本文選題：覆蓋粗糙集　切入點：矩陣　出處：《安徽大學》2017年碩士論文

【摘要】：波蘭學者Z.Pawlak提出了粗糙集理論,它是能夠有效處理不完整和不確定性信息的數(shù)學工具。經(jīng)典粗糙集理論是基于等價關系和劃分的,只有完備的離散型數(shù)據(jù)集中的屬性才能導出論域上的劃分。但是,在現(xiàn)實情況中,信息系統(tǒng)中存在多種類型的數(shù)據(jù),例如集值型數(shù)據(jù)、缺省型數(shù)據(jù)和實值型數(shù)據(jù),經(jīng)典粗糙集不能直接正確有效的處理這些數(shù)據(jù),這就限制了經(jīng)典粗糙集的應用,因此,擴展經(jīng)典粗糙集成為了粗糙集研究的熱點。在這些擴展研究中,Zakowski通過把經(jīng)典粗糙集中論域的劃分放寬為論域的覆蓋,并首先提出基于覆蓋的粗糙集模型。自該模型提出以來,研究者對覆蓋粗糙集模型的研究重心主要集中于集合的近似集和屬性約簡,并提出了很多集合近似集的定義和屬性約簡算法,但這些方法仍然存在時間復雜度較高的問題,針對這個問題本文做了下面的研究:(1)提出了改進的基于矩陣的計算集合下近似集和覆蓋決策信息系統(tǒng)正域的定義。首先,證明現(xiàn)有的基于矩陣的計算集合下近似集和覆蓋決策信息系統(tǒng)正域的方法存在一些沒有必要的運算,這會導致時間復雜度高。然后,提出了改進的基于矩陣的計算集合下近似集和覆蓋決策信息系統(tǒng)正域的定義,它們能夠有效的減少之前計算集合下近似集和覆蓋決策信息系統(tǒng)正域的時間。最后,通過實例和實驗結果驗證了這兩個方法的有效性。(2)本文為了克服現(xiàn)有的尋找分辨矩陣中全部極小元素的算法時間復雜度高的問題。首先,定義了基于矩陣的覆蓋決策信息系統(tǒng)的相對分辨函數(shù),然后,基于這個定義,給出基于矩陣的尋找分辨矩陣中全部極小元素的算法,該算法能夠有效的降低計算覆蓋決策信息系統(tǒng)所有約簡的時間。最后,通過實例和實驗驗證了該算法的有效性。(3)在實際應用中,屬性值的改變會導致覆蓋信息系統(tǒng)中某一個覆蓋發(fā)生變化,此時使用非增量的方法計算集合的上下近似集的時間開銷較大。因此,本文針對屬性值變化產(chǎn)生的動態(tài)覆蓋信息系統(tǒng),提出了基于矩陣的增量方法計算集合的上下近似集。首先,給出增量的方法計算動態(tài)覆蓋的兩種特征矩陣。然后,基于給定的兩種特征矩陣分別給出計算集合上下近似集的增量算法,通過實例呈現(xiàn)了使用增量算法計算集合近似集的過程。最后,通過實驗證明了本文提出的增量算法是有效的。
[Abstract]:Z.Pawlak, a Polish scholar, put forward rough set theory, which is a mathematical tool which can deal with incomplete and uncertain information effectively.The classical rough set theory is based on the equivalence relation and partition. Only the attributes of the complete discrete data set can derive the partition on the domain.However, in reality, there are many types of data in the information system, such as set-valued data, default data and real-valued data.This limits the application of classical rough sets, so the extension of classical rough sets is a hotspot in the research of rough sets.In these extended studies, Zakowski extends the partition of classical rough set domains to cover domains, and proposes a covering based rough set model.Since the model was put forward, the focus of researchers on covering rough set model is mainly on the approximate set of sets and attribute reduction, and many definitions and attribute reduction algorithms of set approximation set are proposed.However, these methods still have high time complexity. In this paper, the following research is done: 1) an improved definition of approximate set under matrix based computing set and positive domain of overlay decision information system is proposed.First of all, it is proved that there are some unnecessary operations for the existing methods of approximate set and positive domain covering decision information system under the matrix based computing set, which will lead to high time complexity.Then, an improved definition of approximate set and positive domain of overlay decision information system based on matrix is proposed, which can effectively reduce the time of computing approximate set and covering decision information system.Finally, the effectiveness of the two methods is verified by examples and experimental results.) in order to overcome the problem of high time complexity of existing algorithms for finding all the minimal elements in the discernment matrix.Firstly, the relative resolution function of the covering decision information system based on matrix is defined. Then, based on this definition, the algorithm of finding all the minimal elements in the matrix is given.This algorithm can effectively reduce the time of computing all reduction of overlay decision information system.Finally, the effectiveness of the algorithm is verified by examples and experiments. In practical application, the change of attribute value will lead to the change of one coverage in the overlay information system.In this case, the time cost of computing the upper and lower approximate sets of the set by using the non-incremental method is large.Therefore, in this paper, an incremental method based on matrix is proposed to calculate the upper and lower approximate sets of the set for the dynamic overlay information system caused by the change of the attribute value.Firstly, two characteristic matrices of dynamic coverage are calculated by incremental method.Then, based on the two given characteristic matrices, the incremental algorithm for computing the upper and lower approximate sets of the set is presented, and the process of computing the approximate set of the set using the incremental algorithm is presented by an example.Finally, the experimental results show that the proposed incremental algorithm is effective.
【學位授予單位】：安徽大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TP18

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本文編號：1728059