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- MakaleYalnız künye2023Scopus SJRQ1Correlation coefficients of simplified neutrosophic multiplicative sets and their applications in clustering analysis
Köseoğlu, Ali; Şahin, Rıdvan
The use of fuzzy sets, intuitionistic fuzzy sets and neutrosophic sets can often handle with real-life problems that contain incomplete and uncertain information. The 0–1 scale is used to deal with such information which is graded symmetrically and uniformly but, some problems consist of unsymmetrical and non-uniform information. Although intuitionistic multiplicative set (IMS) is a powerful tool to deal with this kind of problems, due to the dependence of hesitant information to the membership and non-membership functions in IMS, it brings a restriction to decision-makers while working on the real-life problems such as applications of correlation coefficients and clustering. In this study, we propose novel correlation coefficients (CCs) of simplified neutrosophic multiplicative sets (SNMSs) which is defined recently by removing the shortages of IMSs. Firstly, we give SNMS-based operations, fulfil the deficiencies in the theoretical background of IMS and establish a theoretical structure for the SNMS. Then, we propose novel correlation coefficients (CC) of SNMS and show some of their important properties. Finally, we apply the CCs to a clustering problem to confirm the efficiency of the proposed SNMS and its correlation coefficients.
AtıfScopus5WoS4OpenAlex6
İncele - Kitap BölümüYalnız künye2020A novel similarity measure for single-valued neutrosophic sets and their applications in medical diagnosis, taxonomy, and clustering analysis
Şahin, Ridvan; Karabacak, Mesut
As a generation of Atanassov's intuitionistic fuzzy set, the single-valued neutrosophic set is an important modeling approach for expressing and processing the inconsistent and indeterminate information very well. Similarity measure is an important tool frequently used in a variety of areas, from clustering analysis to medical diagnosis. Although neutrosophic literature has many similarity measures, they have some disadvantages that do not provide the general conditions of the similarity measure for some specific values. In this chapter, we present a novel similarity measure to handle the relationship between two single-valued neutrosophic sets. It uses a matrix norm and a strictly increasing (or decreasing) binary function called fuzzy implication, and provides axiomatic definition properties of similarity measure. The advantage of using fuzzy implications is that it offers not only different final options to decision-makers but also gives a parameterized class of similarity measures of SVNSs. It is appeared that the developed similarity measure gives better results when compared to other existing similarity measures. Finally, several numerical examples related to pattern recognition, such as medical diagnosis and taxonomy approach, and clustering analysis are performed to demonstrate the practical applicability of the proposed similarity measure.
AtıfScopus17OpenAlex14İncele