A general approach to solving a wide class of fuzzy optimization problems

Ekel, Petr; Pedrycz, Witold; Schinzinger, Roland

doi:10.1016/s0165-0114(96)00334-x

Cited by 65 publications

(52 citation statements)

References 9 publications

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“…, q are importance factors of the corresponding criteria, defined as w p ∈ [0, 1] and q p=1 w p = 1. The construction of T (X k , X l ), allows one to obtain the membership function N DT (X k ) of the fuzzy set of nondominated alternatives by subsequently applying (7) and (14) to (19). The intersection…”

Section: A Methods For Multicriteria Decision Making Based On the Orlomentioning

confidence: 99%

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Construction of nonreciprocal fuzzy preference relations with the use of preference functions

Parreiras¹,

Ekel²

2013

Pesqui. Oper.

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ABSTRACT. In order to model the preferences of a decision-maker (DM) by means of fuzzy preference relations, a DM can utilize different preference formats (such as ordering of the alternatives, utility values, multiplicative preference relations, fuzzy estimates, and reciprocal as well as nonreciprocal fuzzy preference relations) to express his/her judgments. Afterward, the obtained information is utilized to construct fuzzy preference relations. Here we introduce a procedure that allows the use of so-called preference functions (which is a preference format utilized in the methods of PROMETHEE family) to construct nonreciprocal fuzzy preference relations. With diverse preference formats being offered, a DM can select the one that is the most convenient to articulate his/her preferences. In order to demonstrate the applicability of the proposed procedure a multicriteria decision-making problem related to the site selection for constructing a new hospital is considered here.

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Section: A Methods For Multicriteria Decision Making Based On the Orlomentioning

confidence: 99%

“…The approaches to dealing with multicriteria (multiattribute) decision-making problems, which, for instance, are discussed in Orlovsky (1978), Chiclana et al (1998), Ekel et al (1998), Chiclana et al (2001), are directed at processing the individual preferences as a pair X, R , X = {X 1 , X 2 , . .…”

Section: Introductionmentioning

confidence: 99%

Construction of nonreciprocal fuzzy preference relations with the use of preference functions

Parreiras¹,

Ekel²

2013

Pesqui. Oper.

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“…We can highlight some papers that solve problems with uncertainties in the set of constraints, as described in (Lee et al, 1999), (Silva et al, 2008), (Trappey et al, 1988) and (Xu, 1989). Other methods deal with the uncertainties present in some parameters that can be coefficients and/or decision variables, as described in (Berredo et al, 2005), (Ekel et al, 1998), (Ekel, 2002) and (Galperin & Ekel, 2005).…”

Section: Introductionmentioning

confidence: 99%

Application of an iterative method and an evolutionary algorithm in fuzzy optimization

2012

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ABSTRACT. This work develops two approaches based on the fuzzy set theory to solve a class of fuzzy mathematical optimization problems with uncertainties in the objective function and in the set of constraints. The first approach is an adaptation of an iterative method that obtains cut levels and later maximizes the membership function of fuzzy decision making using the bound search method. The second one is a metaheuristic approach that adapts a standard genetic algorithm to use fuzzy numbers. Both approaches use a decision criterion called satisfaction level that reaches the best solution in the uncertain environment. Selected examples from the literature are presented to compare and to validate the efficiency of the methods addressed, emphasizing the fuzzy optimization problem in some import-export companies in the south of Spain.

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“…Investigations of recent years show the benefits of applying fuzzy set theory [1,2] to deal with diverse types of uncertainty. Its use in problems of optimization character offers advantages of both fundamental nature (the possibility of validly obtaining more effective, less 'cautious' solutions) and of a computational character [3,4].…”

Section: Introductionmentioning

confidence: 99%

“…• Problems that, from the substantial point of view, may be solved on the basis of a single criterion; however, if the uncertainty of information does not permit one to obtain a unique solution, it is possible to reduce these problems to multicriteria decision making because the use of additional criteria (including criteria of qualitative character) can serve as a convincing means to contract the decision uncertainty regions [3].…”

Section: Introductionmentioning

confidence: 99%

Models and methods of decision making in fuzzy environment and their applications to power engineering problems

Canha

Ekel

Queiroz

et al. 2007

Numerical Linear Algebra App

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SUMMARYResults of research into the use of fuzzy sets for handling various forms of uncertainty in optimization problems are presented. Two types of situations which need the application of a multicriteria approach are classified. According to this, two classes of models ( X, M and X, R models) are considered with utilizing the Bellman-Zadeh approach to decision making in a fuzzy environment and techniques for modelling of fuzzy preference relations for their analysis. The application of the Bellman-Zadeh approach for solving X, M problems conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analysing associated maxmin problems. Analysis of X, R models is considered as part of a general approach to solving problems with fuzzy coefficients. Three techniques for processing of fuzzy preferences relations are considered. The first technique is associated with building and analysing a membership function of a subset of non-dominated alternatives considering all criteria simultaneously. The second technique is of a lexicographic character and consists in step-by-step consideration of criteria. The third technique is based on aggregating membership functions of subsets of non-dominated alternatives for each criterion. The results of the paper are universally applicable and are already being used to solve power engineering problems. It is illustrated by considering problems of multicriteria power and energy shortage allocation, multicriteria power system operation, and substation planning with considering criteria of quantitative as well as of qualitative character.

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A general approach to solving a wide class of fuzzy optimization problems

Cited by 65 publications

References 9 publications

Construction of nonreciprocal fuzzy preference relations with the use of preference functions

Construction of nonreciprocal fuzzy preference relations with the use of preference functions

Application of an iterative method and an evolutionary algorithm in fuzzy optimization

Models and methods of decision making in fuzzy environment and their applications to power engineering problems

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