Taylor series linearization for fully fuzzy multi-objective fractional programming in educational systems

Abstract

This study examines the fully fuzzy multi-objective linear fractional programming problem (FFMOLFPP), whereby both the objective functions and restrictions incorporate fuzzy parameters represented as triangular fuzzy numbers (TFN), without converting them into crisp values. A hybrid solution approach is presented to tackle the intrinsic nonlinearity and uncertainty. Initially, the imprecise numbers are transformed into parametric representations via the y- cut method. A first-order Taylor series expansion is subsequently utilized to linearize each fractional objective function around a fuzzy decision point. The linearized objectives are then consolidated by the weighted sum approach, transforming the multi-objective fuzzy model into a single-objective linear program. Numerical examples validate the strategy and demonstrate the improved accuracy and efficiency of the proposed methodology.