A novel similarity measure for single-valued neutrosophic sets and their applications in medical diagnosis, taxonomy, and clustering analysis

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.