On entropy, similarity measure and cross-entropy of single-valued neutrosophic sets and their application in multi-attribute decision making

Abstract

As a subclass of neutrosophic sets, single-valued neutrosophic sets (SVNS) can be used to represent uncertainty and inconsistent information that exist in real-world situations. Information measures play an important role in SVNS theory, which has received more and more attention in recent years. In this paper, we develop a multi-attribute decision-making (MADM) method based on single-valued neutrosophic information measures. To this end, three axiomatic definitions of information measures are first introduced. These include entropy, similarity measure and cross-entropy. Then, we construct information measure formulas on the basis of the cosine function. The relationship among entropy, similarity measure and cross-entropy as well as their mutual transformations are further discussed. Moreover, an approach to single-valued neutrosophic MADM based on these information measure formulas is presented. Finally, a numerical example of city pollution evaluation is provided. The comparative analysis demonstrates the applicability and effectiveness of the proposed method.