Multi-objective Linear Fractional Programming Problem with Fuzzy Parameters

Abstract

In this paper, a method is developed to derive the acceptable ranges of objective values for a multi-objective linear fractional programming problem(MOLFPP) with fuzzy parameters both in objectives and constraints. $\alpha$- and $\beta$-cuts are respectively used in the objectives and constraints to specify the degrees of satisfaction and transform the fuzzy parameters into closed intervals. Using variable transformation and Taylor series expansion, the interval-valued fractional objectives are approximated by intervals of linear functions. The objective functions are assigned proper weights using analytic hierarchy process. Weighting sum method is used to transform the interval-valued multiple objectives into single objective. MOLFPP in interval-valued form is equivalently formulated as two linear problems which derive the acceptable ranges of objective values. Two numerical examples are illustrated to demonstrate the proposed method.