Fuzzy multiple criteria decision making: Recent …rfuller/fs13.pdf · · 2011-08-28a basis for more systematic and rational decision making with multiple criteria, ... fuzzy mathematical

Fuzzy multiple criteria decision making: Recentdevelopments ∗

Christer [email protected]

Robert [email protected]

Abstract

Multiple Criteria Decision Making (MCDM) shows signs of becoming a maturing field. There arefour quite distinct families of methods: (i) the outranking, (ii) the value and utility theory based, (iii)the multiple objective programming, and (iv) group decision and negotiation theory based methods.Fuzzy MCDM has basically been developed along the same lines, although with the help of fuzzy settheory a number of innovations have been made possible; the most important methods are reviewedand a novel approach - interdependence in MCDM - is introduced.

1 Introduction

Multiple Criteria Decision Making was introduced as a promising and important field of study in theearly 1970’es. Since then the number of contributions to theories and models, which could be used asa basis for more systematic and rational decision making with multiple criteria, has continued to growat a steady rate. A number of surveys, cf e.g. Bana e Costa [2], show the vitality of the field and themultitude of methods which have been developed. When Bellman and Zadeh, and a few years laterZimmermann, introduced fuzzy sets into the field, they cleared the way for a new family of methods todeal with problems which had been inaccessible to and unsolvable with standard MCDM techniques.There are many variations on the theme MCDM depending upon the theoretical basis used for the mod-elling. Zeleny [135] shows that multiple criteria include both multiple attributes and multiple objectives,and there are two major theoretical approaches built around multiple attribute utility theory (MAUT) andmultiple objective linear programming (MOLP), which have served as basis for a number of theoreticalvariations. Bana e Costa and Vincke [3] argue that with MCDM the first contributions to a truly scientificapproach to decision making were made, but find fault with the objectives to carry this all the way aswe have to deal with human decision makers who can never reach the degree of consistency needed.They introduce multiple criteria decision aid MCDA as a remedy; this approach can be given the aim”to enhance the degree of conformity and coherence” in the decision processes carried out among (pre-dominantly groups of) decision makers - this is done with a cross-adaptation of the value systems andthe objectives of those involved in the process. Even if there are some distinctions between MCDM andMCDA the overall objective is the same: to help decision makers solve complex decision problems in asystematic, consistent and more productive way.There are four major families of methods in MCDM: (i) the outranking approach based on the pioneeringwork by Bernard Roy, and implemented in the Electre and Promethee methods; (ii) the value and utilitytheory approaches mainly started by Keeney and Raiffa, and then implemented in a number of methods;

∗The final version of this paper appeared in: C. Carlsson and R. Fuller, Fuzzy multiple criteria decision making: Recentdevelopments, Fuzzy Sets and Systems, 78(1996) 139-153. doi: 10.1016/0165-0114(95)00165-4

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a special method in this family is the Analytic Hierarchy Process (AHP) developed by Thomas L. Saatyand then implemented in the Expert Choice software package; (iii) the largest group is the interactivemultiple objective programming approach with pioneering work done by P.L.Yu, Stanley Zionts, MilanZeleny, Ralph Steuer and a number of others; the MOLP family has been built around utility theory-based trade offs among objectives, with reference point techniques, ideal points, etc and the models havehad a number of features including stochastic and integer variables; one of the best interactive methodsavailable is the VIG software package developed by Pekka Korhonen; (iv) group decision and negotiationtheory introduced new ways to work explicitly with group dynamics and with differences in knowledge,value systems and objectives among group members.When fuzzy set theory was introduced into MCDM research the methods were basically developed alongthe same lines. There are a number of very good surveys of fuzzy MCDM (cf [26, 49, 75, 89, 105] andRibeiro’s contribution in this issue), which is why we will not go into details here but just point to someessential contributions. One of the good surveys is done by Chen and Hwang [26]: they make distinctionsbetween fuzzy ranking methods and fuzzy multiple attribute decision making methods, which contain allthe families (i)- (iv) listed above.The first category contains a number of ways to find a ranking: degree of optimality (Baas-Kwakernaak,Watson, Baldwin-Guild), Hamming distance (Yager, Kerre, Nakamura, Kolodziejczyk, -cuts Adamo,Buckley-Chanas, Mabuchi), comparison function (Dubois-Prade, Tsukamoto, Delgado), fuzzy mean andspread (Lee-Li), proportion to the ideal) McChahone, Zeleny), left and right scores (Jain, Chen, Chen-Hwang), centroid index (Yager, Murakami), area measurement (Yager), and linguistic ranking methods(Efstathiou-Tong, Tong-Bonissone).The second category is built around methods which utilize various ways to assess the relative impor-tance of multiple attributes: fuzzy simple additive weighting methods (Baas-Kwakernaak, Kwaakernak,Dubois-Prade, Chen-McInnis, Bonissone), analytic hierarchy process (Saaty, Laarhoven-Pedrycz, Buck-ley), fuzzy conjunctive / disjunctive methods (Dubois, Prade, Testemale), fuzzy outranking methods(Roy, Sisko, Brans, Takeda), and maximin methods (Bellman-Zadeh, Yager).The category with the most frequent contributions is, of course, fuzzy mathematical programming.Inuiguchi et al [55] give a useful survey of recent developments in fuzzy programming in which theywork with the following families of applications: flexible programming (Tanaka, Zimmermann, Sakawa-Yano), possibilistic programming (Tanaka, Tanaka-Asai, Dubois, Dubois-Prade), possibilistic linearprogramming using fuzzy max (Dubois-Prade, Tanaka, Ramik-Rimanek, Rommelfanger, Luhandjula,Inuiguchi-Kume), robust programming (Dubois-Prade, Negoita, Soyster), possibilistic programmingwith fuzzy preference relations (Orlovski), possibilistic linear programming with fuzzy goals (Inuiguchi,Tanaka, Buckley).In order to introduce some of the key issues in fuzzy multiple criteria decison making we will workthrough a number of examples with a novel approach we have recently introduced (cf Carlsson-Fuller[20]), a method in which we allow the criteria to be interdependent. Then we will a give a brief overviewof the contributions to this issue and close with a fairly comprehensive list of recent publications on fuzzyMCDM problems.

2 Decision-making with interdependent criteria

P.L. Yu explains that we have habitual ways of thinking, acting, judging and responding, which whentaken together form our habitual domain (HD) [134]. This domain is very nicely illustrated with thefollowing example ([134] page 560):

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A retiring chairman wanted to select a successor from two finalists (A andB). The chairmaninvitedA andB to his farm, and gave each finalist an equally good horse. He pointed out thecourse of the race and the rules saying, ”From this point whoever’s horse is slower reachingthe final point will be the new chairman”. This rule of horse racing was outside the habitualways of thinking of A and B. Both of them were puzzled and did not know what to do.After a few minutes, A all of a sudden got a great idea. he jumped out of the constraint ofhis HD. He quickly mounted B’s horse and rode as fast as possible, leaving his own horsebehind. When B realized what was going on, it was too late. A became the new chairman.

Part of the HD of multiple criteria decision-making is the intuitive assumption that all criteria are in-dependent; this was initially introduced as a safeguard to get a feasible solution to a multiple criteriaproblem, as there were no means available to deal with interdependence. Then, gradually, conflicts wereintroduced as we came to realize that multiple goals or objectives almost by necessity represent conflict-ing interests [135, 126]. Here we will ”jump out of the constraints” of the HD of MCDM and leave outthe assumption of independent criteria.Decision-making with interdependent multiple criteria is a surprisingly difficult task. If we have clearlyconflicting objectives there normally is no optimal solution which would simultaneously satisfy all thecriteria. On the other hand, if we have pair-wisely supportive objectives, such that the attainment ofone objective helps us to attain another objective, then we should exploit this property in order to findeffective optimal solutions.In their classical text Theory of Games and Economic Behavior John von Neumann and Oskar Morgen-stern (1947) described the problem with interdependence; in their outline of a social exchange economythey discussed the case of two or more persons exchanging goods with each others (page 11):

. . . then the result for each one will depend in general not merely upon his own actionsbut on those of the others as well. Thus each participant attempts to maximize a function. . . of which he does not control all variables. This is certainly no maximum problem,but a peculiar and disconcerting mixture of several conflicting maximum problems. Everyparticipant is guided by another principle and neither determines all variables which affecthis interest.

This kind of problem is nowhere dealt with in classical mathematics. We emphasize at the risk of beingpedantic that this is no conditional maximum problem, no problem of the calculus of variations, offunctional analysis, etc. It arises in full clarity, even in the most ”elementary” situations, e.g., when allvariables can assume only a finite number of values.This interdependence is part of the economic theory and all market economies, but in most modellingapproaches in multiple criteria decision making there seems to be an implicit assumption that objectivesshould be independent. This appears to be the case, if not earlier then at least at the moment whenwe have to select some optimal compromise among a set of nondominated decision alternatives. MilanZeleny (1982) - and many others - recognizes one part of the interdependence (page 1),

Multiple and conflixting objectives, for example, ”minimize cost” and ”maximize the qual-ity of service” are the real stuff of the decision maker’s or manager’s daily concerns. Suchproblems are more complicated than the convenient assumptions of economics indicate. Im-proving achievement with respect to one objective can be accomplished only at the expenseof another.

but not the other part: objectives could support each others. We will in the following explore the conse-quences of allowing objectives to be interdependent.

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In spite of the significant developements which have taken place in both the theory and the methodologyMCDM is still not an explicit part of managerial decision-making [136]. By not allowing interdepen-dence multiple criteria problems are simplified beyond recognition and the solutions reached by the tra-ditional algorithms have only marginal interest. Zeleny also points to other circumstances [136] whichhave reduced the visibility and usefulness of MCDM: (i) time pressure reduces the number of criteria tobe considered; (ii) the more complete and precise the problem definition, the less criteria are needed; (iii)autonomous decision makers are bound to use more criteria than those being controlled by a strict hier-archical decision system; (iv) isolation from the perturbations of changing environment reduces the needfor multiple criteria; (v) the more complete, comprehensive and integrated knowledge of the problem themore criteria will be used - but partial, limited and non-integrated knowledge will significantly reducethe number of criteria; and (vi) cultures and organisations focused on central planning and collectivedecision-making rely on aggregation and the reduction of criteria in order to reach consensus.Felix [44] presented a novel theory for multiple attribute decision making based on fuzzy relations be-tween objectives, in which the interactive structure of objectives is inferred and represented explicitely.With the following example in [45] he explains the need for a detailed automated reasoning about rela-tionships between goals when we have to deal with nontrivial decision problems.

Example 1 Let us suppose that there is a decision maker who wants to earn money (goal 1) and to havefun (goal 2) simultaneously, and the only way to earn money is to work. Then at least two situations arepossible:

Situation 1: The decision maker does not like to work. Therefore, while working he will not have fun.The alternative working supports goal 1 but hinders goal 2.

Situation 2: The decision maker likes to work. Therefore, while working he will have fun. The alterna-tive working supports both goal 1 and goal 2.

Relationships between two goals are defined using fuzzy inclusion and non-inclusion between the supportand hindering sets of the corresponding goals. Felix [45] also illustrates, with an example, that thedecision-making model based on relationships between goals can be used as a powerful MADM-methodfor solving vector maximum problems.In multiple objective linear programming (MOLP), application functions are established to measure thedegree of fulfillment of the decision maker’s requirements (achievement of goals, nearness to an idealpoint, satisfaction, etc.) on the objective functions (see e.g. [35, 137]) and are extensively used in theprocess of finding ”good compromise” solutions.In [20] we demonstrated that the use of interdependences among objectives of a MOLP in the definitionof the application functions provides for more correct solutions and faster convergence. Generalizingthe principle of application functions to fuzzy multiple objective programs (FMOP) with interdependentobjectives, in [20], we have defined a large family of application functions for FMOP and illustrated ourideas by a simple three-objective program. Let us now discuss our approach to interdependent MCDM.In [20] we have introduced interdependences among the objectives of a crisp multi-objective program-ming problem and developed a new method for finding a compromise solution by using explicitely theinterdependences among the objectives and combining the results of [17, 19, 35, 137].Consider the following problem

maxx∈X

{f1(x), . . . , fk(x)

}(1)

where fi : Rn → R are objective functions, x ∈ Rn is the decision variable, and X is a subset of Rn

without any additional conditions for the moment.

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Definition 1 Let fi and fj be two objective functions of (1). We say that

• fi supports fj on X (denoted by fi ↑ fj) if fi(x′) ≥ fi(x) entails fj(x′) ≥ fj(x), for allx′, x ∈ X;

• fi is in conflict with fj on X (denoted by fi ↓ fj) if fi(x′) ≥ fi(x) entails fj(x′) ≤ fj(x), for allx′, x ∈ X;

• fi and fj are independent on X , otherwise.

Figure 1: A typical example of conflict on R.

Figure 2: Supportive functions on R.

Let fi be an objective function of (1). Then we define the grade of interdependency, denoted by ∆(fi),of fi as

∆(fi) =∑

fi↑fj ,i 6=j

1−∑fi↓fj

1, i = 1, . . . , k. (2)

If ∆(fi) is positive and large then fi supports a majority of the objectives, if ∆(fi) is negative and largethen fi is in conflict with a majority of the objectives, if ∆(fi) is positive and small then fi supportsmore objectives than it hinders, and if ∆(fi) is negative and small then fi hinders more objectives thanit supports. Finally, if ∆(fi) = 0 then fi is independent from the others or supports the same number ofobjectives as it hinders.Following [137, 35] we introduce an application function

hi : R→ [0, 1]

such that hi(t) measures the degree of fulfillment of the decision maker’s requirements about the i-th objective by the value t. In other words, with the notation of Hi(x) = hi(f(x)), Hi(x) may beconsidered as the degree of membership of x in the fuzzy set ”good solutions” for the i-th objective.Then a ”good compromise solution” to (1) may be defined as an x ∈ X being ”as good as possible”for the whole set of objectives. Taking into consideration the nature of Hi(.), i = 1, . . . k, it is quitereasonable to look for such a kind of solution by means of the following auxiliary problem

maxx∈X

{H1(x), . . . ,Hk(x)

}(3)

As max{H1(x), . . . ,Hk(x)

}may be interpreted as a synthetical notation of a conjuction statement

(maximize jointly all objectives) and Hi(x) ∈ [0, 1], it is reasonable to use a t-norm T [108] to representthe connective AND. In this way (3) turns into the single-objective problem

maxx∈X

T (H1(x), . . . ,Hk(x)).

There exist several ways to introduce application functions [59]. Usually, the authors consider increasingmembership functions (the bigger is better) of the form

hi(t) =

1 if t ≥Mi

vi(t) if mi < t < Mi

0 if t ≤ mi

(4)

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where mi := minx∈X fi(x) is the independent mimimum and Mi := maxx∈X fi(x) is the independentmaximum of the i-th criterion.As it has been stated before, our idea is to use explicitely the interdependences in the solution method.To do so, first we define Hi by

Hi(x) =

1 if fi(x) ≥Mi

1−Mi − fi(x)Mi −mi

if mi < fi(x) < Mi

0 if fi(x) ≤ mi

i.e. all membership functions are defined to be linear.

Figure 3: Linear membership function.

Then from (2) we compute ∆(fi) for i = 1, . . . , k, and we change the shapes of Hi according to thevalue of ∆(fi) as follows(1) If ∆(fi) = 0 then we do not change the shape.(2) If ∆(fi) > 0 then instead of the linear membership function we use

Hi(x,∆(fi)) =

1 if fi(x) ≥Mi(1−

Mi − fi(x)Mi −mi

)1/(∆(fi)+1)

if mi < fi(x) < Mi

0 if fi(x) ≤ mi

(3) If ∆(fi) < 0 then instead of the linear membership function we use

Hi(x,∆(fi)) =

1 if fi(x) ≥Mi(

1−Mi − fi(x)Mi −mi

)|∆(fi)|+1

if mi < fi(x) < Mi

0 if fi(x) ≤ mi

Then we solve the following auxiliary problem

maxx∈X

T (H1(x,∆(f1)), . . . ,Hk(x,∆(fk))) (5)

Let us suppose that we have a decision problem with many (k ≥ 7) objective functions (cf Example 2).It is clear (due to the interdependences between the objectives), that we will find optimal compromisesolutions rather closer to the values of independent minima than maxima.The basic idea of introducing this type of shape functions can be explained then as follows: if we manageto increase the value of the i-th objective having a large positive ∆(fi) then it entails the growth of themajority of criteria (because it supports the majority of the objectives), so we are getting essentiallycloser to the optimal value of the scalarizing function (because the losses on the other objectives are notso big, due to their definition).The efficiency of the obtained compromise solutions can be shown by using the results from [35].

Figure 4: Concave membership function.

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Let us now consider a fuzzy version of (1)

maxx∈X

{f1(x), . . . , fk(x)

}(6)

where F(R) denotes the family of fuzzy numbers, fi : Rn → F(R) (i.e. a fuzzy-number-valued func-tion) and X ⊂ Rn.An application function for the FMOP of (6) is defined as

hi : F(R)→ [0, 1]

such that hi(t) measures the degree of fulfillment of the decision maker’s requirements about the i-thobjective by the (fuzzy number) value t. In other words, with the notation of

Hi(x) = hi(fi(x)),

Hi(x) may be considered as the degree of membership of x in the fuzzy set ”good solutions” for the i-thfuzzy objective.To construct such application functions for FMOP problems is usually not an easy task. Suppose thatwe have two reference points from F(R), denoted by mi and Mi, which represent undesired and desiredlevels for each objective function fi. We can now state (6) as follows: find an x∗ ∈ X such that fi(x∗) isas close as possible to the desired point Mi and as far as possible from the undisered point mi, for eachi = 1, . . . , k.We suggest the use of the following family of application functions

Hi(x) = min{

1−1

1 +D(mi, fi(x)),

1

1 +D(Mi, fi(x))

}or, more generally,

Hi(x) = T

(1−

1

1 +D(mi, fi(x)),

1

1 +D(Mi, fi(x))

)(7)

where T is a t-norm, D is a metric in F(R). It is clear that the bigger the value of Hi(x) the closer thevalue of the i-th objective function to the desired level or/and further from the undesired level, and vicaversa the smaller the value of Hi(x) the closer its value to the undesired level or/and further from thedesired level.

Figure 5: Convex membership function.

In (7) the t-norm T measures the degree of satisfaction of two (conflicting) goals ”to be far from theundesired point and to be close to the desired point”. The particular t-norm T should be chosen verycarefully, because it can occur that Hi(x) attends its maximal value at a point which is very far fromthe undesired point, but not close enough to the desired point. For example, if T is the weak t-norm(T (x, y) = min{x, y} if max{x, y} = 1 and T (x, y) = 0 otherwise) then Hi(x) positive if and onlyif fi(x) = Mi, i.e. we have managed to reach completely the desired point, which is rarely the case,because Mi is not necessarily in the range of fi. Another crucial point is the relative setting of thedesired and undesired points. If D(mi, Mi) is small then it is impossible to find an x∗ ∈ X satisfyingthe condition ”fi(x) is close to Mi and is far from mi”.Then, similarly to the crisp case, FMOP (6) turns into the single-objective problem

maxx∈X

T (H1(x), . . . ,Hk(x)). (8)

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It is clear that the bigger the value of the objective function of problem (8) the closer the fuzzy functionsare to their desired levels.Similarly to the crisp case, we shall modify the application functions, Hi, i = 1, . . . , k with respect tothe interdependences among the objectives of FMOP (6).We will now define the interdependences with the help of their application functions.

Definition 2 Let fi and fj be two objective functions of (6), and let Hi and Hj be the associated appli-cation functions. We say that

(i) fi supports fj on X (denoted by fi ↑ fj) if Hi(x′) ≥ Hi(x) entails Hj(x′) ≥ Hj(x) for allx′, x ∈ X;

(ii) fi is in conflict with fj on X (denoted by fi ↓ fj) if Hi(x′) ≥ Hi(x) entails Hj(x′) ≤ Hj(x), forall x′, x ∈ X;

(iii) fi and fj are independent on X , otherwise.

Let fi be an objective function of (6) and let Hi be its application function. We define the grade ofinterdependence, denoted by ∆(fi), of fi as

∆(fi) =∑

Hi↑Hj ,i 6=j

1−∑

Hi↓Hj

1, i = 1, . . . , k. (9)

Then similarly to the crisp case, if ∆(fi) is positive and large then fi supports a majority of the objectives,if ∆(fi) is negative and large then fi is in conflict with a majority of the objectives, if ∆(fi) is positiveand small then fi supports more objectives than it hinders, and if ∆(fi) is negative and small then fi

hinders more objectives than it supports. Finally, if ∆(fi) = 0 then fi is independent from the others orsupports the same number of objectives as it hinders.It should be noted that interdependences among the fuzzy objectives of (6) strongly depend on the def-inition of their application functions. For example, if the application functions are defined in the senseof (7) then by altering the desired or/and undesired levels for the i-th objective function, it can modify∆(fi).We use explicitely the interdependences in the solution method. Namely, first we change the shape of Hi

according to the value of ∆(fi) as follows:if ∆(fi) = 0 then we do not change the shape, i.e Hi(x,∆(fi)) := Hi(x); if ∆(fi) > 0 then instead ofHi(x) we take

Hi(x,∆(fi)) := Hi(x)1/(∆(fi)+1),

finally, if ∆(fi) < 0 then instead of Hi(x) we use

Hi(x,∆(fi)) := Hi(x)|∆(fi)|+1

Then we solve the single objective problem

maxx∈X

T (H1(x,∆(f1)), . . . ,Hk(x,∆(fk))) (10)

As in the crisp case, if we manage to increase the value of the i-th objective having a large positive ∆(fi)then follows that a majority of criteria will grow (because it supports a majority of the objectives); i.e.we are getting essentially closer to the optimal value of the scalarizing function (because the losses onthe conflicting objectives are not so big, due to their definition).

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It should be noted that we can use the above principles when the objective functions of both the crisp andfuzzy MOP are known exactly. If we do not know exactly the behavoir of objectives then we should useapproximate reasoning methods to find good compromise solutions to FMCDM problems. The followingexample illustrates this case.

Example 2 In corporate takeover negotiations the Buyer and the Seller have two conflicting objectives:the Buyer wants the takeover price to be as low as possible c1, but the Seller wants it to be as high aspossible c2. There is, however, much more behind corporate takeovers. In a real case, in which twoFinnish companies were involved and finally merged, there were a number of more objectives whichcould be identified and gradually formulated.

Buyer Sellerc1 aquisition price low c2 aquistion price highc3 overall profits high c4 cash inflow highc5 investments medium c6 max corporate ROCc7 total loans low c8 RD investments high

The Seller’s objectives c4, c6, and c8 all support his objective of getting a high aquisition price; never-theless, the objectives (c4, c6), (c6, c8) and (c8, c4) are all pairwise conflicting.The Buyer’s objective c1 supports his objectives c3, c5 and c7. There is no conflict among his objectives,but the objectives c3 and c7 support each others. There is also some interaction among the Seller’s andthe Buyer’s objectives, which partly explains why they are negotiating: c3 and c4 are supporting eachothers, like c6 and c3, but c5 and c8 are conflicting:

With the notation we introduced for the interdependence above, the takeover has the following objectivestructure:

Buyer: c2 ↑ c4, c2 ↑ c6, c2 ↑ c8, c4 ↓ c6, c6 ↓ c8, c8 ↓ c4

Seller: c1 ↑ c3, c1 ↑ c5, c1 ↑ c7, c3 ↑ c7

Buyer/Seller: c3 ↑ c4, c6 ↑ c3, c5 ↓ c8

It seems clear that it would be rather difficult to find a negotiated solution which would be simultaneouslyoptimal for all the objectives, as the conflicts seem to eliminate this possibility. It should, however, benoted that the conflicts are fuzzy, as most of the objectives are given in a fuzzy form (high, medium,low), which indicates that some other solution than a simultaneous optimum for all the objectives shouldbe attempted. There are two possibilities: (i) a negotiated compromise , based on trade-offs amongthe conflicting objectives (this was carried out in an intuitive fashion in the real case), or (ii) alternateoptima for combinations of subsets of the objectives during a negotiated interval (this was also attemptedby representatives of the Seller, but without any success).Buckley and Hayashi [12] introduced fuzzy genetic algorithms to (approximately) solve fuzzy optimiza-tion problems. Fuzzy genetic algorithms look like an interesting method of producing approximatesolutions to fuzzy optimization problems when the variables can be arbitrary discrete fuzzy subsets ofcertain intervals.

3 Practical Applications

One of the earliest practical application of fuzzy multicriteria decison making is a commercial applicationfor the evaluation of the credit-worthiness of credit card applicants; this was developed eleven years ago

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in Germany [138]. Nowdays one encounters more and more real applications of FMCDM. We will inthe following briefly outline four recent applications (cf [50, 57, 86, 89, 109, 131] for others):

• Evaluation of weapon systems

• A project maturity evaluation system implemented at Mercedes-Benz in Germany

• Technology transfer strategy selection in biotechnology

• Aggregation of market research data

Cheng and Mon [28] propose a new algorithm for evaluating weapon systems by the Analytical HierarchyProcess (AHP) based on fuzzy scales. There are two basic problems in weapon system evaluation: theobjectives of the evaluations are generally multiple and generally in conflict, and the descriptions ofthe weapon systems are usually linguistic and vague. The first problem can be solved by conventionalMCDM techniques, but in order to tackle the second problem we usually need FMCDM techniques.The AHP is a very useful decision analysis tool in dealing with MCDM problems and has successfullybeen applied to many actual decision areas. The systematic procedures used by Saaty’s AHP method[95] results in a cardinal order, which can be used to select or rank alternatives. Cheng and Mon derivea simple and general algorithm for fuzzy AHP by using triangular fuzzy numbers, α-cuts and intervalarithmetic. Triangular fuzzy numbers 1 to 9 are used to build a judgement matrix through pair-wisecomparison techniques. They estimate the fuzzy eigenvectors of the judgement matrix by using an ”indexof optimism” λ indicating the degree of satisfaction of the decision maker. The proposed technique isillustrated with the selection of an anti-aircraft artillery system from several alternatives.In [1] Altrock and Krause present a fuzzy multi-criteria decision-making system for optimizing the de-sign process of truck components, such as gear boxes, axes or steering. For this optimization, it isnecessary to measure the maturity of the design process with a single parameter. The exisiting dataconsists both of numerical data (objective criteria) which describe aspects such as the number of designchanges last month and qualitative data (subjective criteria) such as maturity of parts of a component.After the single parameter describing the design maturity has been derived by the fuzzy data analysissystem, it is used to determine the optimum amount of design effort to be put in the project until com-pletion. Optimality is defined by minimizing the total cost consisting of developement, warranty andopportunity parts. The degree of maturity of the design process is derived from 10 input variables byusing Zimmermann’s γ-operator [138] for the aggregation process. Their hierarchically defined system(using the commercial fuzzy logic design tool fuzzyTECH) is now in use at Mercedes-Benz in Germany.Chang and Chen [25] discuss the potential application of FMCDM techniques the selection of to tech-nology transfer strategies in the area of biotechnology management. The transfer of technology from itssource to the developement of commercial applications is a very complex process. It is clearly a multi-person multi-criteria problem in an ill-structured situation. One should make a careful analysis amongcriteria, alternatives, weight, and decision makers before making a decision. If we want to use conventialcrisp decision methods we will always have to find precise data. The assessments of alternatives on re-lation to various criteria, and the importance weights of these criteria, will have to rely on judgement orapproximation. The authors use linguistic variables and fuzzy numbers to aggregate the decision mak-ers’ subjective assessments of the weighting of criteria. Their method is based on using data input forcomputing the total index of optimism in a multi-person decision-making problem, instead of having adecision maker to give the index of optimism independently. This new approach to using the index ofoptimism reflects the pooled risk-bearing attitude of several decision makers. The index of optimism isdetermined by the evaluation data conveyed by the decision makers at the beginning of the data inputstage. Finally, a novel method is introduced to rank the fuzzy appropriateness indices for choosing the

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best technology transfer strategy.The paper ends with a case study of the selection of a strategy for the transfer of hepatitis B vaccinetechnology.Forecasting consumer purchases of homes, cars, consumer electronics and appliances, and vacations isof great importance to many sectors of the world economy. To address this concern, studies of consumerpreception of business conditions are continuously being conducted to help predict these purchases. In[130] Yager et al. suggest a methodology for using information obtained by market surveys to predictthe values of other related (linguistic) variables of interest to market research analysts. Based upon a useof Shannon’s entropy [61] the authors suggest a measure for calculating the relative predictive powers oftwo linguistic variables. Yager’s OWA operators [126, 129] are used to carry out aggregation of singleconcepts to form complex concepts. Finally, they select the best predictive model by finding the onewhich has the minimum entropy.With the help of a survey of respondents on their attitudes toward some present and future economicconditions the authors illustrate the suggested mechanism. In this case study, respondents were askedto rate each of five economic conditions as being either good, normal, or bad. These five economicconditions were:

1,2. Business conditions now and six months from now.

3,4. The availability of jobs now and six months from now.

5. The family income six months from now.

A follow-up survey was conducted six months later to determine whether or not they had purchased ahouse, a car, an electrical appliance or had taken a vacation in the preceding six months.Using the data obtained from this survey Yager et al construct a model to best aggregate the respondents’answers to the questions on economic conditions as a predictor of their purchasing a house, car etc.As a result of the process they found, for example, that the best predictor of the home purchases wasconsumers who rated three economic conditions as good, while the best predictor of car purchases wasconsumers who rated only two economic conditions as good.

4 Future perspectives

In 1984 French [51] predicted a very pessimistic future for fuzzy decision-making:

It is now some sixteen years since Zadeh awakened interest in the concept of fuzzy sets andover a decade since he and Bellman extended the analysis to decision-making in a fuzzyenvironment. The intervening years have seen the development of a large and growing lit-erature. Yet, despite the enormous amount of research into the theory and applications offuzzy sets, there are still some fundamental questions to be answered. It is my contentionthat these cannot be resolved as favourably as the proponents of fuzzy mathematics suggest.Moreover, I argue that the emphasis placed upon the modelling of imprecision is inappro-priate to many of the applications suggested for the theory.

Fortunately, everything developed exactly contrary to French’s assessments, and the last ten years havejustified Gaines, Zadeh and Zimmermann’s visions [52] of the future possibilities for fuzzy decisionmaking.

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Decision making in practice has shown that fuzzy logic allows decision making with estimated values in-spite of incomplete information. It should be noted, however, that a decision may not be correct and canbe improved later when additional information is available. Of course, a complete lack of informationwill not support any decision making using any form of logic. For difficult problems, conventional (non-fuzzy) methods are usually expensive and depend on mathematical approximations (e.g. linearization ofnonlinear problems), which may lead to poor performance. Under such circumstances, fuzzy systemsoften outperform conventional MCDM methods.A good example of a case where this happened is given by Munakata and Jani [77]:

Yamaichi Fuzzy Fund. This is a premier financial application for trading systems. It handles 65industries and a majority of the stocks listed on Nikkei Dow and consists of approximately 800 fuzzyrules. Rules are determined monthly by a group of experts and modified by senior business analysts asnecessary. The system was tested for two years, and its performance in terms of the return and growthexceeds the Nikkei Avarage by over 20 %. While in testing, the system recommended ”sell” 18 daysbefore the Black Monday in 1987. The system went to commercial operations in 1988. All financialanalysts including Western analysts will agree that the rules for trading are all ”fuzzy”.

And it is just one example from 1500 applications of fuzzy systems listed in 1993 [77]...

5 About the papers

Let us now briefly summarize the contents of each paper from this special issue.The paper Fuzzy multiple attribute decision-making: A review and new preference elicitation techniquesby R.A.Riberio provides an overview of the underlying concepts and theories of decision-making in afuzzy environment and the scope of this type of research. This is a well-written and up-to-date survey ofdifferent kinds of methods for rating, comparison and ranking of alternatives. A new weighting techniqueis introduced to elicit criteria importance. The paper ends with an example illustrating the proposedweighting procedure.Using fuzzy relations and interval valued fuzzy sets as the basic tool for modeling I.B. Turksen and T.Bilgic in Interval valued strict preference with Zadeh triples introduce a new technique to model vaguepreferences with the aim of making a choice at the final stage. They propose that the initial vaguenessin the weak preferences of a decision maker is represented by a fuzzy relation and that further constructsfrom this concept introduce a higher order of vagueness which is represented by interval-valued fuzzysets. It is shown that conditions weaker than min-transitivity on the representation of initial vaguenessare necessary and sufficient for the alternatives to be partially ranked. Conditions for the existence ofnonfuzzy non-dominated alternatives are also explored.The paper Scheduling as a fuzzy multiple criteria optimization problem by W.Slany is dealing with areal-world scheduling problem with uncertain data and vague constraints of different importance, wherecompromises between antagonistic criteria are also allowed. A new type of combination of fuzzy set-based constraints and iterative repair-based heuristics is introduced to model these scheduling problems.Sensitivity analysis is performed by introducing a new consistency test for configuration changes.The paper A fuzzy satisficing method for multiobjective linear optimal control problems by M.Sakawa,M.Inuiguchi and T.Ikeda focuses on multiobjective linear control problems. To solve these problems,they first discretize the time and then replace the system of differential equations with difference equa-tions. Then they formulate approximate linear multi-objective programming problems by introducingauxiliary variables. Assuming that the decision maker may have fuzzy goals for the objective functionsthey determine the corresponding membership functions through interaction with the decision maker.

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Finally, it is shown that the resulting problem can be reduced to a linear programming problem and thatthe satisficing solution for the decision maker can be obtained with the standard simplex method of linearprogramming.In the paper Possible and necessary efficiency in possibilistic multiobjective linear programming prob-lems and possible efficiency test M.Inuiguchi and M.Sakawa extend the concept of efficient solutionsof conventional multi-objective linear programming problems to the case of fuzzy (possibilistic) coef-ficients by introducing possibly and necessarily efficient solution sets. These are defined as fuzzy setswhose membership grades represent the possibility and necessity degrees to which the solution is effi-cient. A test for possible efficiency is presented, when a feasible solution is given. A necessary andsufficient condition for the possible efficiency for the interval case is provided.

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6 Follow ups

The results of this paper have been improved and/or generalized in the following works.

in journals

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A18-c216 J. Ignatius et al, A multi-objective sensitivity approach to training providers’ evaluation andquota allocation planning, INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGYAND DECISION MAKING, 10(2011), issue 1, pp. 147-174. 2011

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A18-c215 A. Choi, W. Woo, Multiple-Criteria Decision-Making Based On Probabilistic EstimationWith Contextual Information For Physiological Signal Monitoring, INTERNATIONAL JOUR-NAL OF INFORMATION TECHNOLOGY AND DECISION MAKING, 10(2011), number 1,pp. 109-120. 2011

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A18-c214 Chi-Cheng Huang and Pin-Yu Chu, Using the fuzzy analytic network process for select-ing technology R&D projects, INTERNATIONAL JOURNAL OF TECHNOLOGY MANAGE-MENT, 53(2011), number 1, pp. 89-115. 2011

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A18-c213 Anjali Awasthi, S S Chauhan, S K Goyal, A multi-criteria decision making approach for lo-cation planning for urban distribution centers under uncertainty, MATHEMATICAL AND COM-PUTER MODELLING, 53(2011), pp. 98-109. 2011

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A18-c212 Kejiang Zhang; Gopal Acharia, Uncertainty propagation in environmental decision makingusing random sets, PROCEDIA ENVIRONMENTAL SCIENCES, 2(2010), 576-584. 2010

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A18-c211 Maninder Jeet Kaur, Moin Uddin, Harsh K Verma, Analysis of Decision Making Operationin Cognitive radio using Fuzzy Logic System, INTERNATIONAL JOURNAL OF COMPUTERAPPLICATIONS, 4(2010), number 10, pp. 35-39. 2010

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A18-c210 Dorit S Hochbaum, Asaf Levin, How to allocate review tasks for robust ranking, ACTAINFORMATICA, 47(2010), number 5-6, pp. 325-345. 2010

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A18-c209 Rajender Kumar, Brahmjit Singh, Comparison of vertical handover mechanisms using genericQoS trigger for next generation network, INTERNATIONAL JOURNAL OF NEXT-GENERATIONNETWORKS, 2(2010), number 3, pp. 80-97 [doi 10.5121/ijngn.2010.2308]. 2010

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A18-c208 V. Peneva, I. Popchev, Fuzzy multi-criteria decision making algorithms, COMPTES REN-DUS DE L’ACADEMIE BULGARE DES SCIENCES, 63(2010), Issue 7, pp. 979-992. 2010

A18-c207 Tony Prato, Sustaining Ecological Integrity with Respect to Climate Change: Adaptive Man-agement Approach, ENVIRONMENTAL MANAGEMENT 45(2010), number 6, pp. 1344-1351.2010

http://dx.doi.org/10.1007/s00267-010-9493-3

The framework employs ex post and ex ante evaluations of ecological integrity. Theex post evaluation uses fuzzy logic (Barrett and Pattanaik 1989; Carlsson and Fuller1996; Andriantiatsaholiniaina and others 2004; Prato 2005, 2009) to test hypothesesabout the vulnerability to losing ecological integrity in an historical period and the exante evaluation determines the best CMA for alleviating potential adverse impacts ofclimate change on ecosystem vulnerability to losing ecological integrity in a futureperiod. (page 1346)

22

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A18-c200 Ling-Zhong Lin, Fuzzy multi-linguistic preferences model of service innovations at whole-sale service delivery, QUALITY AND QUANTITY, 44(2010), pp. 217-237. 2010

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Since 1970, multiple criteria decision making (MCDM) has been a promising and im-portant field of study with many practical application (Carlsson and Fuller 1996). Tradi-tionalMCDM methods have been extended to support the fuzzy decision making. FuzzyMCDM methods have found many practical applications in the real word (Carlsson andFuller 1996; Chen 2001). (page 220)

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A18-c198 Javier Munguia; Joaquim Lloveras; Sonia Llorens; Tahar Laoui, Development of an AI-based Rapid Manufacturing Advice System, INTERNATIONAL JOURNAL OF PRODUCTIONRESEARCH , Volume 48, Issue 8 January 2010 , pages 2261-2278. 2010

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A18-c197 ZHANG Tao; XU Yunyun; LI Zancheng; LIN Zhenrong, Fuzzy Interpolation AlgorithmUsing Vague Set Based Score Function Methods, JOURNAL OF DETECTION & CONTROL,32(2010), number 1, pp. 61-64 (in Chinese). 2010

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A18-c196 G. Uthra, R. Sattanathan, Confidence Analysis for Fuzzy Multicriteria Decision MakingUsing Trapezoidal Fuzzy Numbers, INTERNATIONAL JOURNAL OF INFORMATION TECH-NOLOGY AND KNOWLEDGE MANAGEMENT, 2(2009), pp. 333-336. 2009

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A18-c195 Amir Sanayei, Seyed Farid Mousavi, and Catherine Asadi Shahmirzadi, A Group BasedFuzzy MCDM for Selecting Knowledge Portal System, Proceedings of World Academy of Sci-ence, Engineering and Technology, 52(2009), pp. 455-462. 2009

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This approach helps decision-makers solve complex decision-making problems in asystematic, consistent and productive way [A18] and has been widely applied to tackleDM problems with multiple criteria and alternatives [27]. In short, fuzzy set theoryoffers a mathematically precise way of modeling vague preferences for example whenit comes to setting weights of performance scores on criteria. Simply stated, fuzzyset theory makes it possible to mathematically describe a statement like: ”criterion Xshould have a weight of around 0.8” [28]. (page 457)

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http://dx.doi.org/10.1109/TFUZZ.2008.928599

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A18-c190 Mousumi Dutta, Zakir Husain An application of Multicriteria Decision Making to built her-itage. The case of Calcutta, JOURNAL OF CULTURAL HERITAGE, 10(2009), pp. 237-243.2009

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A18-c186 Torbert, H.A., Krueger, E., Kurtener, D., Potter, K.N. Evaluation of Tillage Systems for GrainSorghum and Wheat Yields and Total N Uptake in The Texas Blackland Prairie, JOURNAL OFSUSTAINABLE AGRICULTURE, 33(2009), pp. 96-106. 2009

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A18-c184 Ni-Bin Chang, Ying-Hsi Chang, Ho-Wen Chen, Fair fund distribution for a municipal in-cinerator using GIS-based fuzzy analytic hierarchy process, JOURNAL OF ENVIRONMENTALMANAGEMENT, 90(2009) 441-454. 2009


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A18-c180 Chung-Tsen Tsao, Applying a fuzzy multiple criteria decision-making approach to the M &A due diligence, EXPERT SYSTEMS WITH APPLICATIONS, Volume 36, Issue 2, Part 1, March2009, Pages 1559-1568. 2009


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A18-c120 Zhang Shichang; Cao Jingyu, Rational considerations on the preference in decision making,SHANDONG SOCIAL SCIENCE, 3(2003), pp. 116-119 (in Chinese). 2003


A18-c119 Li Shao-wen, Xiong Fan-lun, Shan-Mei Shao, Li-Wu Zhu, An evaluation system based onmultilevel model of fuzzy comprehensive evaluation for natural resources in agriculture, JOUR-NAL OF ZHEJIANG UNIVERSITY (AGRICULTURE & LIFE SCIENCES) 28: (2002), nuber1, pp. 102-106 (in Chinese). 2002

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A18-c118 Tan Ansheng, Optimum Seeking Model and Method of Fuzzy Multiobjective Group DecisionMakings with Fuzzy Numbers, OPERATIONS RESEARCH AND MANAGEMENT SCIENCE,11(2002), number 6, pp. 45-51. 2002

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A18-c117 Ta-Chung Chu A Fuzzy Number Interval Arithmetic based Fuzzy MCDM Algorithm IN-TERNATIONAL JOURNAL OF FUZZY SYSTEMS, 4: (4), pp. 867-872. 2002

A18-c116 Yuan YF, Feldhamer S, Gafni A, et al. The development and evaluation of a fuzzy logicexpert system for renal transplantation assignment: Is this a useful tool? EUR J OPER RES 142(1): 152-173 OCT 1 2002.

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A18-c115 Satyadas A, Harigopal U, Cassaigne NP Knowledge management tutorial: An editorialoverview IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS PART C: AP-PLICATIONS AND REVIEWS, 31 (4): 429-437 NOV 2001

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A18-c114 Zhou DN, Ma H, Turban E Journal quality assessment: An integrated subjective and objectiveapproach, IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT, 48 (4): 479-490 NOV2001

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A18-c113 Yu CS, Li HL An algorithm for generalized fuzzy binary linear programming problemsEUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 133 (3): 496-511 SEP 16 2001

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A18-c112 Ekenberg L, Thorbiornson J Second-order decision analysis INTERNATIONAL JOURNALOF UNCERTAINTY, FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 9 (1): 13-37 FEB2001

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A18-c111 Geldermann J, Rentz O, Integrated technique assessment with imprecise information as asupport for the identification of best available techniques (BAT) OR SPEKTRUM, 23 (1): 137-157 FEB 2001

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A18-c110 Sonja Petrovic-Lazarevic, Personnel selection fuzzy model, INTERNATIONAL TRANS-ACTIONS IN OPERATIONAL RESEARCH, 8 pp. 89-105. 2001

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A18-c109 Chian-Son Yu and Han-Lin Li, An algorithm for generalized fuzzy binary linear program-ming problems, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 133 pp. 496-511.2001

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A18-c108 Royes, G.F., Bastos, R.C. Political analysis using fuzzy MCDM Journal of Intelligent andFuzzy Systems, 11 (1-2), pp. 53-64. 2001

A18-c76 Dale, M.B. Functional synonyms and environmental homologues: An empirical approach toguild delimitaton Community Ecology, 2 (1), pp. 67-79. 2001

A18-c107 Jutta Geldermann, Thomas Spengler and Otto Rentz, Fuzzy outranking for environmentalassessment. Case study: iron and steel making industry, FUZZY SETS AND SYSTEMS 115 pp.45-65. 2000

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A18-c106 Chung-Hsing Yeh, Hepu Deng and Yu-Hern Chang, Fuzzy multicriteria analysis for perfor-mance evaluation of bus companies, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH,126(2000) 459-473.

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A18-c105 A. Valls, V. Torra, Using classification as an aggregation tool in MCDM, FUZZY SETS ANDSYSTEMS, 115(1): 159-168 OCT 1 2000

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A18-c104 Cuong BG, On group decision making under linguistic assessments INTERNATIONALJOURNAL OF UNCERTAINTY, FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 7 (4):301-308 AUG 1999

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A18-c103 Blasco F, Cuchillo-Ibanez E, Moron MA, et al. On the monotonicity of the compromise setin multicriteria problems JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 102(1): 69-82 JUL 1999

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A18-c101 F. Herrera, E. Herrera-Viedma, J.L. Verdegay, Linguistic Measures Based on Fuzzy Coinci-dence for Reaching Consensus in Group Decision Making, International Journal of ApproximateReasoning, 16 (1997) 309-334. 1997

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A18-c82 Jenabi M, Naderi B, Fatemi Ghomi S M T, A bi-objective case of no-wait flowshops, 2010IEEE Fifth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA), September 23-26, 2010, Changsha, China, [ISBN 978-1-4244-6437-1], pp. 1048-1056. 2010

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A18-c81 Sohrab Khanmohammadi, Javad Jassbi, Electrical Power Scheduling in Emergency Condi-tions using a new Fuzzy Decision Making Procedure, 2010 IEEE International Conference onSystems Man and Cybernetics (SMC). October 10-13, 2010, Istanbul, Turkey, [ISBN 978-1-4244-6586-6], pp. 257-262. 2010

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A18-c80 Changxing Zhang; Songtao Hu, Fuzzy Multi-Criteria decision making for selection of schemeson cooling and heating source, Seventh International Conference on Fuzzy Systems and Knowl-edge Discovery (FSKD), August 10-12, 2010, Yantai, Shandong, China, [ISBN 978-1-4244-5931-5], pp. 876-878. 2010

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A18-c79 Merentitis, Andreas; Triantafyllopoulou, Dionysia, Transmission power regulation in cooper-ative Cognitive Radio systems under uncertainties, 5th IEEE International Symposium on WirelessPervasive Computing (ISWPC), 5-7 May 2010, Modena, Italy, [E-ISBN 978-1-4244-6857-7, PrintISBN 978-1-4244-6855-3] pp.134-139. 2010

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A18-c78 Praveen Kumar, Pavol Bauer, Progressive Design Methodology for Design of EngineeringSystems, in: Yoel Tenne and Chi-Keong Goh eds., Computational Intelligence in Expensive Op-timization Problems, Evolutionary Learning and Optimization Series, vol 2, part III, Springer,[ISBN 978-3-642-10700-9], pp. 571-607. 2010

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A18-c77 Merentitis, A.; Kaloxylos, A.; Stamatelatos, M.; Alonistioti, N.; Optimal periodic radio sens-ing and low energy reasoning for cognitive devices, 15th IEEE Mediterranean ElectrotechnicalConference, MELECON 2010, 26-28 April 2010, Valletta, Malta, [ISBN 978-1-4244-5793-9], pp.470-475. 2010

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Fuzzy logic is based on fuzzy set theory in which every object has a grade of member-ship in various sets. Inputs are mapped to membership functions, or sets (fuzzificationprocess). Knowledge of a restricted domain is captured in the form of linguistic rules.Relationships between two goals are defined using fuzzy inclusion and non-inclusionbetween the supporting and hindering sets of the corresponding goals [A18]. (page472)

A18-c76 Bui Cong Cuong, Dinh Tuan Long, Nguyen Thanh Huy, Pham Hong Phong, New ComputingProcedure in Multicriteria Analysis, using Fuzzy Collective Solution, 10TH INTERNATIONALCONFERENCE ON INTELLIGENT TECHNOLOGIES, Guilin, China, December 12-15, 2009,pp. 571-577. 2009

A18-c75 Guozheng Zhang, Research on Supplier Selection Based on Fuzzy Sets Group Decision, In-ternational Symposium on Computational Intelligence and Design, Changsha, Hunan, China. De-cember 12-December 14, 2009, [ISBN 978-0-7695-3865-5], pp. 529-531. 2009

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A18-c74 Yong Shi, Shouyang Wang, Yi Peng, Jianping Li and Yong Zeng, Ecological Risk Assess-ment with MCDM of Some Invasive Alien Plants in China, in: Cutting-Edge Research Topics onMultiple Criteria Decision Making, Communications in Computer and Information Science, vol.35/2009, Springer, [ISBN 978-3-642-02297-5], pp. 580-587. 2009

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A18-c73 Ying Jiang; Qiuwen Zhang, Design and Implementation of Dam Failure Risk AssessmentSystem Based on Fuzzy Mathematics, Proceedings of the 2008 IEEE International Symposium onKnowledge Acquisition and Modeling Workshop (KAM 2008 Workshop), 21-22 December 2008,Wuhan, China, pp. 486-489. 2008

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A18-c72 Merentitis, A., Patouni, E., Alonistioti, N., Doubrava, M. To reconfigure or not to reconfigure:Cognitive mechanisms for mobile devices decision making, IEEE Vehicular Technology Confer-ence, VTC 2008-Fall, art. no. 4657099, pp. 1-5. 2008

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A18-c71 M. Tarazzo, Intervals in Finance and Economics: Bridge between Words and Numbers, Lan-guage of Srategy, in: W. Pedrycz, A. Skowron, V. Kreinovich (Eds.) Handbook of GranularComputing , Studies in Computational Intelligence Series, Wiley, [ISBN 9780470035542], pp.1069-1092. 2008

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A18-c70 E. Kornyshova, R. Deneckere, and C. Salinesi, Improving Software Development Processeswith Multicriteria Methods, in: Sophie Ebersold et al eds., Proceedings of the Model Driven Infor-mation Systems Engineering: Enterprise, User and System Models (MoDISE-EUS 2008), Mont-pellier, France, 16-17 June 2008, pp. 103-113. 2008

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A18-c69 James J. Buckley and Leonard J. Jowers, Fuzzy Multiobjective LP, in: Monte Carlo Methodsin Fuzzy Optimization, Studies in Fuzziness and Soft Computing Series, vol. 222, Springer, [ISBN978-3-540-76289-8], pp. 81-88. 2008

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A18-c68 Quan Li, A fuzzy neural network based multi-criteria decision making approach for outsourc-ing supplier evaluation, 3rd IEEE Conference on Industrial Electronics and Applications (ICIEA2008), 3-5 June 2008, pp.192-196. 2008

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As we can see, we have to deal with both quantitative and qualitative criteria during out-sourcing supplier evaluation process, an effective decision making tool must be utilizedto fulfill our needs. Although several fuzzy MCDM methods such as multi-objectivefuzzy decision making (MOFDM), hierarchical weight decision making (HWDM),PROMETHEE, etc. could be utilized to deal with such problem, the complexity ofsuch methods makes it harder to be undertaken [A18] (page 193)

A18-c67 Wen-Hsiang Lai; Pao-Long Chang; Ying-Chyi Chou, Fuzzy MCDM Approach to R&DProject Evaluation in Taiwan’s Public Sectors, Portland International Conference on Managementof Engineering & Technology (PICMET 2008), Cape Town, South Africa, 27-31 July 2008, pp.1523-1532. 2008

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A18-c66 Tsung-Han Chang; Tien-Chin Wang, Fuzzy Preference Relation Based Multi-Criteria De-cision Making Approach for WiMAX License Award, IEEE International Conference on FuzzySystems, 1-6 June 2008, pp. 37-42. 2008

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A18-c65 Jie Lu; Xiaoguang Deng; Vroman, P.; Xianyi Zeng; Jun Ma; Guangquan Zhang, A fuzzymulti-criteria group decision support system for nonwoven based cosmetic product developmentevaluation, IEEE International Conference on Fuzzy Systems, 1-6 June 2008, pp. 1700-1707.2008

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A18-c64 Henryk Piech; Pawel Figat, A Method for Evaluation of Compromise in Multiple CriteriaProblems, in: Artificial Intelligence and Soft Computing – ICAISC 2008, Lecture Notes in Com-puter Science, vol. 5097/2008, Springer Verlag, [978-3-540-69572-1], pp. 1099-1108. 2008

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A18-c63 Michael Arkhipov, Elena Krueger, Dmitry Kurtener, Evaluation of Ecological ConditionsUsing Bioindicators: Application of Fuzzy Modeling, In: : Computational Science and Its Appli-cations - ICCSA 2008, Springer Verlag, pp. 491-500. 2008

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A18-c61 M.J. Beynon, Fuzzy Outranking Methods Including Fuzzy PROMETHEE, in: Jose Galindoed., Handbook of Research on Fuzzy Information Processing in Databases, Idea Group Inc, 2008,pp. 784-804. 2008

A18-c60 Irina Georgescu, Concluding remarks, in: Fuzzy Choice Functions, Studies in Fuzziness andSoft Computing series, vol. 214/2007, Springer, pp. 265-270. 2007

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A18-c59 Hepu Deng, A Discriminative Analysis of Approaches to Ranking Fuzzy Numbers in FuzzyDecision Making, In: Fourth International Conference on Fuzzy Systems and Knowledge Discov-ery (FSKD 2007), pp. 22-27. 2007


A18-c58 Kong, F., Liu, H.-Y., A new fuzzy MADM algorithm based on subjective and objective in-tegrated weights, Proceedings - ICSSSM’07: 2007 International Conference on Service Systemsand Service Management, pp. 1-6, art. no. 4280142. 2007

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A18-c57 Hamed Qahri Saremi, Gholam Ali Montazer, Website Structures Ranking: Applying ExtendedELECTRE III Method Based on Fuzzy Notions, in: Proceedings of the 8th Conference on 8thWSEAS International Conference on Fuzzy Systems - Volume 8, pp. 120-125. 2007

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A18-c55 Zhou H, Peng H, Zhang C, An Interactive Fuzzy Multi-Objective Optimization Approach forCrop Planning and Water Resources Allocation, In: Bio-Inspired Computational Intelligence andApplications, Lecture Notes in Computer Science, vol. 4688, pp. 335-346. 2007

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A18-c54 Mehrzad Samadi,; Ali Afzali-Kusha, Power management with fuzzy decision support sys-tem, 7th International Conference on ASIC (ASICON’07), 22-25 Oct. 2007, [doi: 10.1109/ICA-SIC.2007.4415570], pp.74-77. 2007

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A18-c52 Feng Kong, Hong-yan Liu, A Hybrid Fuzzy LMS Neural Network Model for DeterminingWeights of Criteria in MCDM, Fourth International Conference on Fuzzy Systems and KnowledgeDiscovery (FSKD 2007) Vol.3, pp. 430-434, 2007. 2007


A18-c51 Omar F. El-Gayar and Kanchana Tandekar, An IDSS for Regional Aquaculture Planning,In: Jatinder N. D. Gupta, Guisseppi A. Forgionne and Manuel Mora T. eds., Intelligent Decision-making Support Systems, Foundations, Applications and Challenges, Decision Engineering Series,Springer London, 2007, [ISBN 978-1-84628-228-7] pp. 199-218. 2007

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A18-c50 Wu, P., Clothier, R., Campbell, D., Walker, R., Fuzzy multi-objective mission flight planningin unmanned aerial systems, Proceedings of the 2007 IEEE Symposium on Computational Intelli-gence in Multicriteria Decision Making, MCDM 2007, 2007, Article number 4222975, Pages 2-9.2007

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A18-c49 Vanier D, Tesfamariam S, Sadiq R, Lounis Z, Decision models to prioritize maintenance andrenewal alternatives, Joint International Conference on Computing and Decision Making in Civiland Building Engineering, June 14-16, 2006, Montreal, Canada, pp. 2594-2603.

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A18-c48 Z.K. Ozturk, A review of multi criteria decision making with dependency between criteria,18th International Conference on Multiple Criteria Decision Making, June 19-23, 2006, Chania,Greece. 2006

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A18-c47 Jacobo Feas Vazquez and Paolo Rosato, Multi-Criteria Decision Making in Water ResourcesManagement, in: Carlo Giupponi ed., Sustainable Management of Water Resources: An IntegratedApproach, Edward Elgar Publishing, 2006, [ISBN 1845427459], pp. 98-130. 2006

A18-c46 Kong, F., Liu, H. A fuzzy LMS neural network method for evaluation of importance of indicesin MADM, Lecture Notes in Computer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics), 4234 LNCS - III, pp. 1038-1045. 2006

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A18-c44 Liu, H., Kong, F. A new fuzzy MADM method: Fuzzy RBF neural network model (2006)Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligenceand Lecture Notes in Bioinformatics), 4223 LNAI, pp. 947-950. 2006

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A18-c43 Mehregan MR, Safari H Combination of fuzzy TOPSIS and fuzzy ranking for multi attributedecision making LECTURE NOTES IN COMPUTER SCIENCE 4029: 260-267 2006

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A18-c42 K. Feng, L. Hongyan, A new multi-attribute decision making method based on fuzzy neuralnetwork, Proceedings of the World Congress on Intelligent Control and Automation (WCICA), 1,art. no. 1712849, pp. 2676-2680. 2006

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A18-c41 Borer, N.K., Mavris, D.N. Relative importance modeling in the presence of uncertainty andinterdependent metrics (2006) Collection of Technical Papers - 11th AIAA/ISSMO Multidisci-plinary Analysis and Optimization Conference, vol. 3, pp. 1954-1967. 2006

A18-c40 Zhang, L., Zhou, D., Zhu, P., Li, H. Comparison analysis of MAUT expressed in terms of cho-quet integral and utility axioms 1st International Symposium on Systems and Control in Aerospaceand Astronautics, 2006, art. no. 1627708, pp. 85-89. 2006

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A18-c39 Ta-Chung Chu, Wei-Li Liu, Sz-Shian Liu A Fuzzy Multicriteria Decision Making for Distri-bution Center Location Selection In: 8th Joint Conference on Information Sciences (JCIS 2005).2005

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A18-c38 Feng Kong, Hong-yan Liu, An algorithm for MADM based on subjective preferences, In: Ar-tificial Intelligence Applications and Innovations II, IFIP TC12 and WG12.5 - Second IFIP Con-ference on Artificial Intelligence Applications and Innovations (AIAI-2005), IFIP InternationalFederation for Information Processing, vol.187, pp. 279-289. 2005

A18-c37 Ashley Morris and Piotr Jankowski, Spatial Decision Making Using Fuzzy GIS, in: FrederickE. Petry, Vincent B. Robinson, Maria A. Cobb eds., Fuzzy Modeling with Spatial Information forGeographic Problems, Springer, [ISBN 3-540-23713-5] pp. 275-298. 2005

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A18-c36 Zhu Dazhong, Han-Zhong, Application of Fuzzy Multi-Criteria Decision Making to the De-velopment Sequence of New Products, In: First Symposium of the Taiwan Society of OperationsResearchTechnology and Management Symposium 2004, Taiwan, pp. 874-880. 2004

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A18-c35 P L Kunsch, Ph Fortemps, Evaluation by fuzzy rules of multicriteria valued preferences inAgent-Based Modelling, In: Managing Uncertainty in Decision Support Models (MUDSM 2004),Coimbra, Portugal, September 2004

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A18-c34 Ta-Chung Chu and Tzu-Ming Chang Solving Fuzzy MCDM Using Fuzzy Weighted AverageArithmetic, The 17th International Conference on Multiple Criteria Decision Making Whistler,British Columbia, CANADA, August 6-11, 2004

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A18-c27 C. Mohan and S.K. Verma, Interactive algorithms using fuzzy concepts for solving mathemat-ical models of real life optimization problems, in: J. L. Verdegay ed., Fuzzy Sets based Heuristicsfor Optimization, Studies in Fuzziness and Soft Computing. Vol. 126, Springer Verlag, [ISBN3-540-00551-X], pp. 122-140. 2003

A18-c26 Wei Wang, Kim-Leng Poh, Fuzzy multicriteria decision making under attitude and confidenceanalysis, in: Ajith Abraham, Mario Koppen and Katrin Franke eds., Design and application ofhybrid intelligent systems, [ISBN:1-58603-394-8], IOS Press, pp. 440-447. 2003

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A18-c24 Bailey, D., Goonetilleke, A., Campbell, D. Information analysis and dissemination for siteselection decisions using a fuzzy algorithm in GIS, in: Proceedings of the IASTED InternationalConference on Information and Knowledge Sharing, pp. 223-228. 2003

A18-c23 Michelle R. Lavagna and Amalia Ercoli Finzi, Concurrent Processes within Preliminary Space-craft Design: An Autonomous Decisional Support Based on Genetic Algorithms and Analytic Hi-erarchical Process, in Proceedings of the 17th International Symposium on Space Flight Dynamics,Moscow, Russia, June 2003.

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A18-c19 P.M.L Chan, Y.F. Hu and R.E. Sheriff, Implementation of fuzzy multiple Objective decisionmaking algorithm in a heterogeneous mobile environment, Proc. Wireless Communications andNetworking Conference, vol. 1, 2002, pp. 332-336. 2002

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A18-c17 Tao Wang; Yan-Ping Wang, A new algorithm for nonlinear mathematical programming basedon fuzzy inference, 2002 International Conference on Machine Learning and Cybernetics, Pro-ceedings, [doi 10.1109/ICMLC.2002.1174436], vol.2, pp. 694-698. 2002

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A18-c16 Royes, G.F., Bastos, R.C. Fuzzy MCDM in election prediction Proceedings of the IEEE Inter-national Conference on Systems, Man and Cybernetics, 5, pp. 3258-3263. 2001


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A18-c15 Myung, H.-C., Bien, Z.Z. Interdependent multiobjective control using Biased Neural Network(Biased NN) Annual Conference of the North American Fuzzy Information Processing Society -NAFIPS, 3, pp. 1378-1383. 2001


A18-c14 Tsuen-Ho Hsu; Tzung-Hsin Yang, A new fuzzy synthetic decision model to assist advertisersselect magazine media, 1999 IEEE International Fuzzy Systems Conference (FUZZ-IEEE ’99),vol. 2, pp. 922-927.

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=793075

A18-c13 J. Geldermann and O. Rentz, Fuzzy outranking for environmental assessment as an approachfor the identification of best available techniques (BAT), in: B.De Baets, J. Fodor and L. T .Koczyeds., Proceedings of the Fourth Meeting of the Euro Working Group on Fuzzy Sets and Second In-ternational Conference on Soft and Intelligent Computing (Eurofuse-SIC’99), Budapest, Hungary,25-28 May 1999, Technical University of Budapest, [ISBN 963 7149 21X], 1999 376-381. 1999

A18-c12 Naso, D.; Turchiano, B., A fuzzy multi-criteria algorithm for dynamic routing in FMS, IEEEInternational Conference on Systems, Man, and Cybernetics, 1998, vol.1, pp. 457-462, 11-14 Oct1998


A18-c11 H.-J. Zimmermann, Future research in five areas of fuzzy technology, in: E. H. Ruspini,P.P.Bonissone and W.Pedrycz eds., Handbook of Fuzzy Computation, Institute of Physics Publish-ing, London, [ISBN 0 7503 04278], 1998 H1.2:1-H1.2:3. 1998

A18-c10 J.M.Cadenas and J.L.Verdegay, Using ranking functions in multiobjective fuzzy linear pro-gramming, in: M.Mares et al, eds., Proceedings of the Seventh IFSA World Congress, June 25-29,1997, Academia, Prague, Vol. III, 1997 3-8. 1997

The involvement of different kinds of fuzziness in these problems is a matter whichalso has received a great dealt of work since the early eighties, as it is very frequent thatdecision makers have some lack of precision is stating some of the parameters involvedin the model [A18, . . . ]. (page 3)

A18-c9 R. Felix, Reasoning on relationships between goals and its industrial and business-oriented ap-plications, in: Proceedings of First International Workshop on Preferences and Decisions, Trento,June 5-7, 1997, University of Trento, pp. 21-23. 1997

A18-c8 H.-J.Zimmermann, Fuzzy logic on the frontiers of decision analysis and expert systems, in: Pro-ceedings of First International Workshop on Preferences and Decisions, Trento, June 5-7, 1997,University of Trento, 1997 97-103. 1997

A18-c7 Kahraman C, Ulukan Z, Tolga E, Fuzzy multiobjective linear-programming-based justificationof advanced manufacturing systems, In: International Conference on Engineering and TechnologyManagement, pp. 226-232. 1996

http://dx.doi.org/10.1109/IEMC.1996.547820

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A18-c6 H -J Zimmermann, Fuzzy logic on the frontiers of decision analysis and expert systems In:1996 Biennial Conference of the North American Fuzzy Information Processing Society (NAFIPS1996), pp. 65-69. 1996

http://dx.doi.org/10.1109/NAFIPS.1996.534705

in books

A18-c3 Federico Frattini, Vittorio Chiesa, Evaluation and Performance Measurement of Research andDevelopment: Techniques and Perspectives for Multi-Level Analysis, Edward Elgar Publishing,Cheltenham, [ISBN 978 1 84720 948 1]. 2009

A18-c2 Jie Lu, Guangquan, Zhang, Da Ruan, Fengjie Wu, Multi-objective Group Decision Making:Methods Software and Applications with Fuzzy Set Techniques, Series in Electrical and ComputerEngineering, Vol. 6, Imperial College Press, [ISBN 186094793X]. 2007

A18-c1 J. Smed and H. Hakonen, Algorithms and Networking for Computer Games, John Wiley &Sons, New York, NY, USA, [ISBN 9780470018125], 2006.

in Ph.D. dissertations

• Patrick Meyer, Progressive Methods in Multiple Criteria Decision Analysis, Faculte de Droit, d’Economieet de Finance, Universite du Luxembourg, 2007.

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.124.9749&rep=rep1&type=pdf

• Erkki Patokorpi, ROLE OF ABDUCTIVE REASONING IN DIGITAL INTERACTION, Faculty ofTechnology at Abo Akademi University, December 2006.

• Elcin Kentel, Uncertainty Modeling Health Risk Assessment and Groundwater Resources Manage-ment, Georgia Institute of Technology, August 2006

http://hdl.handle.net/1853/11584

• Mao-Hua Yang, Nash-Stackelberg equilibrium solutions for linear multidivisional multilevel pro-gramming problems, STATE UNIVERSITY OF NEW YORK AT BUFFALO. 2005

http://www.acsu.buffalo.edu/˜bialas/public/pub/Papers/YangMHPhD05.pdf

• Fabian Bastin, Trust-Region Algorithms for Nonlinear Stochastic Programming and Mixed LogitModels, FACULTES UNIVERSITAIRES NOTRE-DAME DE LA PAIX NAMUR, FACULTEDES SCIENCES. 2004

http://hdl.handle.net/2078.2/4153

• Sudaryanto, A fuzzy multi-attribute decision making approach for the identification of the key sectorsof an economy: The case of Indonesia, RWTH Aachen Germany. 2003

http://darwin.bth.rwth-aachen.de/opus3/volltexte/2003/591/

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The main feature of this approach is that the imprecision inherent in the qualitative in-formation can be formalized by applying fuzzy sets theory. The fuzzy-MCDM methodshave basically been developed along the same lines as conventional MCDM methods,but are designed with the help of fuzzy set theory to deal specifically with MCDM prob-lems containing fuzzy data [Zimmmermann, 1987, 1996], [Chen and Hwang, 1992],[Carlsson and Fuller, 1996, p. 139]. The introduction of fuzzy set theory to the field ofdecision making provides a consistent representation of qualitatively or linguisticallyformulated knowledge in such a way that still allows the use of precise operators andalgorithms. (pages 168-169)

• A. Valls Mateu, CLUSDM: a multiple criteria decision making method for heterogeneous data sets,Polytechnic University of Catalonia. 2002

http://www.tesisenred.net/TDX-0206103-205841

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Fuzzy multiple criteria decision making: Recent …rfuller/fs13.pdf · · 2011-08-28a basis for more systematic and rational decision making with multiple criteria, ... fuzzy mathematical

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