【作者】 杜蕾；

【导师】 管延勇；

【作者基本信息】 济南大学 ， 应用数学， 2011， 硕士

【摘要】 经典粗糙集理论建立在等价关系对论域的分类的基础上,适用于离散型的完备信息系统的知识约简。国内外学者在这一方面做出了大量的研究,并取得了丰硕的成果。但在序信息系统中,属性值表达对象之间的优势关系,此时,经典粗糙集模型不再适用。为此,Greco等提出了优势关系粗糙集模型,用以处理序信息系统的知识约简问题。本文基于优势关系粗糙集理论,研究了几类序决策信息系统的属性约简与决策规则获取问题,研究内容主要分为以下几章:第二章主要介绍了优势关系粗糙集理论的基本知识,如序信息系统、优势关系、上、下近似、序决策规则和知识约简等,为后面的研究做好准备。第三章研究了优势关系下序信息系统的协调约简问题。首先,给出协调约简的定义,并证明协调约简与L-约简和Q-约简是等价的。最后,给出一种计算协调约简的区分函数方法。第四章研究了不协调序决策信息系统的下近似约简问题。我们改进袁修久等作者提出的关于下近似约简的计算方法,并给出一种新的计算下近似约简的区分函数方法,同时验证了约简结果的正确性。第五章研究了模糊目标序信息系统的属性约简与优化序决策规则的获取问题。首先在序决策信息系统中定义模糊上(下)近似,由此定义由对象生成的三类序决策规则,并讨论它们的确定度。然后定义对象的三种类型的约简:下近似约简、上近似约简和区间近似约简,并给出相应的判定定理,且构造区分函数用于计算对象的三类近似约简。基于对象的三类约简,我们可以得到三种类型的优化序决策规则。最后,讨论系统的相对约简,并给出具体的计算方法。第六章总结上面几章的主要内容,并对后续工作做出展望。更多还原

【Abstract】 Classical rough set theory is based on the classification of universe determined by equivalent relation and successfully used in knowledge reduction of complete symbolic information systems. However, in ordered information systems, attribute values of the objects represent the dominance relation between the objects. Therefore, classical rough set theory, which is established based on the indiscernibility, is inapplicable in dealing with knowledge reduction problem of the ordered information systems. So Greco et al. proposed the dominance-based rough set approach to draw decision rules and compute reducts of the ordered information systems.In this paper, dominance-based rough set approach and its extended models are used to discuss attribute reduction and decision rule acquisition in ordered information systems. The paper is organized as follows:In Chapter 2, primary knowledge of ordered information systems and dominance-based rough set approach such as dominance relation, upper (lower) appproximation, ordered decision rules and knowledge reduction are introduced. In Chapter 3, the consistent reducts of ordered decision information systems are studied. Firstly, the definition of consistent reduct is proposed. Then, it is proved that the consistent reduct is actually a L - reduct as well as a Q - reduct. Finally, the discernibility function of the consistent reduct is constructed, and used to compute the consistent reduct by using Boolean reasoning techniques. By discussing the consistent reduct, we get a new computing method which employs discernibility function for Q - reduct.In Chapter 4, lower approximation reducts in inconsistent ordered decision information systems based on dominance relation are studied. We improve the computing method of lower approximation reducts proposed by other authors and construct a new discernibility function to compute the lower approximation reducts.In Chapter 5, attribute reduction and optimal decision rules acquisition problems in fuzzy objective ordered information systems are studied. Firstly, fuzzy lower approximation and fuzzy upper approximation are defined, three new types of decision rules generated by an object are proposed, and the degrees of certainty of the decision rules are given. Then, reduct of the object is defined, the judgment theorems are given, and discernibility function with respect to three types of reducts are constructed, by which reducts of the object can be derived. Based on these reducts, three new types of optimal ordered decision can be induced. At last, three kinds of reducts of the systems and their computing methods are given.In Chapter 6, conclusions of the work in this paper are given, and the future work is pointed out.更多还原