Fuzzy Goal Programming Approach for Quadratic Fractional Bilevel Programming
نویسنده
چکیده
This paper presents a fuzzy goal programming methodology for solving bilevel programming problems having quadratic fractional form of objectives of the decision makers. In the proposed procedure, the membership functions for the defined fuzzy goals of objective of the decision makers at both levels are developed first. Then a fuzzy goal programming model is developed to minimize the group regret of degree of satisfactions of both the decision makers and thereby obtaining the most satisfactory solution in the decision making environment. In the solution process a two step linearization technique is adopted to break the fractional part at its first step and Taylor’s series approximation technique is employed to linearize the quadratic membership goals in the next step. Then the problem is solved to reach a compromise decision by minimizing the deviational variables of the goals in the achievement function for overall benefit of the organization. An illustrative numerical example is solved to demonstrate the efficiency of the proposed procedure and the model solution is compared with the solutions obtained for the use of other existing techniques to expound the potential use of the proposed approach.
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