Open Access

ARTICLE

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

Angyan Tu^1,2, Jiancheng Chen³, Bing Wang^1,*

1 School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, 200444, China
2 Department of Computer Science and Engineering, Shaoxing University, Shaoxing, 312000, China
3 Zhejiang Industry Polytechnic College, Shaoxing, 312000, China

* Corresponding Author: Bing Wang. Email:

(This article belongs to the Special Issue: Extension, Modeling and Applications of Fuzzy Set Theory in Engineering and Science)

Computer Modeling in Engineering & Sciences 2022, 133(2), 377-387. https://doi.org/10.32604/cmes.2022.021299

Received 06 January 2022; Accepted 10 March 2022; Issue published 21 July 2022

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.

---

Keywords

---