Generalized techniques for solving intuitionistic fuzzy multi-objective non-linear optimization problems

Abstract

This paper focuses on the methods for the efficient solution of multi-objective non-linear optimization problems with uncertain parameters represented as intuitionistic fuzzy numbers. In most of the existing techniques for such problems, generally linear membership (satisfaction) functions have been used. But every real life problem cannot be justified and modeled using the linear functions, so the efficient solution methodologies from the literature such as Zimmermann’s technique, Maximum additive operator technique, γ-operator technique have been extended in this paper by defining the non-linear membership functions in place of the linear ones. Unlike the classical versions of these techniques, the non-linear non-membership (dissatisfaction) functions have also been incorporated along with the memberships. Intuitionistic fuzzy number with non-linear grade functions has been introduced. Appropriate theorems have been proved to support the claims. Two numerical examples in the intuitionistic fuzzy environment from the field of manufacturing and transportation have been considered for the illustration of the proposed technique. The obtained results show the applicability and reliability of the suggested extensions and their comparison with the results obtained from that of the non-modified (traditional) techniques reflects its effectiveness.