基于扩展粗糙集的不确定决策及应用研究

发布时间：2018-06-25 20:36

本文选题：扩展粗糙集 + 优势关系　；参考：《安徽工业大学》2017年硕士论文

【摘要】：粗糙集理论是波兰数学家Pawlak提出的能有效处理不确定性数据的数学工具,相比较于模糊集的隶属度函数的确定及证据理论的基本概率赋值(BPA)的确定,粗集模型无需任何先验知识及假设,而仅仅需要基础数据即可,因而在多属性决策问题中的指标选择和方案排序选优等方面有很好的应用潜力。经典粗糙集理论是基于等价关系的,该关系对数据的要求较为严格,导致经典粗糙集在实际应用中存在诸多缺陷,本文以经典粗糙集为基础延伸出了两类扩展粗糙集,分别是基于优势关系的粗糙集以及与支持向量机相结合的杂合粗糙集,并根据这两类扩展粗糙集的优势去解决特定的不确定性多属性决策问题,并取得了不错的效果。在处理实际问题时,有许多决策问题是基于优势关系的。例如,对于两家上市公司而言,其大部分的财务指标都是带有偏好的,投资者更倾向于关注资产负债率低而投资回报率高的企业。对于这种情况,属性值的偏好也是一种重要的决策信息,而经典的粗糙集理论不能有效处理该类问题。本文先给出优势关系粗糙集的基本概念以及性质,利用信息熵以及互信息的知识给出了其约简方法,并在此基础上结合证据理论给出了对象的不确定性推理。同时考虑到实际问题中,有些决策系统的数据需要用区间值表示,本文利用区间数与可能度的关系,提出了基于可能度优势关系的区间序粗糙集模型,再结合优势度的知识,能够很好地处理备选方案的排序问题。另外,粗糙集在实际应用中对于数据的敏感度较高,而在现实的情况中,由于数据的收集以及数据各种处理比较难以精确控制,导致粗糙集在作为信息识别系统时的预测精度不是很让人满意。同时,考虑到支持向量机以结构化风险最小化为原则而使其有很强的泛化能力。此外,SVM算法能够较好地解决小样本学习问题以及能够有效处理“维数灾难”问题。因此,本文将考虑将两者有机结合,一方面利用粗糙集有效的属性约简能力,一方面利用支持向量机的高精度预测能力,并用来处理个人信用评估这一实际问题。
[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.
【学位授予单位】：安徽工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F406.7;F425;F224

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