Bi-criteria multi facility location problem in fuzzy environment
TL;DR: In this article, a fuzzy goal programming model for locating multiple new facilities on a plane bounded by a convex polygon under the criteria: (1) minimize the sum of all the transportation costs and (2) minimise the maximum distances from the facilities to the demand points.
About: This article is published in Fuzzy Sets and Systems.The article was published on 1993-06-10. It has received 43 citations till now. The article focuses on the topics: Convex polygon & Facility location problem.
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TL;DR: A review on recent efforts and development in multi-criteria location problems in three categories including bi-objective, multiobjective and multi-attribute problems and their solution methods is provided in this article.
551 citations
Cites background from "Bi-criteria multi facility location..."
...[32] developed a fuzzy goal programming for their convex multi-facility location problem with minisum (transportation cost) and minimax (distance) objectives with rectilinear distances....
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TL;DR: This work presents a fuzzy TOPSIS model under group decisions for solving the facility location selection problem, where the ratings of various alternative locations under different subjective attributes and the importance weights of all attributes are assessed in linguistic values represented by fuzzy numbers.
Abstract: This work presents a fuzzy TOPSIS model under group decisions for solving the facility location selection problem, where the ratings of various alternative locations under different subjective attributes and the importance weights of all attributes are assessed in linguistic values represented by fuzzy numbers. The objective attributes are transformed into dimensionless indices to ensure compatibility with the linguistic ratings of the subjective attributes. Furthermore, the membership function of the aggregation of the ratings and weights for each alternative location versus each attribute can be developed by interval arithmetic and α -cuts of fuzzy numbers. The ranking method of the mean of the integral values is applied to help derive the ideal and negative-ideal fuzzy solutions to complete the proposed fuzzy TOPSIS model. Finally, a numerical example demonstrates the computational process of the proposed model.
290 citations
TL;DR: This paper provides a survey of the application of fuzzy set theory in production management research, and identifies selected bibliographies on fuzzy sets and applications.
Abstract: Fuzzy set theory has been used to model systems that are hard to define precisely. As a methodology, fuzzy set theory incorporates imprecision and subjectivity into the model formulation and solution process. Fuzzy set theory represents an attractive tool to aid research in production management when the dynamics of the production environment limit the specification of model objectives, constraints and the precise measurement of model parameters. This paper provides a survey of the application of fuzzy set theory in production management research. The literature review that we compiled consists of 73 journal articles and nine books. A classification scheme for fuzzy applications in production management research is defined. We also identify selected bibliographies on fuzzy sets and applications.
182 citations
Cites background from "Bi-criteria multi facility location..."
...Bhattacharya et al. (1993) formulate a fuzzy goal programming model for locating a single facility within a given convex region subject to the simultaneous consideration of two criteria: (1) minimize the sum of all transportation costs; and (2) minimize the maximum distances from the facilities to the demand points....
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TL;DR: Three types of fuzzy programming models – fuzzy expected cost minimization model, fuzzy a-cost minimizationmodel, and credibility maximization model – are proposed according to different decision criteria in order to model capacitated location–allocation problem with fuzzy demands.
122 citations
Cites background from "Bi-criteria multi facility location..."
...For example, in Bhattacharya, Rao, and Tiwari (1992, 1993) new facilities are considered to be located under multiple fuzzy criteria, and a fuzzy goal programming approach has been developed to deal with the problems....
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TL;DR: In this paper, a new model named α-cost model under the Hurwicz criterion is presented with fuzzy demands, and the simplex algorithm, fuzzy simulations and a genetic algorithm are integrated to produce a hybrid intelligent algorithm.
102 citations
References
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TL;DR: In this article, the authors consider statistical mechanics as a form of statistical inference rather than as a physical theory, and show that the usual computational rules, starting with the determination of the partition function, are an immediate consequence of the maximum-entropy principle.
Abstract: Information theory provides a constructive criterion for setting up probability distributions on the basis of partial knowledge, and leads to a type of statistical inference which is called the maximum-entropy estimate. It is the least biased estimate possible on the given information; i.e., it is maximally noncommittal with regard to missing information. If one considers statistical mechanics as a form of statistical inference rather than as a physical theory, it is found that the usual computational rules, starting with the determination of the partition function, are an immediate consequence of the maximum-entropy principle. In the resulting "subjective statistical mechanics," the usual rules are thus justified independently of any physical argument, and in particular independently of experimental verification; whether or not the results agree with experiment, they still represent the best estimates that could have been made on the basis of the information available.It is concluded that statistical mechanics need not be regarded as a physical theory dependent for its validity on the truth of additional assumptions not contained in the laws of mechanics (such as ergodicity, metric transitivity, equal a priori probabilities, etc.). Furthermore, it is possible to maintain a sharp distinction between its physical and statistical aspects. The former consists only of the correct enumeration of the states of a system and their properties; the latter is a straightforward example of statistical inference.
12,099 citations
TL;DR: It is shown that solutions obtained by fuzzy linear programming are always efficient solutions and the consequences of using different ways of combining individual objective functions in order to determine an “optimal” compromise solution are shown.
3,357 citations
TL;DR: In this paper, the concept of proper efficiency was introduced to eliminate efficient points of a certain anomalous nature in the problem of vector maximization, which is related in spirit to the notion of "proper" efficiency introduced by Kuhn and Tucker in their celebrated paper of 1950.
1,272 citations
TL;DR: An interactive mathematical programming approach to multi-criterion optimization is developed, and then illustrated by an application to the aggregated operating problem of an academic department.
Abstract: An interactive mathematical programming approach to multi-criterion optimization is developed, and then illustrated by an application to the aggregated operating problem of an academic department.
837 citations
01 Jan 1973
TL;DR: The main concern is with the application of the theory of fuzzy sets to decision problems involving fuzzy goals and strategies, etc., as defined by R. E. Bellman and L. A. Zadeh.
Abstract: In problems of system analysis, it is customary to treat imprecision by the use of probability theory. It is becoming increasingly clear, however, that in the case of many real world problems involving large scale systems such as economic systems, social systems, mass service systems, etc., the major source of imprecision should more properly be labeled ‘fuzziness’ rather than ‘randomness.’ By fuzziness, we mean the type of imprecision which is associated with the lack of sharp transition from membership to nonmembership, as in tall men, small numbers, likely events, etc. In this paper our main concern is with the application of the theory of fuzzy sets to decision problems involving fuzzy goals and strategies, etc., as defined by R. E. Bellman and L. A. Zadeh [1]. However, in our approach, the emphasis is on mathematical programming and the use of the concept of a level set to extend some of the classical results to problems involving fuzzy constraints and objective functions.
593 citations