Full Fuzzy Fractional Programming Based on the Extension Principle

Abstract

We address the full fuzzy linear fractional programming problem with LR fuzzy numbers. Our goal is to revitalize a strict use of extension principle by employing it in all stages of our solution approach, thus deriving results that fully comply to it. Using the a-cuts of the coefficients we present the linear optimization models that empirically derive the a-cuts of the optimal objective fuzzy value, and discuss the optimization models able to derive the exact endpoints of the optimal objective values intervals. For initial maximization (minimization) problems the main issue is related to how to solve two stage min-max (max-min) problems to obtain the left (right) most endpoints. Our goals are as it follows: to obtain exact solutions to small-size problems; to obtain relevant information about solutions to large-scale problems that are in accordance to the extension principle; and to provide a procedure able to measure to which extent the solutions obtained by an approach to full fuzzy linear fractional programming comply to the extension principle. We illustrate the theoretical findings reporting numerical results, and including a relevant comparison to the results from the literature.