CUBIC HESITANT FUZZY SOFT SET AND ITS APPLICATION TO MULTI-CRITERIA DECISION-MAKING

Abstract

In this paper, a novel concept of Cubic Hesitant Fuzzy Soft Sets (Cubic HFSSs) is introduced by integrating the theories of cubic sets and hesitant fuzzy soft sets. Fundamental operational laws of Cubic HFSSs are developed, and their essential properties are thoroughly investigated. Furthermore, several new aggregation operators are proposed, including the Cubic Hesitant Fuzzy Soft Weighted Averaging (Cubic HFSWA), Cubic Hesitant Fuzzy Soft Weighted Geometric (Cubic HFSWG), Cubic Hesitant Fuzzy Soft Ordered Weighted Averaging (Cubic HFOWA), Cubic Hesitant Fuzzy Soft Ordered Weighted Geometric (Cubic HFOWG), and Cubic Hesitant Fuzzy Hybrid Averaging and Geometric operators. The mathematical characteristics of these operators are systematically analyzed. The proposed framework provides a unified and simplified structure encompassing fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and cubic fuzzy sets. In addition, a multi-criteria decision-making (MCDM) approach based on the developed aggregation operators is formulated within the cubic hesitant fuzzy soft environment. A practical numerical example related to the selection of the most suitable crop is presented to demonstrate the applicability and effectiveness of the proposed method. Sensitivity analysis is conducted to examine the stability of the results. Finally, a comparative analysis is performed to validate the superiority and efficiency of the proposed approach over existing decision-making methods.

Keywords : Cubic Hesitant Fuzzy Soft Set; Aggregation Operators; Multi-Criteria Decision-Making; Cubic Fuzzy Set; Hesitant Fuzzy Soft Set.