Stability on multiobjective linear programming problems with fuzzy parameters

This paper deals with multiobjective linear programming problems with fuzzy parameters. For such problems, some stability notions as the solvability set and the stability set of the first kind (SSK1) are defined and characterized. Two algorithms for the determination of the set (SSK1) are proposed. One of these algorithms is applied when the fuzzy multiobjective problem remains linear after introducing the so-called α-level set of the fuzzy numbers, while the other algorithm is applied when the fuzzy multiobjective problem becomes nonlinear. Finally, a numerical example is given to illustrate the theory developed in the paper.