New Concepts of Feasibility and Efficiency of Solutions in Fuzzy Mathematical Programming Problems

AbstractSome new concepts in regards to ᾱ-feasibility and ᾱ-efficiency of solutions in fuzzy mathematical programming problems are introduced in this paper, where ᾱ is a vector of distinct satisfaction degrees. Based on the defined concepts, a new method is suggested to solve fuzzy mathematical programming problems. In this sense, the proposed approach enables decision makers to take into account more flexible solutions by allowing desired distinct satisfactions in constraints. In the case of linear problems with fuzzy constraints, multi-parametric programming is employed to obtain the optimal solution as an affine function of distinct satisfaction degrees. In particular, it proves that the obtained solution is convex and continuous. Therefore, the different optimal solutions can be obtained by a simple substituting the new values of satisfaction parameters into the parametric profiles without any further optimization calculations, which is desirable for online optimization and sensitivity analysis of the profit to satisfaction parameters