A Bi-Level Non-Linear Multi-Objective Decision Making under Fuzziness

Abstract

This paper studies a bi-level non-linear multi-objective decision making (BLN — MODM) problem with linear (or nonlinear) constraints, and in which the objective function at each levels are nonlinear functions, which are to be maximized. The BLN-MODM problem can be thought of as a static version of the Stackelberg leader-follower game in which a Stackelberg strategy is used by the leader (or the higher — level decision maker (HLDM)), given the rational reaction of the follower (or the lower-level decision maker (LLDM)). From this point of view, this paper proposes a two-planner bi-level multi-objective decision-making model and solution method for solving this problem. This method uses the concepts of tolerance membership function and multi-objective optimization (MOO) (at each level) to develop a fuzzy max — min decision model for generating Pareto optimal (satisfactory) solution for BLN — MODM problem. The HLDM specifies his/her objective functions and decisions with possible tolerances, which are described by membership functions of fuzzy set theory. Then, the LLDM uses this preference information for HLDM and solves his/her problem subject to the HLDMs’ restrictions. An illustrative numerical example is given to demonstrate the obtained results.