粗糙模糊集和模糊粗糙集的新的构造方式及其不确定性度量

【作者】 张洪涛；

【导师】 袁学海；

【作者基本信息】 辽宁师范大学 ， 应用数学， 2005， 硕士

【摘要】 粗糙集理论是在对不精确和不完全信息的分类和数据处理实践中由Pawlak提出来的. 粗糙集理论最初在人工智能的某些分支,例如推理,自动分类,模式识别,学习算法等的研究中是很重要的. 近年来,随着粗糙集理论的发展,粗糙集理论推动了分类理论,聚类分析,度量理论等理论的研究和应用.粗糙集理论的关键是建立两个被称为下、上近似的子集来近似表示论域上的任意集合. 主要有两种生成粗糙集的方法:构造性方法和公理化方法. 在构造性方法中,下、上近似算子不是最基本的概念. 它们是由其他概念构造的,例如论域上的二元关系,论域的分类和覆盖,偏序集,格,布尔代数和布尔子代数等.本文的主要目的是通过构造性方法构造新的粗糙模糊集模型和模糊粗糙集模型. 对模糊概念取截集精确化后,利用Pawlak 粗糙集理论和表现定理就可以得到一个新的粗糙集模型. 在本文中,首先讨论区间[0,1] 上的粗糙模糊集模型;其次构造区间[0,1] 上的模糊粗糙集模型;然后定义F 格上的粗糙模糊集模型和模糊粗糙集模型.本文也讨论了粗糙模糊集和模糊粗糙集的不确定性度量. 这种不确定性中的模糊性是用模糊熵来度量的. 这个被称为粗糙熵的不确定性度量是在信息熵的基础上得到的.更多还原

【Abstract】 The theory of rough sets is proposed by Pawlak in practice of classificationand data analysis with imprecise and incomplete information. The rough set conceptcan be of some importance, primarily in some branches of artificial intelligence, suchas reasoning, automatic classification, pattern recognition, learning algorithms, etc. Inrecent years, with the development of rough set theory, the idea of rough set leads to afurther research and applications in classification theory, cluster analysis, measurementtheory, etc.The key of the rough set theory is deal with the approximation of an arbitrarysubset of a universe by two subsets called lower and upper approximations. Thereare mainly two methods for the development of this theory, the constructive and alge-braic(axiomatic) approaches. In constructive methods, lower and upper approximationsare not primitive notions. They are constructed from other concepts, such as binary re-lations on a universe, partitions and coverings of a universe, and partially ordered sets,lattice, Boolean algebras and their subalgebras, etc.The main aim of the paper is to construct new models of rough fuzzy sets and fuzzyrough sets by the constructive method. After the accuracy of fuzzy concepts with levelsets, A new model of rough set is obtained by the use of Pawlak rough set theory andrepresentation theorem. In the paper, the rough fuzzy set model in the interval [0,1] isdiscussed at first. Secondly, the fuzzy rough set model in the interval [0,1] is proposed.Thirdly, the rough fuzzy set model in F lattice is defined. fourthly, the fuzzy rough setmodel in F lattice is obtained.In this paper, the uncertainty measurement of rough fuzzy sets and fuzzy rough setsis also discussed. The fuzziness of the uncertainty is measured with fuzzy entropy. Theuncertainty measurement called rough entropy is obtained on the basis of informationentropy.更多还原