.12

2.1. Fuzzy multiple attribute decision making

There are many methods of decision making. The focus of this paper is on Yagers23

method that is general enough to deal both with multiple objective and multiple

attribute problems. Concentrating on multiple attribute decision making problems,

only a single objective is considered, that a selecting the best from a set of

alternative. All other objectives are considered criteria. The method assumes the

max-min principle approach. Formally, let A = {A1, A2, . . . , An} be the set of

alternatives, C = {C1, C2, . . . , C m} be the set of criteria which can be given as

fuzzy sets in the space of alternatives, and Gthe goal, which can also be given by

a fuzzy set. Hence, the fuzzy set decision is the intersection of all criteria (and/or

goals):

D(A) = min(G(A), C1(A), C2(A), . . . , CM(A))


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The main difference is that the importance of criteria is represented as exponen-

tial scalars. This is based on the idea of linguistic hedges.25 The rationale behind

using weights (importance) as exponents is that the higher the importance of cri-teria the larger should be exponent because of the minimum rule. Conversely, the

less important, the smaller the weight. This seems intuitive. Formally,

D(A) = min((G(A))1(C1(A))

2, (C2(A))3, . . . , (CM(A))

m) for > 0 .

Consider the problem of selecting a site from the set {A,B,C} for a new in-pit

crusher in a quarry, with the goal, G, of spending the minimum investment possible

and for criteria evaluation to be located near the pit and the processing plant,

respectively C1 and C2. The judgment scale used is 1-equally important, 3-weakly

more important, 5-strongly more important, 7-demonstrably more important and9-absolutely more important. The values between (2, 4, 6, 8) show compromise

judgments.

Yager suggests the use of Saatys21 method for pair-wise comparison of the

criteria (attributes). A pair-wise comparison of attributes (criteria) could improve

and facilitate the assessment of criteria importance. Saaty developed a procedure

for obtaining a ratio scale for the elements compared. To obtain the importance

the decision-maker is asked to judge the criteria in pair-wise comparisons and the

values assigned are wij = 1/wij. Having obtained the judgments, the mxm matrix

B is constructed so that: (a) bii = 1; (b) bij = wij ; (c) bji = bij. To sum up,Yager suggests that the resulting eigenvector should be used to express the decision

makers empirical estimate of importance (the reciprocal matrix in which the values

are given by the decision maker) for each criteria in the decision and criteria 1 and

2, respectively C1 and C2, are three times as important as G, and the pair-wise

comparison reciprocal matrix is:

G C1 C2

G 1 1/3 1/3

C1 3 1 1C2 3 1 1

.

Hence, the eigenvalues of the reciprocal matrix are = [0, 3, 0] and therefore

max = 3. All values except one are zero.21 The weights of the criteria are finally

achieved in the eigenvector of the matrix, eigenvector = {0.299, 0.688, 0.688}with

max. The eigenvector corresponds to the weights to be associated with the member-

ships of each attribute/feature/goal. Thus, the exponential weighting is1= 0.299,

2 = 0.688, 3= 0.688 and the final decision (membership decision function) about

the site location is given as follows:

D(A) = min(G0.299, C0.6881

, C0.6882

)


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C2 = [0.4/A1, 0.2/A2, 0.9/A3]0.688 = [0.53/A1, 0.33/A2, 0.93/A3]

D(A) = (0.53/A1, 0.33/A2, 0.62/A3) .

And the optimal solution,20 corresponding to the maximum membership 0/63, is

A3(D(A) = 0.62/A3).

3. Application of Fuzzy Set Theory in Mining

In spite of many advantages of the approach, only few applications of fuzzy set

theory to mining industry problems have been reported in the literature. Some of

these applications are briefly reviewed here:

Nguyen et al.

17,18

studied some fuzzy set applications in mining geomechanicsand determining fuzziness of rock mass classification.

Bandopadhyay et al.1,2 developed fuzzy algorithm for selection of post-mining

uses of land and for decision making in mining engineering.

Bandopadhyay3 indicated partial ranking of primary stripping equipment in sur-

face mine planning and fuzzy algorithm. It deals with the process of ranking

alternatives after determining their rating. Determining the optimal decision al-

ternatives, when the results are crisp, is straightforward (just select the alter-

native with the highest support). It also considers that the supports for each

alternative are themselves fuzzy sets. Therefore, in order to select the bestalternative more sophisticated methods of comparison are needed.

Gershon et al.8 studied mining method selection: a decision support system in-

tegrating multi-attribute utility theory and expert systems.

Herzoget al.9 indicated ranking of optimum beneficiation methods via the analyt-

ical hierarchy process. This process measures relative fuzziness by structuring

the criteria and objectives of a system, hierarchically, in a multiple attribute

framework.

Bascetin et al.5 studied the application of fuzzy boolean linear programming

technique to solve problems of selective mining. Boolean linear programming

problems deal with problems of maximizing or minimizing a function of many

variables subject to inequality and equality constraints and integrality restrictions

on some or all of the variables (boolean variables). To have some difficulties when

modelling a real world problem by means of a boolean programming problem is

normal. One of such difficulties is either in the fact that goals and constraints

are often represented by the vague linguistic form or in the fact that the pa-

rameters are not known exactly. Often in a real world problem a decision-maker

or an expert gives approximate estimates about the true values of the objective

coefficients rather than the exact values of these, moreover those estimates can

be given with some vagueness.

Bascetin et al.6 handled the study of a fuzzy set theory for the selection of an


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BLACK SEA

merli Dam

Fig. 2. Location of the mine site.

4. Case Studies

In order to demonstrate the potential for this approach, two case studies are rep-

resented. They show how fuzzy multiple attribute decision making can be used to

optimise the best system (method) among the alternatives under various sets of

criteria. The work detailed in this paper has been based on the brown coal (lignite)

mine situated in Black Sea coast at North-west of Arnavutkoy, Istanbul, Turkey

(see Fig. 2). There two mine site are in this region: existing open pit mine and

future planning underground mine.

Case I:

In this case study, some research has been conducted on loading-hauling systems for

overburden removal of an open-pit coal mine. Technical parameters of the working

site, which affect the systems, have been evaluated thoroughly and summarised

below in detail.

The mine site is of average size, with a pit area of 600 by 350 m and a total

of 60 m of overburden being removed in six 10 m high benches. The mine will beworked over 8 years at the rate of one ten-hour shift per day, seven days a week for

300 days per year, the scheduled operating time being 3000 h/year. The average

coal production is planned to be 550,000 t/year, which implies an average annual

overburden removal of 2,200,000 m3, i.e. the economic mine life is based on a 4:1

stripping ratio.

The average rain and temperatures are varying between 1074-mm and 717 mm,

30C and 4C, respectively. The maximum daily rain fall is resulting in 76 to

101 mm/day between in August and September. Winds in the pit can exceeds

80 km/h. Snow removal obviously delays equipment movements during the winter

varying between 15 and 30 days and fog can affect operations 20 to 30 days per

year.


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Table 1. Technical parameters calculated for each system.

Overburden 2,200,000 m3/year

Active workday 7 days/week, 300 days/year, 10 h/day (1 shift/day)

Overburden material Sand, sandstone, clay

Rock density 1.2 ton/m3

Overburden thickness 20 to 60 m (2 to 5 benches)

Soil property Moisture

Blasting None

Haulage distance 900 to 1000 m

Average grade resistance 4%

Average rolling resistance 3%

Digging level Front Shovel: 11 m Loader: 6.57 m

Dump level Front Shovel: 7.5 m Loader: 3.72 m, Truck (LoadingHeight: 3.10 m).

Bucket capacity Shovel: 4 m3, Loader: 6 m3

Bucket fill factor 90%

Belt conveyor 4 m/sec speed, 370 m long total, 900 mm wide

In-pit crusher Two 400 ton/hour capacity

Operating weight Front Shovel: 83,800 kg Loader: 45,297 kg Truck: 31,250 kg

Useful life Front Shovel: 25,000 h Loader: 20,000 h Truck: 15,000 h

Conveyor: 25,000 h

Loading time Front Shovel: 21 sec Loader: 30 sec

Cycle time Truck: 230 sec

Capital cost Front Shovel: $550,000, Loader: $400,000, Truck: $270 000,In-pit crusher and belt conveyor: $1,900,000

Operating cost A1 = $0.67/m3, A2 = $0.72/m3, A3 = $0.62/m3

conveyor (A3) systems. The characteristic of the mine-site and the equipment spec-

ifications are given in Table 1.

The following are some of the given linguistic results produced from various so-lution methods (linear programming, expert systems, etc.) and therefore presented

by the experts to questions posed (what if. . . ? or if. . . ?, etc.) Each system has

shown its own advantages. In this case, it did not appear that an easy solution to

the problem could be obtained. From the solution point of view, application of the

fuzzy set theory would be a proper choice, and therefore used in this paper.

The overburden thickness is thin, so A1 is better to choose.

The road conditions differ from season to season. Thus the rolling resistance gives

rather low point in dry season while it reaches the high in winter. Diggibility is not being difficult so the front-shovel can be selected unhesitatingly.

The front shovel as regards to the ground condition has more advantage (it is


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Maximum material size is about 1 m. This shows the truck haulage to good

advantage from the loading point of view.

The front-shovel is a much better excavator in terms of the bench planned tohave a 10 m height.

All combinations (systems) are suitable in regard to the height of dump but the

front-shovel can make much more safe loading.

The haulage distance varies between 900 and 1000 m. In this case, A3 can be

considered as a better combination of loading-hauling system.

A3 is the better system in terms of the working stability.

A2 has the lowest capital cost.

A1 andA2 are the best alternatives in terms of the mobility in the system.

A3 is more suitable according to haulage capacity.

The criteria of each operation is summarised in Table 2 and in the following, an

optimum loading-hauling system selection procedure is given.

Let A = {A1, A2, A3} be the set of alternative systems and C = {C1, C2,

C3, . . . , C m} be the set of criteria. The decision-maker is then asked to define the

membership grade of each criterion that is conferred with experts on this subject.

Following that procedure the membership grade of each criterion is given in detail:

C1 ={0.85/A1, 0.80/A2, 0.90/A3} C14 ={0.90/A1, 0.85/A2, 0.95/A3}

C2 ={0.90/A1, 0.65/A2, 0.92/A3} C15 ={0.95/A1, 0.95/A2, 0.80/A3}C3 ={0.95/A1, 0.80/A2, 0.95/A3} C16 ={0.80/A1, 0.80/A2, 0.95/A3}

C4 ={0.95/A1, 0.95/A2, 0.75/A3} C17 ={0.90/A1, 0.90/A2, 0.92/A3}

C5 ={0.90/A1, 0.85/A2, 0.92/A3} C18 ={0.88/A1, 0.88/A2, 0.95/A3}

C6 ={0.85/A1, 0.85/A2, 0.90/A3} C19 ={0.87/A1, 0.83/A2, 0.90/A3}

C7 ={0.90/A1, 0.70/A2, 0.90/A3} C20 ={0.97/A1, 0.93/A2, 0.85/A3}

C8 ={0.90/A1, 0.80/A2, 0.90/A3} C21 ={0.80/A1, 0.75/A2, 0.88/A3}

C9 ={0.95/A1, 0.80/A2, 0.95/A3} C22 ={0.72/A1, 0.68/A2, 0.80/A3}

C10 ={0.87/A1, 0.85/A2, 0.95/A3} C23 ={0.82/A1, 0.80/A2, 0.92/A3}

C11 ={0.85/A1, 0.95/A2, 0.75/A3} C24 ={0.85/A1, 0.82/A2, 0.79/A3}C12 ={0.90/A1, 0.85/A2, 0.95/A3} C25 ={0.85/A1, 0.75/A2, 0.95/A3}

C13 ={0.90/A1, 0.88/A2, 0.92/A3} C26 ={0.90/A1, 0.95/A2, 0.80/A3}.

Additionally, the mxm matrix (Fig. 3) was constructed to express the decision-

makers empirical estimate of importance for each criterion. Then, the maximum

eigenvector was obtained using the Matlab16 (version 5.0). The judgment scale

used here as: 1 equally important; 1.5 weakly more important; 2 strongly more

important; 2.5 demonstrably more important; 3 absolutely more important.

Hence, the maximum eigenvalue of the reciprocal matrix is = 27.2357. The

weights of the criteria are finally obtained in the eigenvector of the matrix. Eigen

vector = {0.1055, 0.1214, 0.1520, 0.1165, 0.1440, 0.1063, 0.1569, 0.1143, 0.1905,


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Table 2. Criteria of each operation.

Criterion Operation Criterion Operation

C1 Production C14 Cycle Time

C2 Overburden thickness C15 Moisture

C3 Digging Condition C16 Environment

C4 Material Size C17 Grade

C5 The Ground Condition C18 Rolling Resistance

C6 Haul Road Condition C19 Weather Conditions

C7 The Height of Digging C20 Flexibility

C8 The Height of Dump C21 Availability

C9 Working Stability C22 UtilisationC10 Haulage Distance C23 Continuous

C11 Mobility C24 Support

C12 Haulage Capacity C25 Capital Cost

C13 Economic Life C26 Operating Cost

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C 11 C 12 C 13 C 14 C 15 C 16 C 17 C 18 C 19 C 20 C 21 C 22 C 23 C 24 C 25 C 26

C1 1 1/2 1 1/2,5 1 /2 1 1/3 1 /1,5 1 /2 1 1/1,5 1/2,5 1 /2 1/3 1 1 1,5 1 /1,5 1 /2 1 /2,5 1 /2 1 /2,5 1/1,5 1/1,5 1/1,5 1 /2

C2 2 1 1,5 2 1 1 1 1,5 1/2 1/2 1/2,5 1/3 1/2,5 1/3 1/1,5 1,5 1/1,5 1/1,5 1 1/2 1/2 1/3 1/1,5 1/2 1/2 1/2,5

C3 1 1/1,5 1 1 1/1,5 2 1/2 2 1/1,5 1 1/2,5 1/1,5 1/2,5 1 2 1,5 2 1,5 1/1,5 1/2 1/2 1/1,5 1 1 1 1/1,5

C4 2,5 1/2 1 1 1 2 1/2,5 1,5 1/1,5 1/2 1/3 1/2,5 1/2 1/3 1,5 1 1 1 1/1,5 1/2,5 1/2,5 1/2 1/2 1/1,5 1/2,5 1/3

C5 2 1 1,5 1 1 2 1 1,5 1/1,5 1,5 1/1,5 1/1,5 1/2 1/2,5 2 1,5 1,5 1 1 1/2 1/2 1/2,5 1/2 1/1,5 1/2 1/2,5

C6 1 1 1/2 1/2 1/2 1 1/2 1/1,5 1/2 1 1/2 1/2,5 1/2,5 1/1,5 2 1/1,5 1 1 1 1/2,5 1/2,5 1/2 1/1,5 1/1,5 1/2,5 1/3

C7 3 1 2 2,5 1 2 1 1,5 2 1 1/2 1/2 1/2,5 1/2 1 1,5 1,5 1,5 1/1,5 1/2 1/2 1/2 1/1,5 1/2 1/2,5 1/3

C8 1, 5 1/1,5 1 ,5 1 /1, 5 1/1,5 1 ,5 1 /1,5 1 1/2 1 1/2,5 1 /3 1 /2,5 1 /2 1 1,5 1,5 1 /1,5 1 1/2 1/2 1 /2,5 1 /2 1/2 1 /2,5 1 /3

C9 2 2 1,5 1,5 1,5 2 1/2 2 1 2 1 1/1,5 1/1,5 1/2 2,5 2 2 1,5 2 1/1,5 1/1,5 1/1,5 1 1 1/1,5 1/2,5

C10 1 2 1 2 1/1,5 1 1 1 1/2 1 1/2 1/2,5 1/2,5 1/1,5 2 1,5 1,5 1,5 1,5 1/2 1/2 1/2 1/1,5 1/1,5 1/2 1/3

C11 1,5 2,5 2,5 3 1,5 2 2 2,5 1 2 1 1 1/1,5 1 2,5 2 2 2,5 2,5 1/1,5 1/1,5 1/2 1 1,5 1/1,5 1/2

C12 2 ,5 3 1,5 2,5 1,5 2,5 2 3 1,5 2,5 1 1 1 1,5 1,5 1 1 1 1/1,5 1/2,5 1/2,5 1/2,5 1/1,5 1/2 1/1,5 1/2,5

C13 2,5 3 1,5 2,5 1,5 2,5 2 3 1,5 2,5 1 1 1 1,5 2 2 2,5 2,5 2 1/2 1/1,5 1/1,5 1,5 2 1/1,5 1/2,5

C14 3 3 1 3 2,5 1,5 2 2 2 1,5 1 1/1,5 1/1,5 1 1/1,5 1 2 1,5 1/2 1/2,5 1/2 1/2,5 1/1,5 1/1,5 1/2 1/3

C 15 1 1 ,5 1/ 2 1 /1, 5 1 /2 1 /2 1 1 1/ 2, 5 1 /2 1/ 2, 5 1 /1, 5 1 /2 1, 5 1 1 /1, 5 1/ 1, 5 1/ 1, 5 1/ 1, 5 1 /3 1/ 2, 5 1 /2, 5 1 /2 1/ 1, 5 1/ 2, 5 1 /3

C16 1 1/1,5 1/1,5 1 1/1,5 1 ,5 1 /1,5 1/1, 5 1/2 1 /1,5 1 /2 1 1/2 1 1,5 1 1 1/1,5 1 1/2,5 1/2,5 1/2,5 1 /2 1/2 1/2 1 /2, 5

C17 1/1,5 1 ,5 1/2 1 1/1,5 1 1/ 1,5 1/1,5 1 /2 1 /1,5 1 /2 1 1/2,5 1 /2 1,5 1 1 1/1,5 1/1,5 1/2,5 1 /2 1/2 1/2 1/2 1 /2,5 1 /3

C18 1, 5 1,5 1 /1,5 1 1 1 1/ 1,5 1 ,5 1 /1,5 1/1,5 1/2,5 1 1/2,5 1/1,5 1 ,5 1,5 1,5 1 1/1,5 1/2,5 1 /2 1/2 1/2 1/2 1 /2,5 1 /3

C19 2 1 1,5 1,5 1 1 1,5 1 1/2 1/1,5 1/2,5 1,5 1/2 2 1,5 1 1,5 1,5 1 1/2,5 1/2 1/2 1/1,5 1/2 1/2 1/2,5

C20 2,5 2 2 2,5 2 2,5 2 2 1,5 2 1,5 2,5 2 2,5 3 2,5 2,5 2,5 2,5 1 1 1/1,5 1,5 1 1 1/1,5

C21 2 2 2 2,5 2 2,5 2 2 1,5 2 1,5 2,5 1,5 2 2,5 2,5 2 2 2 1 1 1/1,5 1,5 1,5 1/1,5 1/2

C22 2,5 3 1,5 2 2,5 2 2 2,5 1,5 2 2 2,5 1,5 2,5 2,5 2,5 2 2 2 1,5 1,5 1 2 2 1,5 1

C23 1,5 1,5 1 2 2 1,5 1,5 2 1 1,5 1 1,5 1/1,5 1,5 2 2 2 2 1,5 1/1,5 1/1,5 1/2 1 1,5 1/1,5 1/2

C24 1,5 2 1 1,5 1,5 1,5 2 2 1 1,5 1/1,5 2 1/2 1,5 1,5 2 2 2 2 1 1/1,5 1/2 1/1,5 1 1/2 1/2,5

C25 1,5 2 1 2,5 2 2,5 2 ,5 2,5 1,5 2 1,5 1,5 1 2 2,5 2 2,5 2,5 2 1 1,5 1/1,5 1,5 2 1 1/2

C26 2 2,5 1,5 3 2,5 3 3 3 2,5 3 2 2,5 1,5 3 3 2,5 3 3 2,5 1,5 2 1 2 2,5 2 1

Fig. 3. Criteria comparison.

The eigenvector corresponds to the weights to be associated with the mem-

berships of each attribute/feature/goal. Thus, the exponential weighting is 1 =

0.1055, 2 = 0.1214, 3 = 0.1520, 4 = 0.1165, 5 = 0.1440, 6 = 0.1063,


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0.1239, 19 = 0.1508, 20 = 0.2905, 21 = 0.2697, 22 = 0.3182, 23 = 0.2031,

24 = 0.1980, 25 = 0.2694, 26 = 0.3723 and the final decision is obtained as

follows:

D(A) = min(C1(A)1, C2(A)

2, . . . , Cm(Am)

for > 0 and the optimal decision

D(A) = maxAD(A) whereA

is the optimal decision.

C1 ={0.85/A1, 0.80/A2, 0.90/A3}0.1055 ={0.98/A1, 0.98/A2, 0.99/A3}

C2 ={0.90/A1, 0.65/A2, 0.92/A3}0.1214 ={0.99/A1, 0.94/A2, 0.99/A3}

C3 ={0.95/A1, 0.80/A2, 0.95/A3}0.1520

={0.99/A1, 0.97/A2, 0.99/A3}C4 ={0.95/A1, 0.95/A2, 0.75/A3}0.1165 ={0.99/A1, 0.99/A2, 0.97/A3}

C5 ={0.90/A1, 0.85/A2, 0.92/A3}0.1440 ={0.98/A1, 0.98/A2, 0.99/A3}

C6 ={0.85/A1, 0.85/A2, 0.90/A3}0.1063 ={0.98/A1, 0.98/A2, 0.99/A3}

C7 ={0.90/A1, 0.70/A2, 0.90/A3}0.1569 ={0.98/A1, 0.94/A2, 0.98/A3}

C8 ={0.90/A1, 0.80/A2, 0.90/A3}0.1143 ={0.99/A1, 0.97/A2, 0.99/A3}

C9 ={0.95/A1, 0.80/A2, 0.95/A3}0.1905 ={0.99/A1, 0.96/A2, 0.99/A3}

C10 ={0.87/A1, 0.85/A2, 0.95/A3}0.1387 ={0.98/A1, 0.98/A2, 0.99/A3}

C11 ={0.85/A1, 0.95/A2, 0.75/A3}0.2297 ={0.96/A1, 0.98/A2, 0.94/A3}

C12

={0.90/A1

, 0.85/A2

, 0.95/A3

}

0.1980

={0.98/A1

, 0.97/A2

, 0.99/A3

}C13 ={0.90/A1, 0.88/A2, 0.92/A3}0.2481 ={0.97/A1, 0.97/A2, 0.98/A3}

C14 ={0.90/A1, 0.85/A2, 0.95/A3}0.1877 ={0.98/A1, 0.97/A2, 0.99/A3}

C15 ={0.95/A1, 0.95/A2, 0.80/A3}0.1045 ={0.99/A1, 0.99/A2, 0.98/A3}

C16 ={0.80/A1, 0.80/A2, 0.95/A3}0.1138 ={0.97/A1, 0.97/A2, 0.99/A3}

C17 ={0.90/A1, 0.90/A2, 0.92/A3}0.1074 ={0.99/A1, 0.99/A2, 0.99/A3}

C18 ={0.88/A1, 0.88/A2, 0.95/A3}0.1239 ={0.98/A1, 0.98/A2, 0.99/A3}

C19 ={0.87/A1, 0.83/A2, 0.90/A3}0.1508 ={0.98/A1, 0.97/A2, 0.98/A3}

C20 ={0.97/A1, 0.93/A2, 0.85/A3}0.2905 ={0.99/A1, 0.98/A2, 0.95/A3}

C21 ={0.80/A1, 0.75/A2, 0.88/A3}0.2697 ={0.94/A1, 0.92/A2, 0.97/A3}

C22 ={0.72/A1, 0.68/A2, 0.80/A3}0.3182 ={0.90/A1, 0.88/A2, 0.93/A3}

C23 ={0.82/A1, 0.80/A2, 0.92/A3}0.2030 ={0.96/A1, 0.95/A2, 0.98/A3}

C24 ={0.85/A1, 0.82/A2, 0.79/A3}0.1980 ={0.97/A1, 0.96/A2, 0.95/A3}

C25 ={0.85/A1, 0.75/A2, 0.95/A3}0.2694 ={0.96/A1, 0.93/A2, 0.99/A3}

C26 ={0.90/A1, 0.95/A2, 0.80/A3}0.3723 ={0.96/A1, 0.98/A2, 0.92/A3}

D(A}= {0.90/A1, 0.88/A2, 0.92/A3} and the optimal solution is,

D(A) = 0.92/A3 .

Case II:

This study has been done by Karadogan et al.11 for searching the optimum under-


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Table 3. Technical parameters determined as selection criterion.

Geometric shape of the lignite deposit Plate state (layered)

Thickness of the lignite seam 2.1 m (average)

Seam inclination 7

Ore depth 50 m (average)

Soundness degree of the lignite Low strength

Contact state of hanging and foot wall Not clear

Hanging wall Clay, low strength (compressivestrength: 2.2 kg/cm2)

Foot wall Clay, low strength (compressivestrength: 2.2 kg/cm2)

Subsidence effect Risky (seam is close to surface)Roof support Necessary

Settlement area Exist over the coal seam

Combustion Combustible coal properties

Ground water Exist because of the sea

Black Sea open pit mining may be restricted in the future. Therefore, application

of one of the underground mining methods is unavoidable for producing coal.

The needed physical parameters such as geologic and geotechnique propertiesof ore, hanging and foot wall, economic effects, environmental impacts, which are

established with field and laboratory tests together with other uncertain variables

were determined. The generated parameters for the method selection are given

briefly in Table 3 together with related criterion.

Initial analysis of the method selection system suggests the following alterna-

tives: longwall with filling (direction of inclination rising) (A1), longwall with filling

(direction of inclination decline) (A2), longwall with filling (progressed) (A3), long-

wall with filling (returned) (A4), or room and pillar with filing (A5) systems.

Some of the linguistic results produced as follows:

According to dimension, A3 is the best method.

Seam thickness is average 2.1 meters, therefore A3 can be chosen.

A5 is suitable in terms of seam inclination.

A5 is more safety according to soundness degree of the hanging wall.

From the viewpoint of safety of ground water A1 can be best choice.

Before underground mining method selection procedure, the following eighteen

criteria of each operation have been considered in the decision making (Table 4).

At the end of the evaluations (determining the membership grade of each crite-

rion and building mxm matrix, obtaining the maximum eigenvalue of the reciprocal


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Table 4. Criteria of each operation.

Criterion Operation Criterion Operation

C1 Geometric shape of the deposit C10 Roof support

C2 Coal thickness C11 Settlement area

C3 Seam inclination C12 Combustion

C4 Ore depth C13 Methane existence

C5 Soundness degree of the lignite C14 Ground water

C6 Contact state of the lignite seam C15 Mining cost

C7 Soundness degree of the hanging wall C16 Capital cost

C8 Soundness degree of the foot wall C17 Production ratio

C9 Subsidence effect C18 Labour cost

D(A) ={0.81/A1, 0.79/A2, 0.89/A3, 0.87/A4, 0.92/A5}

And the optimal solution is,

D(A) = 0.92/A5.

In conclusion, room and pillar method with filling (A5) resulted in more suitable

method with 0.92 membership degree than others.

5. Conclusions

By the development of computer technology and programming of colloquial lan-

guage with expert systems have considerably reduced decision makers burden.

Thus, this paper has discussed decision making in a fuzzy environment for solving

multiple attribute problems of optimum equipment selection in surface mining and

optimum underground mining method selection. The most important approaches

and basic concepts were introduced. Since the focus is on fuzzy multiple attribute

problems, a detailed discussion of the most important methods for solving these

problems was presented.

Fuzzy multiple attribute decision making can result in final design that is more

practical and financially efficient than conventional approaches. Inclusion of real

operating constraints during the optimisation process as opposed to the normal

technique of cyclic modification of optimal conditions offers potential savings in

design times and costs. The method proposed can be programmed to run effectively

on relatively low cost computing systems, thus providing the potential for wide

spread exploitation of the technique within the mining industry worldwide.

References

1 S B d dh d A Ch tt dh S l ti f t i i f l d i


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