Some new generalized entropy formulas of fuzzy sets

Aim To study some new generalized entropy formulas for fuzzy sets.Methods Extend(k,q) order generalized entropy of discrete random variables to the fuzzy sets theory,and define(k,q) order generalized entropy and q order Shannon entropy of fuzzy sets.Then the relations between q order Shannon fuzzy entropy and q order Renyi fuzzy entropy are discussed.Results Various properties of(k,q) order generalized entropy and q order Shannon entropy of fuzzy sets are obtained,and q order Shannon fuzzy entropy is proved a σ-entropy on F(X) when q≥0.5.Conclusion Fuzzy entropy is generalized and new idea for more development of fuzzy informations.