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.
Highlights
Multiple attribute decision making is an important constituent of modern decision science and management, which is a procevss of evaluating and selecting the optimal alternative by scientific and reasonable approaches based upon the selected multiple attributes and assessment information
In order to cope with this defect and describe the uncertainty and fuzziness of information more effectively, the fuzzy set (FS) [1] theory and its expansions form intuitionistic fuzzy set (IFS) [2], interval-valued intuitionistic fuzzy set (IVIFS) [3] are propounded and these fuzzy sets are wide-ranging utilized to handle decision making (DM) problems [4]–[12]
The mainly intentions and contributions of this research are outline following: 1) To extend ACC to SVN and propound several novel general operational rules of single-valued neutrosophic number (SVNN); 2) To combine Power average (PA) operator and the new operation to develop a series of SVN power aggregation operators (AOs) including SVN copula power average(SVNCPA) operator, weighted SVN copula power average (WSVNCPA) operator, order weighted SVN copula power average (OWSVNCPA) operator and corresponding geometric operators; 3) To extend the proposed AOs to their generalized version namely GWSVNCPA operator, GOWSVNCPA operator,GWSVNCPG operator and GOWSVNCPG operator; 4) To set up an multi-attribute decision-making (MADM) approach with the weight information unknown based on the propounded AOs; 5) To confirm the validity and strength of propounded method through empirical application and comparative study
Summary
Multiple attribute decision making is an important constituent of modern decision science and management, which is a procevss of evaluating and selecting the optimal alternative by scientific and reasonable approaches based upon the selected multiple attributes and assessment information. The mainly intentions and contributions of this research are outline following: 1) To extend ACC to SVN and propound several novel general operational rules of SVNN; 2) To combine PA operator and the new operation to develop a series of SVN power AOs including SVN copula power average(SVNCPA) operator, weighted SVN copula power average (WSVNCPA) operator, order weighted SVN copula power average (OWSVNCPA) operator and corresponding geometric operators; 3) To extend the proposed AOs to their generalized version namely GWSVNCPA operator, GOWSVNCPA operator,GWSVNCPG operator and GOWSVNCPG operator; 4) To set up an MADM approach with the weight information unknown based on the propounded AOs; 5) To confirm the validity and strength of propounded method through empirical application and comparative study.
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