Correlation Coefficients of Consistency Neutrosophic Sets Regarding Neutrosophic Multi-valued Sets and Their Multi-attribute Decision-Making Method

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 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.

Automated summary

This study introduces the concept of neutrosophic multi-valued sets and proposes a method to transform them into consistency single-valued neutrosophic sets, allowing for better expression and operation of different lengths/cardinalities of neutrosophic multi-valued elements. Two correlation coefficients and a decision-making approach are established based on this transformation, and the effectiveness and rationality of the method are demonstrated through an illustrative example and comparison with existing methods.