New similarity measures for single-valued neutrosophic sets with applications in pattern recognition and medical diagnosis problems

Jia Syuen Chai,Bay Vo,Quang-Thinh Bui,Ganeshsree Selvachandran,Vassilis C Gerogiannis,Le Hoang Son,Florentin Smarandache

doi:10.1007/s40747-020-00220-w

Abstract

The single-valued neutrosophic set (SVNS) is a well-known model for handling uncertain and indeterminate information. Information measures such as distance measures, similarity measures and entropy measures are very useful tools to be used in many applications such as multi-criteria decision making (MCDM), medical diagnosis, pattern recognition and clustering problems. A lot of such information measures have been proposed for the SVNS model. However, many of these measures have inherent problems that prevent them from producing reasonable or consistent results to the decision makers. In this paper, we propose several new distance and similarity measures for the SVNS model. The proposed measures have been verified and proven to comply with the axiomatic definition of the distance and similarity measure for the SVNS model. A detailed and comprehensive comparative analysis between the proposed similarity measures and other well-known existing similarity measures has been done. Based on the comparison results, it is clearly proven that the proposed similarity measures are able to overcome the shortcomings that are inherent in existing similarity measures. Finally, an extensive set of numerical examples, related to pattern recognition and medical diagnosis, is given to demonstrate the practical applicability of the proposed similarity measures. In all numerical examples, it is proven that the proposed similarity measures are able to produce accurate and reasonable results. To further verify the superiority of the suggested similarity measures, the Spearman’s rank correlation coefficient test is performed on the ranking results that were obtained from the numerical examples, and it was again proven that the proposed similarity measures produced the most consistent ranking results compared to other existing similarity measures.

Highlights

The connection between precision and uncertainty has perplexed humanity for centuries
Smarandache [8] initially proposed the idea of the neutrosophic set (NS) which, from a philosophical point of view, more effectively deals with imprecise, indeterminate and inconsistent information, that often exists in real-life decision making problems, compared to the classical fuzzy set model [3] and the intuitionistic fuzzy set (IFS) model [7]
We focus on the single-valued neutrosophic set (SVNS) which was presented by Wang et al [10]

Summary

Introduction

The connection between precision and uncertainty has perplexed humanity for centuries. To overcome the problem of handling uncertain and imprecise information in decision making, Zadeh [3] presented the concept of fuzzy set, where the membership degree of each element in B. The IFS model definitely extends the classical fuzzy set model; it is often difficult to be applied in real-life decision making situations, as only incomplete and vague information can be dealt with but not indeterminate or inconsistent information. Smarandache [8] initially proposed the idea of the neutrosophic set (NS) which, from a philosophical point of view, more effectively deals with imprecise, indeterminate and inconsistent information, that often exists in real-life decision making problems, compared to the classical fuzzy set model [3] and the IFS model [7]

Objectives

Discussion

Conclusion