本文選題：擴展粗糙集 + 優(yōu)勢關系　； 參考：《安徽工業(yè)大學》2017年碩士論文

【摘要】：粗糙集理論是波蘭數(shù)學家Pawlak提出的能有效處理不確定性數(shù)據(jù)的數(shù)學工具,相比較于模糊集的隸屬度函數(shù)的確定及證據(jù)理論的基本概率賦值(BPA)的確定,粗集模型無需任何先驗知識及假設,而僅僅需要基礎數(shù)據(jù)即可,因而在多屬性決策問題中的指標選擇和方案排序選優(yōu)等方面有很好的應用潛力。經(jīng)典粗糙集理論是基于等價關系的,該關系對數(shù)據(jù)的要求較為嚴格,導致經(jīng)典粗糙集在實際應用中存在諸多缺陷,本文以經(jīng)典粗糙集為基礎延伸出了兩類擴展粗糙集,分別是基于優(yōu)勢關系的粗糙集以及與支持向量機相結合的雜合粗糙集,并根據(jù)這兩類擴展粗糙集的優(yōu)勢去解決特定的不確定性多屬性決策問題,并取得了不錯的效果。在處理實際問題時,有許多決策問題是基于優(yōu)勢關系的。例如,對于兩家上市公司而言,其大部分的財務指標都是帶有偏好的,投資者更傾向于關注資產(chǎn)負債率低而投資回報率高的企業(yè)。對于這種情況,屬性值的偏好也是一種重要的決策信息,而經(jīng)典的粗糙集理論不能有效處理該類問題。本文先給出優(yōu)勢關系粗糙集的基本概念以及性質(zhì),利用信息熵以及互信息的知識給出了其約簡方法,并在此基礎上結合證據(jù)理論給出了對象的不確定性推理。同時考慮到實際問題中,有些決策系統(tǒng)的數(shù)據(jù)需要用區(qū)間值表示,本文利用區(qū)間數(shù)與可能度的關系,提出了基于可能度優(yōu)勢關系的區(qū)間序粗糙集模型,再結合優(yōu)勢度的知識,能夠很好地處理備選方案的排序問題。另外,粗糙集在實際應用中對于數(shù)據(jù)的敏感度較高,而在現(xiàn)實的情況中,由于數(shù)據(jù)的收集以及數(shù)據(jù)各種處理比較難以精確控制,導致粗糙集在作為信息識別系統(tǒng)時的預測精度不是很讓人滿意。同時,考慮到支持向量機以結構化風險最小化為原則而使其有很強的泛化能力。此外,SVM算法能夠較好地解決小樣本學習問題以及能夠有效處理“維數(shù)災難”問題。因此,本文將考慮將兩者有機結合,一方面利用粗糙集有效的屬性約簡能力,一方面利用支持向量機的高精度預測能力,并用來處理個人信用評估這一實際問題。
[Abstract]:Rough set theory is a mathematical tool put forward by Pawlak, a Polish mathematician, which can deal with uncertain data effectively. Compared with the determination of membership function of fuzzy sets and the determination of basic probability assignment (BPA) of evidence theory, rough set theory can deal with uncertain data effectively. Rough set model does not need any prior knowledge and hypothesis, but only needs basic data, so it has a good application potential in multi-attribute decision making problems such as index selection and scheme ranking selection. The classical rough set theory is based on the equivalence relation, which requires strict data, which leads to many defects in the practical application of classical rough set. In this paper, two kinds of extended rough sets are extended based on classical rough set. Rough sets based on dominance relationship and hybrid rough sets combined with support vector machine are used to solve the uncertain multi-attribute decision making problem according to the advantages of these two kinds of extended rough sets and good results are obtained. When dealing with practical problems, there are many decision-making problems based on advantage relationship. For example, for two listed companies, most of their financial indicators are biased, with investors more likely to focus on companies with low asset-liability ratios and high returns on investment. In this case, the preference of attribute value is also an important decision information, but the classical rough set theory can not deal with this kind of problem effectively. In this paper, the basic concepts and properties of the rough set of dominance relations are given, and the reduction method is given by using the knowledge of information entropy and mutual information, and the uncertainty reasoning of the object is given based on the evidence theory. At the same time, considering the practical problems, some data of decision system need to be represented by interval value. In this paper, an interval order rough set model based on the dominance relation of possibility degree is put forward by using the relation between interval number and possibility degree, and then the knowledge of dominance degree is combined. It can deal with the scheduling problem of alternatives well. In addition, rough set is sensitive to data in practical application, but in reality, it is difficult to accurately control data collection and data processing. The prediction accuracy of rough set as an information recognition system is not satisfactory. At the same time, the support vector machine (SVM) has a strong generalization ability based on the principle of structural risk minimization. In addition, SVM algorithm can solve the problem of small sample learning and effectively deal with the problem of "dimension disaster". Therefore, this paper will consider the combination of the two methods. On the one hand, we will make use of the effective attribute reduction ability of rough set; on the other hand, we will use the high precision prediction ability of support vector machine, and use it to deal with the practical problem of personal credit evaluation.
【學位授予單位】：安徽工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：F406.7;F425;F224

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