本文關(guān)鍵詞： 模糊二元關(guān)系 不確定性度量 信息熵 信息粒子　出處：《渤海大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：關(guān)系是刻畫元素之間相互聯(lián)系的一個(gè)重要概念,關(guān)系被廣泛應(yīng)用在學(xué)術(shù)智能領(lǐng)域,例如,關(guān)系數(shù)據(jù)庫,聚類分析,近似推理,屬性約簡,分類和決策。近年來一些特殊關(guān)系的不確定性度量用信息熵來表示。然而到目前為止,還沒有一個(gè)系統(tǒng)的方法將這些不確定性度量構(gòu)建成一個(gè)理論框架。在這篇文章中,新的信息熵被提出來,這種信息熵能夠?qū)⑵渌厥怅P(guān)系的不確定度量方法統(tǒng)一在一個(gè)理論框架中。1.一般模糊二元關(guān)系的信息熵首先引入了一個(gè)新的熵去度量模糊二元關(guān)系的信息量并且給出了聯(lián)合熵,條件熵與互信息,討論了這些不確定性度量的性質(zhì)。然后將這種熵運(yùn)用到信息表與決策表中來刻畫基于熵的屬性約簡定義。最后,提出了一般模糊二元關(guān)系的另一種不確定性度量—模糊鄰域熵與它的派生熵,并討論了兩種熵的等價(jià)性。一般模糊二元關(guān)系的信息熵是特殊關(guān)系熵的推廣,不僅能夠處理單一結(jié)構(gòu)關(guān)系(等價(jià)關(guān)系、相似關(guān)系、優(yōu)勢關(guān)系)的不確定信息,而且能夠度量異構(gòu)關(guān)系的不確定性,在數(shù)據(jù)處理及信息挖掘領(lǐng)域具有潛在應(yīng)用。2.一般模糊二元關(guān)系的廣義信息熵一般模糊二元關(guān)系的模糊信息熵忽略了模糊鄰域的部分信息,只考慮其局部信息。為此,本文定義一般模糊關(guān)系的廣義模糊信息熵的概念,該熵是Shannon熵的另一種推廣形式。同時(shí),給出了廣義模糊聯(lián)合熵,廣義條件熵和互信息的概念,討論了這些不確定性度量的關(guān)系及其重要性質(zhì),并討論了廣義模糊熵與一般模糊關(guān)系熵的區(qū)別與聯(lián)系。最后,將所提出的廣義模糊熵運(yùn)用到信息表與決策表中來刻畫屬性約簡的定義。較一般模糊二元關(guān)系的信息熵相比,廣義模糊信息熵考慮了模糊關(guān)系的更多信息。
[Abstract]:Relationship is an important concept to describe the interrelation between elements. It is widely used in the field of academic intelligence, such as relational database, clustering analysis, approximate reasoning, attribute reduction. Classification and decision making. In recent years, some uncertainty measures of special relationships are represented by information entropy. However, so far, there is no systematic method to construct these uncertainty measures into a theoretical framework. New information entropy is proposed, This information entropy can unify the uncertain measures of other special relationships in a theoretical framework. Firstly, a new entropy is introduced to measure the information content of fuzzy binary relations and the joint entropy is given. The properties of these uncertainty measures are discussed. Then the entropy is applied to the information table and decision table to describe the definition of attribute reduction based on entropy. In this paper, another uncertainty measure of the general fuzzy binary relation, fuzzy neighborhood entropy and its derived entropy, is proposed, and the equivalence of the two kinds of entropy is discussed. The information entropy of the general fuzzy binary relation is a generalization of the special relation entropy. It can not only deal with uncertain information of a single structural relationship (equivalence relation, similarity relation, advantage relationship), but also measure the uncertainty of heterogeneous relationship. There are potential applications in data processing and information mining. The generalized information entropy of general fuzzy binary relation and fuzzy information entropy of general fuzzy binary relation ignore some information of fuzzy neighborhood and only consider local information. In this paper, the concept of generalized fuzzy information entropy of general fuzzy relation is defined, which is another extension of Shannon entropy. At the same time, the concepts of generalized fuzzy joint entropy, generalized conditional entropy and mutual information are given. The relations and important properties of these uncertainty measures are discussed, and the difference and relation between generalized fuzzy entropy and general fuzzy relation entropy are discussed. The proposed generalized fuzzy entropy is applied to the information table and decision table to describe the definition of attribute reduction. Compared with the information entropy of the general fuzzy binary relation, the generalized fuzzy information entropy considers more information of the fuzzy relation.
【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】：O159

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本文編號：1552590