Bi-Level Linear Fuzzy Fractional Programming Problem Under Trapezoidal Fuzzy Environment: A Solution Approach

Abstract

This paper proposes a method to solve a bi-level linear fuzzy fractional programming problem comprising all its constants and coefficients expressed in form of trapezoidal fuzzy numbers. Fuzzy $$\alpha , \beta $$ -cuts are respectively used in the objective functions and constraints to equivalently transform the bi-level fuzzy optimization into bi-level interval valued form. Subsequently, a bi-level bi-objective linear fractional programming problem is generated. Change of variable method is implemented to construct linear fuzzy membership functions at upper and lower level. Fuzzy goal programming eliminating over deviations from aspiration level of fuzzy membership functions along with a proposed modified linearization process of fractional functions are together used to determine the compromise solution of the problem. To illustrate and justify the feasibility of the proposed method, an existing numerical problem is solved and the results obtained are comparatively analyzed.