Cubical fuzzy Hamacher aggregation operators in multi-attribute decision-making problems

Abstract

Cubical fuzzy sets, a novel structure, deal with the fuzziness of information more effectively than picture fuzzy sets and spherical fuzzy sets. Each member of a CFS is an ordered quadruple consisting of an element of the universe of discourse and three numbers in the unit interval called, respectively, membership grade, neutral membership grade, and non-membership grade, such that their cubic sum is bounded by one. CFSs, being an extension of PFSs and CFSs by enlarging the space of membership grades, give decision-makers more leeway in assigning values. In this paper, we first integrate the notion of Hamacher T-norm and T-conorm with the structure of CFSs to devise the novel cubical fuzzy Hamacher operations and discuss their essential properties. Then, by employing the idea of cubical fuzzy Hamacher operations, we introduce novel aggregation operators called cubical fuzzy Hamacher aggregation operators. The concepts of the cubical fuzzy Hamacher weighted average operator, the cubical fuzzy Hamacher ordered weighted average operator, and the cubical fuzzy Hamacher hybrid average weighted operator are presented and discussed thoroughly in the first section of this work. The cubical fuzzy Hamacher weighted geometric operator, the cubical fuzzy Hamacher ordered weighted geometric operator, and the cubical fuzzy Hamacher hybrid geometric operator are introduced in the second portion, and its essential features are explored. The proposed operators are then used to create some strategies for solving cubical fuzzy information-based multiple attribute decision-making issues. Finally, to demonstrate the applicability and efficiency of the proposed methodology, a real-world example of cyclone disaster appraisal is provided. © 2023, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.