Journal
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS
Volume 42, Issue 1, Pages 283-293Publisher
IOS PRESS
DOI: 10.3233/JIFS-219192
Keywords
Fully fuzzy multi-objective linear programming problem; compromise solution; ranking method; distance method and zero-sum game
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This study proposes a new algorithm that converts FFMOLP problems into FFLP problems and finds fuzzy compromise solutions through a game theory approach.
Solving multi-objective linear programming (MOLP) problems and fully fuzzy multi-objective linear programming (FFMOLP) problems involves the trade-off process among several objectives. A new algorithm extended where FFMOLP problems are solved using a 2-player zero-sum game approach to deal with this case. Firstly, The FFMOLP problem is separated into a certain number of fully fuzzy linear programming (FFLP) problems and each is solved by applying any method. After forming a ratio matrix, a game theory approach is applied for finding the weights of objective functions and a weighted LP problem is constructed by these weights. Solving the weighted LP problem, a fuzzy compromise solution of the FFMOLP problem is found. Constructing different ratio matrices, it is also possible to obtain more than one compromise solution to be offered to the decision-maker(s). Some examples are given to show the applicability of the algorithm.
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