The Study Of The Measure Of Uncertainty Of Single Value Neutrosophic Sets

Uncertainty information processing is a hot research issue in the field of artificial intelligence,and information measure is a particularly important part of information processing.The mathematical tools of uncertainty information processing mainly include:fuzzy sets,rough sets,neutrosophic sets and so on.Smarandache proposed the concept of neutrosophic set in 1998.The neutrosophic set describes the uncertain objects with true membership function,false membership function and uncertainty function.It is a generalization model of fuzzy set and intuitionistic fuzzy set.The theory of neutrosophic sets has been widely used in the fields of multi-attribute decision-making and pattern recognition.There are three kinds of inclusion relationships between single value neutrosophic sets.Most of the existing measures are based on two classical inclusion relationships of single value neutrosophic sets.The new inclusion relationship of the single value neutrosophic sets can deal with some uncertain information from a new point of view.However,most of the existing measures are not suitable for this new inclusion relationship.In this paper,we mainly study the cross-entropy,distance and similarity measures of single value neutrosophic sets,and have achieved the following research results:1.The basic properties of cross-entropy and distance are studied.It is proved that fuzzy cross-entropy is a distance measure between fuzzy sets,and the cross-entropy of single value neutrosophic sets is a distance measure between single value neutrosophic sets.2.Based on the new inclusion relationship of single value neutrosophic sets,the axiomatic definition of distance measure and the corresponding similarity are proposed.The new distance and similarity based on the cross-entropy are construted.