Generalized Heptagonal Membership Function for Fully Fuzzy Linear Fractional Programming Problems

Abstract

Identifying the optimum solution that satisfies the restrictions and maximizes or minimizes the objective function is the aim of fully fuzzy fractional programming (FFFLP). Due to the inclusion of both fuzzy parameters and fractional variables, this problem is difficult to solve. Several approaches, including linear programming, nonlinear programming, genetic algorithms, and computational intelligence algorithms, have been suggested to handle fully fuzzy fractional linear programming (FFFL) problems. For describing the uncertainty, vagueness, or imprecision of information in the real world, triangular and trapezoidal fuzzy numbers are frequently used. Indeed, it is not always practical to limit the membership function to a triangle or trapezoid. This paper submits a new type of Heptagonal fuzzy number and a novel ranking function approach based on generalized heptagonal membership functions suggested for ordering heptagonal fuzzy numbers. On the other hand, we develop the algorithm of the simplex method to find the optimal fuzzy solution for (FFFLP).

Keywords

• Fully Fuzzy Linear Fractional Programming
• Heptagonal Fuzzy Number
• Arithmetic Heptagonal Operations
• Membership Function
• Ranking function
• Fully Fuzzy Simplex method