A New Definition of Cross-Entropy for Uncertain Sets

Cross-entropy for uncertain sets is used to measure the divergence between two membership functions. Sine cross-entropy, logarithm cross-entropy and quadratic cross-entropy for uncertain sets have been proposed, all the definitions fail to measure the degree of divergence associated with some uncertain sets. Thus, this paper presents a new definition of cross-entropy for uncertain sets as a supplement, and investigates its properties. In addition, this paper also proposes a definition of generalized cross-entropy for uncertain sets, and discusses its properties.