Employing Novel Ranking Function for Solving Fully Fuzzy Fractional Linear Programming Problems

Abstract

Fuzzy programming is especially useful in cases where the coefficients are ambiguous. Because of this feature, in recent years, numerous techniques have emerged for addressing uncertainty. This paper proposes a novel ranking function technique with variables of type decagonal fuzzy numbers for solving fully fuzzy fractional linear programming (FFFLP) problems. This technique is dependent on introducing a new membership function for a decagonal fuzzy number and using a fully fuzzy simplex method. After converting the FFFLP problem to the fully fuzzy linear programming (FFLP) problem by a complementary method, then solved with the fully fuzzy simplex tables, in which all the values are fuzzy decagonal numbers. With the aid of the arithmetic operations of decagonal numbers, the new iteration of the simplex table is reached. Steps are repeated until the optimal fuzzy solution is reached. To demonstrate the proposed method a numerical example is provided to illustrate the steps of finding an optimal fuzzy solution to the problem.

Keywords

• Arithmetic Decagonal Operations, Decagonal membership function, Fully Fuzzy Fractional Linear Programming, Fully Fuzzy Simplex Method, and Ranking function