Abstract
This paper deals with the divergence of fuzzy variables from a priori one. Within the framework of credibility theory, a fuzzy cross-entropy is defined to measure the divergence, and some mathematical properties are investigated. Furthermore, a minimum cross-entropy principle is proposed, which tells us that out of all membership functions satisfying given moment constraints, we should choose the one that is closest to the given a priori membership function.
Highlights
Fuzzy entropy provides a quantitative measure of the uncertainty associated with each fuzzy variable
In order to meet these requirements, within the framework of credibility theory, Li and Liu [8] provided a new definition of fuzzy entropy to characterize the uncertainty resulting from information deficiency which is caused by the impossibility to predict the specified value that a fuzzy variable takes
Minimum cross-entropy principle In many real problems, the membership function of a fuzzy variable is unavailable except some partial information, for example, moment constraints, which may be based on observations
Summary
Fuzzy entropy provides a quantitative measure of the uncertainty associated with each fuzzy variable. In order to meet these requirements, within the framework of credibility theory, Li and Liu [8] provided a new definition of fuzzy entropy to characterize the uncertainty resulting from information deficiency which is caused by the impossibility to predict the specified value that a fuzzy variable takes. Li and Liu [9] proposed the fuzzy maximum entropy principle and proved some maximum entropy theorems.
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