Cotangent Similarity Measure of Consistent Neutrosophic Sets and Application to Multiple Attribute Decision-Making Problems in Neutrosophic Multi-Valued Setting

Abstract

A neutrosophic multi-valued set (NMVS) is a crucial representation for true, false, and indeterminate multi-valued information. Then, a consistent single-valued neutrosophic set (CSVNS) can effectively reflect the mean and consistency degree of true, false, and indeterminate multi-valued sequences and solve the operational issues between different multi-valued sequence lengths in NMVS. However, there has been no research on consistent single-valued neutrosophic similarity measures in the existing literature. This paper proposes cotangent similarity measures and weighted cotangent similarity measures between CSVNSs based on cotangent function in the neutrosophic multi-valued setting. The cosine similarity measures show the cosine of the angle between two vectors projected into a multidimensional space, rather than their distance. The cotangent similarity measures in this study can alleviate several shortcomings of cosine similarity measures in vector space to a certain extent. Then, a decision-making approach is presented in view of the established cotangent similarity measures in the case of NMVSs. Finally, the developed decision-making approach is applied to selection problems of potential cars. The proposed approach has obtained two different results, which have the same sort sequence as the compared literature. The decision results prove its validity and effectiveness. Meantime, it also provides a new manner for neutrosophic multi-valued decision-making issues.