Abstract
Information measures play an important role in the interval neutrosophic sets (INS) theory. The main purpose of this paper is to study the similarity and entropy of INS and its application in multi-attribute decision-making. We propose a new inclusion relation between interval neutrosophic sets where the importance of the three membership functions may be different. Then, we propose the axiomatic definitions of the similarity measure and entropy of the interval neutrosophic set (INS) based on the new inclusion relation. Based on the Hamming distance, cosine function and cotangent function, some new similarity measures and entropies of INS are constructed. Finally, based on the new similarity and entropy, we propose a multi-attribute decision-making method and illustrate that these new similarities and entropies are reasonable and effective.
Highlights
Zadeh [1,2] put forward the theory of fuzzy sets in 1965, which is an effective method to deal with fuzzy information, but only limited to the truth-membership function
Wang et al [5,6] proposed the concept of single-valued neutrosophic sets (SVNS) and interval neutrosophic sets (INS), which are the subclasses of neutrosophic sets, and the set-theoretic operators and various properties of
Based on the existing inclusion relation of the wisdom set in the interval, this paper combines the new inclusion relation type-3 of the single-valued neutrosophic sets proposed by Zhang [18,19], and gives the inclusion relationship of the new interval neutrosophic sets
Summary
Zadeh [1,2] put forward the theory of fuzzy sets in 1965, which is an effective method to deal with fuzzy information, but only limited to the truth-membership function. A single-valued neutrosophic cross-entropy measurement method is proposed and applied to multi-attribute decision-making in single-valued neutrosophic environment. Ye [10] proposed the Hamming distance and the Euclidean distance in INSs and defined similarity measure based on distance, and applied them to multi-attribute decision-making with interval neutrosophic information. We first give the definitions of the neutrosophic sets, interval neutrosophic sets, define the new inclusion relationship of the interval neutrosophic sets, and give the new similarity and entropy based on the new inclusion relationship
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