Generalized Single-Valued Neutrosophic Power Aggregation Operators Based on Archimedean Copula and Co-Copula and Their Application to Multi-Attribute Decision-Making

Abstract

Single-valued neutrosophic set (SVN) can valid depict the incompleteness, nondeterminacy and inconsistency of evaluation opinion, and the Power average (PA) operator can take into account the correlation of multiple discussed data. Meanwhile, Archimedean copula and co-copula (ACC) can significant generate operational laws based upon diverse copulas. In this paper, we first redefine several novel operational laws of single-valued neutrosophic number (SVNN) based on ACC and discuss the associated properties of them. In view of these operational rules, we propound several novel power aggregation operators (AOs) to fuse SVN information, i.e., SVN copula power average (SVNCPA) operator, weighted SVNCPA (WSVNCPA) operator, order WSVNCPA operator, and SVN copula power geometric (SVNCPG) operator, weighted SVNCPG (WSVNCPG) operator, order WSVNCPG operator. At the same time, several significant characteristics and particular cases of these operators are examined in detail. Moreover, we extend these operators to their generalized form named generalized SVNCPA and SVNCPG operator. In addition, a methodology is designed based on these operators to cope with multi-attribute decision-making (MADM) problems with SVN information. Consequently, the effectiveness and utility of the designed approach is validated by a empirical example. A comparative and sensitivity analysis are carried out to elaborate the strength and preponderance of the propounded approach. INDEX TERMS Multi-attribute decision-making, single-valued neutrosophic set, aggregation operator, archimedean copula and co-copula, power average.

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“…(2) For the proffered method, the score values of six teachers are first monotonically increasing when κ ∈ [1, 2] and then decreasing monotonically when κ ∈ [2,5]. The PFRWMSM and PFRWGMSM operator undergo the transformation from averaging operator to geometric operator and geometric operator to averaging operator when parameter κ changes from 1 to 5, severally.…”

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