Finding compromise solutions for fully fuzzy multi-objective linear programming problems by using game theory approach - Temelcan, Gizem; Kocken, Hale Gonce; Albayrak, Inci (IOS PRESS, 2022)
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.
Keywords: Fully fuzzy multi-objective linear programming problem; compromise solution; ranking method; distance method and zero-sum game; DEVIATION DEGREE; OPTIMIZATION; ALGORITHM; Computer Science