Journal ArticleDOI
Using fuzzy numbers in linear programming
José Manuel Cadenas,José L. Verdegay +1 more
- Vol. 27, Iss: 6, pp 1016-1022
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TLDR
This paper studies a linear programming problem in which all its elements are defined as fuzzy sets, and shows how it is possible to address and solve linear programming problems with data given in a qualitative form, instead of the usual quantitative and precise way.Abstract:
Managers, decision makers, and experts dealing with optimization problems often have a lack of information on the exact values of some parameters used in their problems. To deal with this kind of imprecise data, fuzzy sets provide a powerful tool to model and solve these problems. This paper studies a linear programming (LP) problem in which all its elements are defined as fuzzy sets. Special cases of this general model are found and reproduced, and it is shown that they coincide with the particular problems proposed in the literature by different authors and distinct approaches. Solution methods are also provided. They show how it is possible to address and solve linear programming problems with data given in a qualitative form, instead of the usual quantitative and precise way.read more
Citations
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Theory and practice of uncertain programming
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Multiple criteria decision making
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TL;DR: In this Chapter, a decision maker (or a group of experts) trying to establish or examine fair procedures to combine opinions about alternatives related to different points of view is imagined.
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Linear programming with fuzzy parameters: an interactive method resolution
TL;DR: A fuzzy ranking method is used to rank the fuzzy objective values and to deal with the inequality relation on constraints in linear programming problems where all the coefficients are, in general, fuzzy numbers.
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Expected value operator of random fuzzy variable and random fuzzy expected value models
Yian-Kui Liu,Baoding Liu +1 more
TL;DR: A new definition of the expected value operator of a random fuzzy variable is presented, and the linearity of the operator is proved, and aRandom fuzzy simulation approach, which combines fuzzy simulation and random simulation, is designed to estimate the expectedvalue of arandom fuzzy variable.
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Fuzzy optimization for supply chain planning under supply, demand and process uncertainties
TL;DR: A fuzzy mathematical programming model for supply chain planning which considers supply, demand and process uncertainties, formulated as a fuzzy mixed-integer linear programming model where data are ill-known and modelled by triangular fuzzy numbers is proposed.
References
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Book
Fuzzy sets
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Journal ArticleDOI
The concept of a linguistic variable and its application to approximate reasoning—II☆
TL;DR: Much of what constitutes the core of scientific knowledge may be regarded as a reservoir of concepts and techniques which can be drawn upon to construct mathematical models of various types of systems and thereby yield quantitative information concerning their behavior.
Book
Fuzzy Sets and Systems: Theory and Applications
Didier Dubois,Henri Prade +1 more
TL;DR: This book effectively constitutes a detailed annotated bibliography in quasitextbook style of the some thousand contributions deemed by Messrs. Dubois and Prade to belong to the area of fuzzy set theory and its applications or interactions in a wide spectrum of scientific disciplines.
Book ChapterDOI
Multiple criteria decision making
János Fodor,Marc Roubens +1 more
TL;DR: In this Chapter, a decision maker (or a group of experts) trying to establish or examine fair procedures to combine opinions about alternatives related to different points of view is imagined.