【作者】 李季；

【导师】 王长忠；

【作者基本信息】 渤海大学 ， 应用数学， 2020， 硕士

【摘要】 关系是描述数据的一个重要概念,被广泛的应用于人工智能领域。熵是度量关系的不确定性的一个重要方法,被越来越多的学者所重视,并被广泛应用。然而在实际应用当中,大部分的关系都是模糊的而不是分明等价关系,因此研究模糊关系的熵是有必要的。目前对于模糊等价关系、分明等价关系、模糊相似关系以及其他关系的不确定性度量都有一定的研究。但是,对于模糊关系尤其是模糊二元关系的不确定性的研究还不够充分。因此,研究模糊二元关系的熵,进而将熵推广到模糊信息系统当中是有必要的。本文从关系的角度给出了基于香农熵的新的熵的定义,同时给出了新的熵的派生熵的定义,来计算模糊不可分辨关系的信息。在新的定义的基础上,将香农熵的一些相关的定义和性质在模糊二元关系中进行了推广。同时给出了联合熵、条件熵以及互信息的相关定义,并讨论了其相关性质。进而将相关的定义推广至模糊信息系统当中,给出了在模糊系统中的联合熵、条件熵以及互信息的相关定义,并讨论了其相关性质。最后定义了相对熵、相对联合熵以及相对条件熵的概念,并讨论了相关性质。更多还原

【Abstract】 Relationship is an important concept to describe data,which is widely used in the field of artificial intelligence.Entropy is an important method to measure the uncertainty of relation,which is paid more and more attention by scholars and widely used.In practical application,most of the data are fuzzy relations rather than clear equivalent relations,so it is necessary to study the entropy of fuzzy relations.At present,there are some researches on fuzzy equivalence relation,clear equivalence relation,fuzzy similarity relation and uncertainty measurement of other relations.However,the study on the uncertainty measurement of fuzzy relation especially fuzzy binary relation is not enough.Therefore,it is necessary to study the entropy of fuzzy relation and then extend the entropy to fuzzy information system.In this paper,a new definition of entropy based on Shannon entropy is given from the perspective of relation,and a new definition of entropy derived from entropy is also presented to calculate the information of fuzzy and indistinguishable relation.Based on the new definition,some related definitions and properties of Shannon entropy are extended in fuzzy binary relation.The definitions of joint entropy,conditional entropy and mutual information correlation are given,and their related properties are discussed.Furthermore,the related definitions are extended to fuzzy information systems.The related definitions of joint entropy,conditional entropy and mutual information in fuzzy systems are given,and their related properties are discussed.At the same time,the attribute reduction based on entropy is defined.Finally,the concepts of relative entropy,relative joint entropy and relative conditional entropy are defined,and the related properties are discussed.更多还原