AN APPROACH FOR SOLVING BILEVEL LINEAR FRACTIONAL PROGRAMMING PROBLEMS USING PENTAGONAL INTUITIONISTIC FUZZY NUMBER
This study presents a novel methodology for addressing intuitionistic fuzzy bilevel linear fractional programming problems (IFBLFPP). The proposed approach utilizes pentagonal intuitionistic fuzzy numbers to represent the cost coefficients of the objective function, resource constraints, and technological coefficients. To solve the IFBLFPP, the problem is first transformed into an intuitionistic fuzzy bilevel linear programming problem (IFBLPP), which is subsequently converted into a crisp bilevel linear fractional programming problem (CBLFPP) through a rigorously defined accuracy function. Several theorems are established to demonstrate that an efficient solution of the CBLFPP also serves as an efficient solution for the IFBLFPP. By applying Zimmermann's technique along with suitable non-linear membership functions, the CBLFPP is further simplified into a single-objective linear programming problem. The practicality and effectiveness of the proposed methodology are illustrated through a numerical example.
Pentagonal Intuitionistic Fuzzy Number, Efficient Solution, Linear Membership Function, Bilevel Linear Programming.