Complex Hesitant Fuzzy Set-Based Multi-Criteria Decision-Making using Hamacher Aggregation Operators

Abstract

Multi-criteria decision-making (MCDM) has become a critical tool for addressing real-world decision-making problems under uncertainty. Classical extensions of fuzzy sets (FSs), such as hesitant fuzzy sets (HFS) and complex hesitant fuzzy sets (CHFS), provide a flexible framework for modelling expert judgment ambiguity. Nevertheless, none of the aggregation operators (AOs) for Hamacher t-norms and t-conorms have been developed within the CHFS framework, thereby limiting their theoretical richness and practical use. To fill this void, this paper presents Hamacher AOs in the framework of CHFS that are complex hesitant fuzzy (CHF) Hamacher weighted averaging (CHFHWA) operator, CHF Hamacher weighted geometric (CHFHWG) operator, and their generalizations (generalized CHFHWA and generalized CHFHWG). Moreover, a systematic MCDM approach is developed using newly defined operators to address complex decision problems with multiple and hesitant criteria. The practical applicability and efficiency of the proposed approach are illustrated by a real-life inspired numerical example of student scholarship selection. The comparative analysis with existing models shows that the proposed operators not only increase the flexibility of information aggregation but also improve decision-making accuracy and robustness.