Banzhaf–Choquet-copula-based aggregation operators for managing q-rung orthopair fuzzy information

Abstract

Information fusion of fuzzy numbers has played a vital role in the decision support systems under the environment of q-rung orthopair fuzzy set (q-ROFS), which is an effective extension of intuitionistic fuzzy set and fuzzy set. The goals of the present work are to build a family of new aggregation operators (AOs) under q-ROF environment and apply them to MADM problems. First, the extended Archimedean copula (EAC) and extended Archimedean co-copula (EACC) are proposed to handle q-ROF information; consequently, the operational law of q-ROFNs is defined based on EAC and EACC. In order to comprehensively consider the relationship between attributes, the q-rung orthopair fuzzy Banzhaf–Choquet-copula AOs ( $$BCCA^q$$ ) and q-rung orthopair fuzzy Banzhaf–Choquet-copula geometric operators ( $$BCCG^q$$ ) are introduced on the basis of the operation of q-rung orthopair fuzzy numbers (q-ROFNs); consequently, some special cases of $$BCCA^q$$ / $$BCCG^q$$ operators are investigated when the generators of copula take different functions which satisfy the condition of the generators of copulas. In addition, to determine the fuzzy measure (FM) of attribute sets objectively, the improved maximum deviation method and Banzhaf function model are built. Finally, the corresponding decision-making approaches are constructed based on the proposed AOs and proposed models. Proposed approaches can effectively address the some decision-making problems (DMPs), in which the weights of attributes are incompletely unknown (completely unknown), and the correlation also exists among all attribute sets.