本文選題：二元關(guān)系 + 不確定性　； 參考：《渤海大學(xué)》2017年碩士論文

【摘要】：信息熵是不確定性度量的一個有效措施。中外著名學(xué)者已經(jīng)提出了很多測量不確定性的方法,并取得了令人矚目的成就,為我們獲取有用的知識奠定了堅實的基礎(chǔ),并大大提高我們獲取信息的效率。而關(guān)系是建立論域中一組元素之間聯(lián)系的基本概念,集合和關(guān)系的定義是構(gòu)成現(xiàn)代數(shù)學(xué)的基礎(chǔ)。另外,關(guān)系已經(jīng)被廣泛應(yīng)用于數(shù)據(jù)的離散化,模糊聚類和屬性約簡。關(guān)系中的等價關(guān)系、相似關(guān)系、鄰域關(guān)系是粗糙集模型的基礎(chǔ)。特殊關(guān)系的不確定性度量已有很多好的衡量方法,然而,一般二元關(guān)系不確定性的研究很少。因此本文主要針對一般二元關(guān)系間的不確定性進(jìn)行研究。本文的總體思想是:將后繼鄰域,信息系統(tǒng)的基礎(chǔ)知識和信息熵相結(jié)合,分別提出了一般二元關(guān)系熵,廣義鄰域熵,然后對它們的性質(zhì)進(jìn)行了詳細(xì)的討論,具體工作如下:1.為了計算一般二元關(guān)系熵,聯(lián)合熵,條件熵和互信息,主要通過后繼鄰域?qū)φ撚蛐纬蓜澐?從而來計算一般二元關(guān)系的熵、聯(lián)合熵、條件熵和互信息,并提出了一些基本性質(zhì),然后與鄰域熵進(jìn)行比較,通過證明說明這兩種熵的定義是等價的。2.在鄰域熵的基礎(chǔ)上,通過后繼鄰域重新定義了廣義鄰域熵,提出了廣義鄰域熵,條件熵,聯(lián)合熵及互信等概念,并對它們的性質(zhì)進(jìn)行了討論,最后與鄰域熵進(jìn)行比較,發(fā)現(xiàn)這是一種更全面,更精確的計算信息系統(tǒng)不確定性的一種熵。
[Abstract]:Information entropy is an effective measure to measure uncertainty.Famous scholars at home and abroad have put forward many methods to measure uncertainty, and have made remarkable achievements, which have laid a solid foundation for us to obtain useful knowledge and greatly improve the efficiency of our access to information.The relation is the basic concept of establishing the relation between a group of elements in the domain, and the definition of set and relation is the foundation of modern mathematics.In addition, relationships have been widely used in data discretization, fuzzy clustering and attribute reduction.The equivalence relation, similarity relation and neighborhood relation in relation are the basis of rough set model.There are many good methods to measure uncertainty of special relationships, however, there are few researches on uncertainty of binary relationships.Therefore, this paper mainly focuses on the uncertainty between general binary relations.The general idea of this paper is as follows: combining the basic knowledge and information entropy of subsequent neighborhood and information system, the general binary relation entropy and generalized neighborhood entropy are proposed, and their properties are discussed in detail. The specific work is as follows: 1.In order to calculate the general binary relation entropy, joint entropy, conditional entropy and mutual information, the entropy, joint entropy, conditional entropy and mutual information of the general binary relation are calculated by dividing the domain by the following neighborhood, and some basic properties are proposed.Then compared with the neighborhood entropy, it is proved that the definition of these two kinds of entropy is equivalent. 2.On the basis of neighborhood entropy, the generalized neighborhood entropy is redefined by successive neighborhood entropy. The concepts of generalized neighborhood entropy, conditional entropy, joint entropy and mutual trust are proposed, and their properties are discussed.It is found that this is a more comprehensive, more accurate calculation of information system uncertainty an entropy.
【學(xué)位授予單位】：渤海大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O236

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本文編號：1744319