基于熵的模糊信息测度研究

Entropy-Based Fuzzy Information Measures

模糊信息测度(Fuzzy Information Measures,FIM)是度量两个模糊集之间相似性大小的一种量度,在模式识别、机器学习、聚类分析等研究中,起着重要的作用.文中对模糊测度进行了分析,研究了基于熵的模糊信息测度理论:首先,概述了模糊测度理论,指出了其优缺点;其次,基于信息熵理论,研究了模糊熵理论,建立了模糊熵公理化体系,讨论了各种模糊熵,在此基础上,提出了模糊绝对熵测度、模糊相对熵测度等模糊熵测度;最后,基于交互熵理论,建立了模糊交互熵理论,进而提出了模糊交互熵测度.这些测度理论,不仅丰富与发展了FIM理论,而且为模式识别、机器学习、聚类分析等理论与应用研究提供了新的研究方法.

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.