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An epsilon‐constraint method for fully fuzzy multiobjective linear programming
Author(s) -
PérezCañedo Boris,
Verdegay José Luis,
Miranda Pérez Ridelio
Publication year - 2020
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.22219
Subject(s) - mathematical optimization , fuzzy number , fuzzy set operations , mathematics , lexicographical order , fuzzy logic , defuzzification , constraint (computer aided design) , ranking (information retrieval) , fuzzy transportation , linear programming , fuzzy classification , pareto principle , fuzzy set , computer science , artificial intelligence , combinatorics , geometry
Linear ranking functions are often used to transform fuzzy multiobjective linear programming (MOLP) problems into crisp ones. The crisp MOLP problems are then solved by using classical methods (eg, weighted sum, epsilon‐constraint, etc), or fuzzy ones based on Bellman and Zadeh's decision‐making model. In this paper, we show that this transformation does not guarantee Pareto optimal fuzzy solutions for the original fuzzy problems. By using lexicographic ranking criteria, we propose a fuzzy epsilon‐constraint method that yields Pareto optimal fuzzy solutions of fuzzy variable and fully fuzzy MOLP problems, in which all parameters and decision variables take on LR fuzzy numbers. The proposed method is illustrated by means of three numerical examples, including a fully fuzzy multiobjective project crashing problem.