New similarity measures for single-valued neutrosophic sets with applications in pattern recognition and medical diagnos
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ORIGINAL ARTICLE
New similarity measures for single-valued neutrosophic sets with applications in pattern recognition and medical diagnosis problems Jia Syuen Chai1 · Ganeshsree Selvachandran1 · Florentin Smarandache2 · Vassilis C. Gerogiannis3 · Le Hoang Son4 · Quang-Thinh Bui5,6 · Bay Vo7 Received: 15 July 2020 / Accepted: 10 October 2020 © The Author(s) 2020
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. Keywords Single-valued neutrosophic set · Fuzzy sets · Multi-criteria decision making · Similarity measures · Distance measures
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Introduction The connection between precision and uncertainty has perplexed humanity for centuries. Lukasiewicz [1], a Polish logician and philosopher, gave the first formulation of multivalued logic which led to the study of possibility theory. The first simple fuzzy set and fundamental thoughts of fuzzy set operations were proposed by Black [2]. 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
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Bay Vo [email protected]
Extended author information available on the last page of the article
a fuzzy set is a single value in the interval of [0
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