A fuzzy approach with required minimum decision tolerances for multi-level multi-objective decision-making problems

Abstract

This paper investigates multi-level multi-objective linear programming problems in fuzzy environments, where each decision level has one decision-maker (DM) with a vector of decision variables and possibly more than one objective function. The objective functions of each DM and the decision variables of higher-level DMs are characterized by membership functions, which are considered as fuzzy goals. In related studies, the tolerances used to define membership functions of higher-level DMs' decision variables are usually subjectively determined. This may lead to infeasible solutions. This paper focuses on the determination of required minimum tolerances for higher-level DMs' decision variables to ensure feasibility in the solution process. A fuzzy goal programming model is established to optimally satisfy all defined fuzzy goals by minimizing satisfaction deviations under the constraint of the leader-follower relationship. A numerical example is provided for demonstrating the proposed approaches. It is shown that existing approaches may not have feasible solutions if the required minimum tolerances are not adopted.