模糊相似关系下的模糊粗糙集

【作者】 郭海刚；

【导师】 张振良； 陈世联；

【作者基本信息】 昆明理工大学 ， 系统理论， 2003， 硕士

【摘要】 粗糙集理论是二十世纪八十年代初由波兰数学家Z．Pawlak首先提出的一种处理不确定性知识的数学理论，它能有效地分析和处理不精确，不确定与不完整等各种不完备信息，并从中发现隐含的知识，揭示潜在的规律。近几年来，它在机器学习和知识发现，数据挖掘，决策支持与分析等方面都有广泛的应用。1991年，Z．Pawlak的专著《粗糙集——关于数据推理的理论》(Rough Sets——Theoretical Aspects ofReasoning about Data)的问世，标志着粗糙集理论及其应用的研究进入了活跃时期。目前，粗糙集理论已经成为信息科学最为活跃的研究领域之一，同时，该理论还在医学、化学、材料学、地理学、管理科学和金融等其它学科得到了成功的应用。 粗糙集理论的主要思想就是利用已知的知识库，将不精确的或不确定的知识用已知的知识库来近似刻画。模糊理论是美国计算机和控制专家L．A．gadeh于1965年提出的刻画模糊现象或模糊概念的数学理论，它是通过对象关于集合的隶属程度来近似描述的。 模糊集的隶属函数和粗糙集的隶属函数都反映了概念的模糊性，前者大多是由专家凭经验给出的，因此往往带有很强烈的主观意志，而粗糙集的隶属函数的计算是从被分析的数据中直接获得的，非常客观。也正因为如此。将模糊集和粗糙集进行某些整合后去描述知识的不确定性和不精确性足非常有意义的。 本文正是基于模糊集和粗糙集的结合，首次提出了相似关系下的模糊粗糙集、模糊相似关系下的粗糙集和模糊相似关系下的模糊粗糙集。研究了它们的一些基本性质，并讨论了该模糊粗糙集的上、下近似在相似关系下的并、交、合成、补等代数运算。最后还讨论了模糊相似关系下的模糊粗糙集在α、β参数下的上、下近似，并且使用近似精度和粗糙度对之进行衡量，得出了模糊相似关系下的模糊粗糙集的上、下近似的λ-截集表示。更多还原

【Abstract】 The rough set theory was put forward by Professor Z. Pawlak, Poland Mathematic, as a math theory to study uncertain knowledge. It can analysis and process effectively all kinds of immaturity information as inexactness, uncertain, uncompleted, find implicative knowledge and open out potential rules. The main idea of the rough set theory depicts approximately learning of inaccurate and uncertain by using the known. Fuzzy theory was advanced by L.A.Zadeh, an America specialist in the field of computer and control in 1965, as a math theory to process fuzzy phenomena and fuzzy notion. It depicts approximately affiliated degree about fuzzy set by object. At the last few years, it has extensive use in the fields of machine- learning and knowledge acquisition, data mining, decision support andanalysis. The mom jraph of Z. Pawlak that <<Rough Sets-- Theoretical Aspects ofReasoning about Da come out in 1991, marked that the research about the theories and application of roug sets had gotten into a new phase. At present, the theory of rough sets has always becon - the most lively domain in the information science, besides, it has achieved successful application in the subject of medicine, chemistry, material, geography, management science and finance.Affiliated degree about fuzzy set and affiliated degree about rough set reflect the faintness of notion, the former are given mostly based on specialist’s experience so it sometimes has strong owner will, but affiliated degree about rough set is obtained through the analytical data so it is impersonal. Just for this, the conformity between the fuzzy set and rough set is significance for it to depict the uncertain and the inexactness.The paper is just based on combine between fuzzy set and rough set, and the fuzzy rough set under the condition of similar relation and fuzzy similar relation are first brought forward. In the paper their some basic properties are research and algebra operation as the combination, the cross, the patch about the upper approximation and the lowerapproximation are discussed. Finally the parameter a ,B are introduced in the fuzzyrough set and -insection denotation of the fuzzy rough set under fuzzy similar relation isobtained.更多还原