Hybrid approach for solving fuzzy fractional linear optimization problems
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In this paper, a new method is proposed to solve fuzzy fractional linear problems with triangular fuzzy coefficients. It consists of a combination of two resolution approaches in order to deduce a more efficient hybrid method. Indeed, this hybridization combines Veeramani-Sumathi method and Dinckelbach's theorem. To solve fuzzy fractional linear problems, our new method proceeds in four stages. First, it transforms fuzzy fractional linear program into a deterministic fractional linear multiobjective program. Then, it transforms this second form into a linear mono-objective program. Thereafter, it solves the obtained last form of the problem by using the Danztig's simplex method. Finally, it uses the arithmetic fuzzy operations to bring back the obtained solution in the fuzzy set. For our new method, a theorem have been produced to highlight the justification of the theoretical mathematical foundations and two didactic examples are been solved to prove its numerical performances.
Abstract
In this paper, a new method is proposed to solve fuzzy fractional linear problems with triangular fuzzy coefficients. It consists of a combination of two resolution approaches in order to deduce a more efficient hybrid method. Indeed, this hybridization combines Veeramani-Sumathi method and Dinckelbach's theorem. To solve fuzzy fractional linear problems, our new method proceeds in four stages. First, it transforms fuzzy fractional linear program into a deterministic fractional linear multiobjective program. Then, it transforms this second form into a linear mono-objective program. Thereafter, it solves the obtained last form of the problem by using the Danztig's simplex method. Finally, it uses the arithmetic fuzzy operations to bring back the obtained solution in the fuzzy set. For our new method, a theorem have been produced to highlight the justification of the theoretical mathematical foundations and two didactic examples are been solved to prove its numerical performances.
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