Solving multi-objective optimization problem in Bipolar Hesitant Fuzzy environment

Department of Mathematics, University of Kalyani, Kalyani, Nadia, West Bengal, India

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 1 February 2024
Accepted: 7 November 2025

Abstract

Multi-objective optimization problems are pervasive in various fields, ranging from engineering and economics to environmental management and decision-making processes. These problems involve the simultaneous optimization of multiple conflicting objectives, often leading to complex and non-linear relationships between decision variables. To tackle such intricate problems, this article introduces a novel approach: Bipolar Hesitant Fuzzy Optimization (BHFO) method. This method extends traditional fuzzy, hesitant fuzzy and bipolar fuzzy optimization techniques by incorporating bipolar hesitant fuzzy sets (BHFS), which allow decision-makers to assign degrees of hesitation and bipolarity to their preferences, reflecting the inherent uncertainty and ambiguity associated with real-world decision-making. This approach recognizes that decision-makers may not always be completely certain about their preferences, which is a common scenario in practical multi-objective optimization problems. In this article, we present the theoretical foundations of the BHFO method, including the representation of the parameter as generalized bipolar parabolic fuzzy numbers and operations on these numbers. The proposed approach empowers decision-makers to navigate the complexities of multi-objective optimization problems effectively, accommodating hesitant and bipolar preferences. Furthermore, we illustrate the application of the BHFO method by solving multi objective production planning problem and the result is compared with the other existing methods.