A Novel Hesitant Cubical Dombi Fuzzy Aggregation Operators for Selecting Green Supplier Chain Managements

A hesitant fuzzy (HF) set enhances the concept of fuzzy sets by addressing disagreements among decision-makers about the membership degree of an element. Similarly, the Cubical Fuzzy Set (CFS) is useful for managing uncertainty in decision-making problems. However, existing methods often lack integration of hesitation and cubical uncertainty, and there is limited exploration of their combined effects on aggregation processes. In this paper, we introduce the Hesitant Cubical Fuzzy Set (HCFS), which integrates the principles of HF sets and CFS to address these limitations. We define several set-theoretical operations for HCFSs and develop Dombi operations for them. Furthermore, we present a range of aggregation operators based on Dombi operations, including the Hesitant Cubical Dombi Fuzzy Weighted Arithmetic Averaging (HCDFWAA) Operator, the Hesitant Cubical Dombi Fuzzy Weighted Geometric Averaging (HCDFWGA) Operator, the Hesitant Cubical Dombi Fuzzy Ordered Weighted Arithmetic Averaging (HCDFOWAA) Operator, and the Hesitant Cubical Dombi Fuzzy Ordered Weighted Geometric Averaging (HCDFOWGA) Operator, and examine their properties. Additionally, we propose a multi-criteria group decision-making method and algorithm within the Hesitant Cubical Fuzzy framework. To address gaps in practical application, we provide an example of the selection of green suppliers in supply chain management. We also perform a comparative analysis with existing operators to highlight the advantages and effectiveness of our approach, emphasizing how the integration of hesitation and cubical uncertainty can enhance decision-making processes.