An Iterative Fuzzy Goal Programming Method to Solve Fuzzified Multiobjective Fractional Programming Problems
This paper presents a fuzzy goal programming (FGP) approach for modeling and solving multiobjective fractional programming problems (MOFPPs) with fuzzy numbers parameter sets. In the proposed approach, first the notion of α-cut in fuzzy sets (FSs) is used to transform a problem into conventional MOFPP by using the tolerance membership functions in FSs. In model formulation, membership functions are converted into fuzzy goals for measuring the degree of satisfaction of decision maker (DM) with the solution for achievement of fuzzily described objectives of the problem. In the solution process, an iterative parametric method is addressed within the framework of minsum FGP model to reach the highest membership value (unity) to the extent possible in the decision making environment. The efficiency of the proposed approach is illustrated by a numerical example. The model solution is also compared with the solution obtained by using other approaches studied previously.
KeywordsFractional programming Fuzzy Goal programming Iterative parametric method Membership functions Triangular fuzzy number
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