模糊集的一类新广义熵

Some new generalized entropy formulas of fuzzy sets

目的研究模糊集的一类新的广义熵。方法将离散随机变量的(k,q)阶广义熵推广到模糊集理论中,定义模糊集的(k,q)阶广义熵和q阶Shannon熵,讨论q阶Shannon模糊熵和q阶Re-nyi模糊熵之间的关系。结果得到了(k,q)阶广义熵和q阶Shannon模糊熵的一系列性质,并且证明了当q≥0.5时,q阶Shannon模糊熵是F(X)上的一个σ-熵。结论拓广了模糊熵,为模糊信息学的深入发展提出了新的思路。

Aim To study some new generalized entropy formulas ior iuzzy sets. Metnoes Extena （k, q） omer 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 30.5. Conclusion Fuzzy entropy is generalized and new idea for more development of fuzzy informations.