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

Article type: Research Article

Authors: Chen, Liang-Hsuan | Chen, Hsin-Hung

Affiliations: Department of Industrial and Information Management, National Cheng Kung University, Taiwan, R.O.C.

Note: [] Corresponding author. Liang-Hsuan Chen, Department of Industrial and Information Management, National Cheng Kung University, Taiwan, R.O.C. Tel.: +886 6 2757575/Ext. 53140; Fax: +886 6 2362162; E-mail: [email protected]

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.

Keywords: Multi-level decision-making, multiple objectives, fuzzy mathematical programming

DOI: 10.3233/IFS-141292

Journal: Journal of Intelligent & Fuzzy Systems, vol. 28, no. 1, pp. 217-224, 2015