Solving optimization problems under hesitant fuzzy environment

Abstract

The values of parameters of real-life optimization problem are assigned by experts, and naturally these are imprecise and uncertain due to inexact information. Several researchers have presented computational methods for the solutions of optimization problems based on fixed values, fuzzy values, intuitionistic fuzzy values, and in those methods only single membership degree were used. But, it is very interesting to note that experts’ opinion regarding numerical values of parameters of problem under consideration are slightly different and conflicting; therefore, single membership degree of the uncertain parameters does not deal properly the uncertain situations. Hesitant fuzzy set (HFS) is characterized by set of possible membership degrees of single value. So computational method based on HFS provides a perfect framework for modelling and decision-making of optimization problems under uncertainty and hesitation instead of fuzzy set or intuitionistic fuzzy set (IFS). In this paper, first we introduce the concept of hesitant fuzzy number, triangular hesitant fuzzy number and its expected values. The hesitant fuzzy linear programming and some arithmetic operations of THFN are presented in this paper also. Further, we present an easiest solution methodology for the hesitant optimization problem, and it is numerically illustrated by an example, and further it is applied in meat production planning.