一种基于交互熵的模糊信息测度

A Fuzzy Information Measure Based on Cross Entropy

通过借用Shannon信息理论中的相关概念,对已有文献中基于模糊熵测度的模糊对称交互熵(FSCE)进行了改进,提出了对称改进模糊交互熵(SIFCE)这一距离测度.接下来证明了它是度量空间中的度量,满足非负性、对称性、三角不等式三个条件,并且满足有界性,还讨论了它与模糊熵之间的关系.最后提出基于该测度的模糊贴近度σSIF,利用数值例子说明了在模糊模式识别中,σSIF与常见的模糊贴近度可以得到一致的识别结果,从而为模糊模式识别提供了新的研究方法.

By borrowing some relative concepts in Shannon information theory,this paper improves the fuzzy symmetric cross entropy(FSCE)based on the fuzzy entropy measure in[1],and presents a new distance measure symmetric improved fuzzy cross entropy(SIFCE).Next,this paper proves that the new measure is a metric which satisfies the conditions of non-negativity,symmetry and triangle inequality.It also satisfies boundedness.Then the relationship between SIFCE and fuzzy entropy is discussed.At last,this paper presents a new fuzzy nearness degreeσSIF based on the new measure.By using numerical examples in fuzzy pattern recognition,we illustrate that the recognition results are accordant withσSIFand other most common fuzzy nearness degree.So it can provide a new research approach for fuzzy pattern recognition.