Abstract
Fuzzy clustering is widely used in business, biology, geography, coding for the internet and more. A single-valued neutrosophic set is a generalized fuzzy set, and its clustering algorithm has attracted more and more attention. An equivalence matrix is a common tool in clustering algorithms. At present, there exist no results constructing a single-valued neutrosophic number equivalence matrix using t-norm and t-conorm. First, the concept of a ( T , S ) -based composition matrix is defined in this paper, where ( T , S ) is a dual pair of triangular modules. Then, a ( T , S ) -based single-valued neutrosophic number equivalence matrix is given. A λ -cutting matrix of single-valued neutrosophic number matrix is also introduced. Moreover, their related properties are studied. Finally, an example and comparison experiment are given to illustrate the effectiveness and superiority of our proposed clustering algorithm.
Highlights
IntroductionIn 1965, Zadeh [1] proposed the concept of a fuzzy set (FS) for dealing with uncertain information
In 1965, Zadeh [1] proposed the concept of a fuzzy set (FS) for dealing with uncertain information.Intuitionistic fuzzy sets (IFS) were introduced by Atanassov [2] in 1986
We introduce the concept of a ( T, S)-based SVNN composition matrix and investigate its properties
Summary
In 1965, Zadeh [1] proposed the concept of a fuzzy set (FS) for dealing with uncertain information. For IFS, Zhang et al [19] proposed an intuitionistic fuzzy equivalence matrix clustering algorithm. The main work of this paper is to propose the operation of the ( T, S)-based composition matrix and ( T, S)-based single-valued neutrosophic number equivalence matrix.
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