A fuzzy mathematical model to solve multi-objective trapezoidal fuzzy fractional programming problems

Abstract

Decision making problems with ambiguous data often arise in numerous practical fields which can be formulated as optimization models in fuzzy environment. This paper develops a new mathematical model using a proposed methodology to efficiently solve a multi-objective linear fuzzy fractional programming problem in trapezoidal fuzzy environment and generate a set of nondominated solutions. The concept of fuzzy cuts with different degrees of satisfaction is implemented which transforms the fuzzy optimization into an equivalent interval valued optimization. Subsequently, interval valued linear functions approximate the fuzzy valued fractional functions based on Taylor’s series expansion. Finally, a proposed concept using weighting sum approach with varying weight vectors is utilized to design a mathematical model which generates the set of nondominated solutions. Two numerical examples including an existing problem and an additional practical problem in the field of production, are solved for the illustration of the proposed model. The results of the numerical problems are comparatively discussed with graphical analysis to justify the feasibility and applicability of the proposed model.