Generalized Pentagonal Linear and Non-linear Functions for Solving Fully Fuzzy Linear Programming Problems

Fuzzy linear programming problems (FLPP) are advanced approaches for solving linear programming problems (LPP) that involve fuzzy coefficients and variables with constraints on the problem. Numerous applications exist for the pentagonal function and ranking membership in geometry and the sciences, especially mathematics. This study suggests a novel approach for solving fully fuzzy linear programming problems (FFLPP) using the ranking function with pentagonal functions. The project aims to determine the maximum (minimum) solution to the problems where all variables, including the objective function, constraints and the right hand, are pentagonal fuzzy numbers. Additionally, generalizations of both linear and nonlinear pentagonal functions were derived, which will be useful in a wide range of future applications. In our research, the optimal solution for (FFLPP) was studied in two cases when Δ1=Δ2and whenΔ1≠Δ2 with proposed linear and nonlinear pentagonal fuzzy numbers with proposed ranking functions and they were compared with each other to find the best solution. To illustrate the effectiveness and dependability of the suggested approach, numerical example of (FFLPP) will be included. Additionally, tables containing the instances have been supplied to confirm the technique’s validity.