覆盖粗糙模糊集的组合熵与组合粒度研究  

Combination Entropy and Combination Granulation of Covering Rough Fuzzy Set

作　　者：王青海[1] 郭占龙[1] 彭少杨[1] 

机构地区：[1]青海师范大学计算机系,西宁810008

出　　处：《小型微型计算机系统》2013年第8期1886-1890,共5页Journal of Chinese Computer Systems

基　　金：教育部人文社会科学研究项目(DMA100348)资助;青海师范大学本科生创新项目(青师教字(2012)16号)资助;青海师范大学创新基金项目(青师科字(2012)4号)资助

摘　　要：针对覆盖粗糙模糊集的组合熵与组合粒度的度量问题.定义了覆盖粗糙集下对象的相容类,构造了覆盖粗糙集模型的相容关系,提出覆盖近似空间的覆盖簇,引入了覆盖粗糙模糊集模型的组合熵和组合粒度概念,讨论了组合熵和组合粒度的结构并证明了相关的性质并提出了覆盖粗糙模糊集的组合熵粗糙度度量.定义了覆盖簇的相容关系下对象的相容度,提出了相容度下的组合熵概念,证明了相关的定理和性质.最后,引入相容度下组合粒度概念,证明了组合粒度粗糙度存在随覆盖变细,度量单调减少的规律,并通过实例进行了验证.从而为进一步揭示粗糙集、粗糙模糊集及覆盖粗糙模糊集之间的不确定性度量规律提供了理论依据.Aiming at the measurement of the combination entropy and combination granulation for covering rough set. Firstly, the tol- erance class among elements under coveting rough set is defined and the relationship class of covering rough set model is constructed. Covering cluster of covering approximate space is proposed and the concepts of combination entropy as well as combination granula- tion of covering rough fuzzy set model are introduced. Correlative properties are proved and structure of defined concepts is discussed and, the measurement of roughness based on rough entropy is established. Then, the tolerance degrees of elements under tolerance re- lation is defined and combination entropy is proposed, and correlative theorems and properties are proved. Finally, by introducing concept of combination granulation based on tolerance degrees, the conclusion that measuring of rough degree under combination granulation is monotonously decreasing with the subdivision of covering sets is obtained and an example is given to show the validity of the method of this model. The theoretical evidence of measuring of uncertainty among rough sets , rough fuzzy set and coving rough set is provided.

关 键 词：覆盖粗糙模糊集 覆盖簇 组合熵 组合粒度 组合粗糙度 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]