The Relationships Among Several Similarity Measures Of Single-valued Neutrosophic Sets

Neutrosophic set theory is a mathematical tool for dealing with uncertain problems.It has a wide application background in the fields of multi-attribute decision making,pattern recognition and fault diagnosis.It is a generalization model of fuzzy set and intuitionistic fuzzy set to describe uncertain objects with the help of true membership function,false membership function and uncertainty degree function.The similarity measure between neutrosophic sets is an important research problem in the theory of neutrosophic sets.Based on different application backgrounds,people put forward several kinds of similarity measures of neutrosophic sets.On the basis of related researches,this paper discusses the relationship between the similarity measures of neutrosophic sets and the construction of the similarity measures for totally dependent-neutrosophic sets,and mainly obtains the following research results:1.Aiming at the similarity measures and weighted similarity measures of single-valued sets based on trigonometric function,distance,vector inner product and logical operator,we discuss the basic properties and the magnitude relation of them;we put forward the definition of equivalence for similarity measures and further analysis the equivalence between some similarity measures.2.From the point of view of construction method of similarity measures for intuitionistic fuzzy sets and based on the existing similarity measures of single-valued neutrosophic sets,the cosine similarity measures,cotangent similarity measures and tangent similarity measures for totally dependent-neutrosophic sets are presented with their basic properties being discussed.