New similarity and entropy measures of single-valued neutrosophic sets with applications in multi-attribute decision mak
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METHODOLOGIES AND APPLICATION
New similarity and entropy measures of single-valued neutrosophic sets with applications in multi-attribute decision making Keyun Qin1 · Lu Wang1
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Information measures play a fundamental role in single-valued neutrosophic set (SVNS) theory. The main purpose of this paper is to study the similarity and entropy measures of SVNS with applications in multi-attribute decision making. We proposed the axiomatic definitions of similarity and entropy for single-valued neutrosophic values (SVNVs) with respect to a new kind of inclusion relation between SVNVs. On the basis of Hamming distance, cosine function and cotangent function, three similarity measures and three entropies for SVNVs are constructed. Then, we extended the definitions and construction methods of similarity and entropy for SVNVs to SVNSs by using some aggregation operators. Finally, by using the new similarity and entropy measures we presented a SVNSs based multi-attribute decision making method. It demonstrated that the new information measures presented in this study are applicable and efficient. Keywords Single-valued neutrosophic set · Inclusion relation · Similarity measure · Entropy · Multi-attribute decision making
1 Introduction Because of different types of uncertainties in real world, there are many mathematical tools for dealing with incomplete, indeterminate and inconsistent information. Zadeh (1965) firstly proposed the theory of fuzzy set which is applied successfully in various fields. Subsequently, several new concepts of high-order fuzzy sets have been presented. Among them, intuitionistic fuzzy set (IFS) introduced by Atanassov (1986) is a typical generalization of fuzzy set. An IFS consists of a membership function and a non-membership function of the universe and provides a flexible mathematical framework to uncertain information processing. Smarandache (1998) originally proposed the notion of a neutrosophic set which is a generalization of fuzzy set and intuitionistic fuzzy set (Smarandache 2005). A neutrosophic set is characterized independently by a truth membership funcCommunicated by V. Loia.
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Lu Wang [email protected] Keyun Qin [email protected]
1
College of Mathematics, Southwest Jiaotong University, Chengdu 610031, Sichuan, China
tion, a falsity membership function and an indeterminacy membership function and is more suitable to handle incomplete, indeterminate and inconsistent information. In order to easily use the neutrosophic set in real scientific and engineering fields, Wang et al. (2010) proposed the notion of single-valued neutrosophic set (SVNS), which is an instance of neutrosophic set, and provided some set-theoretic operations on SVNSs. The single-valued neutrosophic set theory has been proven to be useful in many scientific fields, such as multi-attribute decision making, machine learning, medical diagnosis, fault diagnosis and so on (see Deli 2017; Guo et la. 2014; Guo and Cheng 2009; Liu et al. 2014; Peng et a
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