A novel cross-entropy and entropy measures of IFSs and their applications

In this paper we discussed novel cross-entropy and entropy models on intuitionism and fuzziness of intuitionistic fuzzy sets (IFSs). In order to measure the discrimination uncertain information, cross-entropy and symmetric cross-entropy are defined based on intuitionistic factor and fuzzy factor. In particular, the constructive principle of entropy is refined; relationship between cross-entropy and entropy is investigated, so we establish a novel intuitionistic fuzzy entropy formula that simultaneously takes into account intuitionistic entropy and fuzzy entropy. We also propose concepts of marginal rate of substitution (MRS) and elasticity of substitution (ES) to describe substitution effect between intuitionism and fuzziness. Moreover, we extend the cross-entropy and entropy models to general version, which could be adjusted by different parameters, and comparative analysis with other existed cross-entropy and entropy measures are presented. Finally, we give applications of pattern recognition and decision making to demonstrate the efficiency of the cross-entropy and entropy models.