Entropy-Based Fuzzy Information Measures
Ding Shi · Chinese Journal of Computers · 2012
Fuzzy Information Measures(FIM) are to be used to measure similarity between two fuzzy sets and plays an important part in pattern recognition,machine learning,clustering analysis.In this paper,FIM theory is studied based on information entropy.Firstly,the existing FIM theories are introduced and some advantages and disadvantages are pointed out.Secondly,based on information entropy,the fuzzy information entropy is studied,four axioms about fuzzy entropy are set up,and all kinds of definitions of fuzzy entropy are discussed.Based on fuzzy entropy,two new fuzzy entropy measures,fuzzy absolute information measure(FAIM) and fuzzy relative information measure(FRIM) are proposed.At last,based on cross entropy,the fuzzy cross entropy is discussed,and fuzzy cross entropy measure(FCEM) is set up.All these measures,not only enrich and develop FIM theory,but also provide a new research approach for studies on pattern recognition,machine learning,clustering analysis et al in theory and application.