A novel approach for the solution of multiobjective optimization problem using hesitant fuzzy aggregation operator

¹ SQC & OR Unit, Indian Statistical Institute, Bangalore, India
² Indian Institute of Technology, Gandhinagar, Gujarat, India
³ Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh, India

^* Corresponding author: firoz.ahmad02@gmail.com

Received: 1 September 2021
Accepted: 9 January 2022

Abstract

Many decision-making problems can solve successfully by traditional optimization methods with a well-defined configuration. The formulation of such optimization problems depends on crisply objective functions and a specific system of constraints. Nevertheless, in reality, in any decision-making process, it is often observed that due to some doubt or hesitation, it is pretty tricky for decision-maker(s) to specify the precise/crisp value of any parameters and compelled to take opinions from different experts which leads towards a set of conflicting values regarding satisfaction level of decision-maker(s). Therefore the real decision-making problem cannot always be deterministic. Various types of uncertainties in parameters make it fuzzy. This paper presents a practical mathematical framework to reflect the reality involved in any decision-making process. The proposed method has taken advantage of the hesitant fuzzy aggregation operator and presents a particular way to emerge in a decision-making process. For this purpose, we have discussed a couple of different hesitant fuzzy aggregation operators and developed linear and hyperbolic membership functions under hesitant fuzziness, which contains the concept of hesitant degrees for different objectives. Finally, an example based on a multiobjective optimization problem is presented to illustrate the validity and applicability of our proposed models.