Correlation Coefficients of Consistency Neutrosophic Sets Regarding Neutrosophic Multi-valued Sets and Their Multi-attri
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Correlation Coefficients of Consistency Neutrosophic Sets Regarding Neutrosophic Multi-valued Sets and Their Multiattribute Decision-Making Method Jun Ye1,2
•
Jiamin Song1 • Shigui Du1
Received: 3 June 2020 / Revised: 25 September 2020 / Accepted: 9 October 2020 Taiwan Fuzzy Systems Association 2020
Abstract To overcome the insufficiencies of existing information expression and operations of single-valued neutrosophic multisets (SVNMs) and multi-valued/hesitant neutrosophic sets (MVNSs), this study first introduces neutrosophic multi-valued sets (NMVSs), including SVNMs and MVNSs, as a general concept. Then, we propose a method that transforms NMVSs into consistency single-valued neutrosophic sets (CSVNSs) based on the average values and consistency degrees (complement of standard deviations) of the truth, indeterminacy, falsity multi-valued sequences in NMVSs. CSVNSs not only can realize the reasonable information expression and operation of different sequence lengths/cardinalities between neutrosophic multi-valued elements, but also can reflect the multi-valued sequences close to corresponding average levels in each neutrosophic multi-valued element. Next, we present two correlation coefficients between CSVNSs in the setting of NMVSs. Based on the correlation coefficients of CSVNSs, a decision-making (DM) approach is established in the NMVS setting. Lastly, an illustrative example and comparison with existing methods are presented to demonstrate the effectiveness and rationality of the
& Jun Ye [email protected]; [email protected] Jiamin Song [email protected] Shigui Du [email protected] 1
School of Civil and Environmental Engineering, Ningbo University, Ningbo 315211, People’s Republic of China
2
Department of Electrical and Information Engineering, Shaoxing University, Shaoxing 312000, People’s Republic of China
established DM method in the NMVS setting. The developed DM approach not only makes the DM process more reasonable and credible, but also provides the new modeling method for multi-attribute DM problems in NMVS setting. Keywords Neutrosophic multi-valued set Consistency single-valued neutrosophic set Correlation coefficient Multi-attribute decision-making
1 Introduction The decision-making (DM) problem based on fuzzy theory [1] is an important research topic in management science. Then, one of major problems in the fuzzy DM study is how to represent the complicated fuzzy information effectively and reasonably. Although an (interval-valued) intuitionistic fuzzy set (IFS) [2, 3] can express the membership degree and the nonmembership degree, their range must satisfy the condition that the sum of the membership degree and the nonmembership degree is within the closed interval [0, 1]. Also (interval-valued) IFSs cannot express the information of indeterminacy and inconsistency. To overcome these limitations, interval neutrosophic sets (INSs) [4], singlevalued neutrosophic sets (SVNSs) [5] and simplified neutrosophic sets (SNSs) [6], which are subclasses of neutrosophic sets [7], can be
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