Intuitionistic Fuzzy Sets and Dynamic Programming for Multi-objective Non-linear Programming Problems

Abstract

The practical applications of engineering designs are often concerned by the presence of interrelated decisions. Naturally, these decisions are induced by solving many conflicting and incommensurable objectives. To deal with the interlinked decisions as well as the paradox natures among objectives, this paper presents an integrated approach based on dynamic programming approach (DPA) and intuitionistic fuzzy set (IFS) denoted as DPA-IFS for solving multi-objective optimization problem (MOOP). In DPA-IFS, the principle of DPA aims to generate an efficient solution of MOOP. In contrast, IFS aims to handle conflicting natures among the objective functions by means of the satisfaction (maximization the degree of membership) and dissatisfaction (minimization the degree of non-membership) concepts. The illustration is investigated by numerical illustrations taken from the literature. Furthermore, a new closeness strategy-based distance function is introduced to measure the worth of a satisfactory solution. The proposed methodology is validated on the IEEE 30-bus with six generators as a real test paradigm in the electrical power system. The results obtained by the DPA-IFS show the superior results than those obtained by different approaches.