Hesitant intuitionistic fuzzy algorithm for multiobjective optimization problem

Abstract

Every real-life optimization problem with uncertainty and hesitation can not be with a single objective, and consequently, a class of multiobjective linear optimization problems (MOLOP) appears in the literature. Further, the experts assign values of uncertain parameters, and the expert’s opinions about the parameters are conflicting in nature. There are concerning methods based on fuzzy sets, or their other versions are available in the literature that only covers partial uncertainty and hesitation, but the hesitant intuitionistic fuzzy sets provides a collective understanding of the real-life MOLOP under uncertainty and hesitation, and it also reflects better practical aspects of decision-making of MOLOP. In this context, the paper defines the hesitant fuzzy membership function and nonmembership function to tackle the uncertainty and hesitation of the parameters. Here, a new solution called hesitant intuitionistic fuzzy Pareto optimal solution is defined, and some theorems are stated and proved. For the decision-making of MOLOP, we develop an iterative method, and an illustrative example shows the superiority of the proposed method. And lastly, the calculated results are compared with some popular methods.