Fuzzy Goal Programming Procedures for Multi-Level Multi-Objective Linear Fractional Programming Problems

Document Type : Original Article


Department of Basic Sciences, Faculty of Engineering, Benha University, EL-Qalyoubia - Egypt.


This paper presents two fuzzy goal programming (FGP) procedures for solving multi-level multi-objective linear fractional programming (ML-MOLFP) problems. In the proposed procedures, the membership functions for the defined fuzzy goals of all objective functions at all levels as well as the membership functions for vectors of fuzzy goals of the decision variables, controlled by decision makers at the top levels, are developed in the model formulation of the problem. Then fuzzy goal programming 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. The first proposed FGP procedure makes an extension work of Pramanik and Roy [23] and of B.B. Pal et al. [17,20]. The second proposed procedure my be seem as lexicographic methods for solving multiobjective programming problems that follows Shih et al. concept [28] but by using the FGP approach. The method of variable change on the under- and over-deviational variables of the membership goals associated with the fuzzy goals of the model is introduced to solve the problem efficiently by using linear goal programming (LGP) methodology. Illustrative numerical example is given to demonstrate the algorithms.