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.

Optimizing the Flood Limit Water Level of Reservoirs in Sediment-Laden Rivers under Changing Water and Sediment Conditions: A Case Study of the Xiaolangdi Reservoir

“…During the solving process, there is no apparent boundary between high and low FLWLs, and a certain degree of fuzzy connection exists between the comprehensive objectives and each sub-objective. Therefore, this study used a multi-objective fuzzy optimization method to research the FLWL optimization and established a comprehensive benefit evaluation model to evaluate the effects of different FLWL operation modes based on the fuzzy optimization theory [32][33][34] and artificial neural network (ANN) with error feedback [35,36].…”