Fuzzy goal programming algorithm for solving decentralized bi-level multi-objective programming problems

This paper presents fuzzy goal programming (FGP) algorithm for solving decentralized bi-level multi-objective programming (DBL-MOP) problems with a single decision maker at the upper level and multiple decision makers at the lower level. A FGP algorithm for DBL-multi-objective linear programming (DBL-MOLP) problems is proposed. This algorithm is extended to solve bi-level multi-objective linear fractional programming (DBL-MOLFP) problems. In the proposed algorithm, the membership functions for the defined fuzzy goals of all objective functions at the two levels as well as the membership functions for vector of fuzzy goals of the decision variables controlled by ULDM are developed in the model formulation of the problem. Then FGP approach is used to achieve highest degree of each of the membership goals by minimizing their deviational variables and thereby obtaining the most satisfactory solution for all decision makers. Illustrative numerical examples are given to demonstrate the proposed algorithm.