α－先验概率优势关系下的粗糙集模型研究

南京大学学报(自然科学版) ›› 2016, Vol. 52 ›› Issue (5): 899–.

α－先验概率优势关系下的粗糙集模型研究

施玉杰1*，杨宏志2，徐久成3

出版日期:2016-09-25 发布日期:2016-09-25
作者简介: 1.郑州大学数学与统计学院，郑州，450001；2.河南财经政法大学，郑州，450046；3．河南师范大学计算机与信息工程学院，新乡，453007
基金资助:
基金项目：国家自然科学基金(61370169，61402153)，河南省科技攻关重点项目(142102210056)
收稿日期：2016－07－14
*通讯联系人，Email：shiyujiezzu@126.com

The study of rough set model under αprior probability dominance relation

Shi Yujie1*，Yang Hongzhi2，Xu Jiucheng3

Online:2016-09-25 Published:2016-09-25
About author: 1.School of Mathematics and Statistics，Zhengzhou University，Zhengzhou，450001，China；2．Henan University of Economics and Law，Zhengzhou，450046，China；3．College of Computer & Information Engineering，Henan Normal University，Xinxiang，453007，China

摘要/Abstract

摘要： 序信息系统涉及了多属性决策领域的比较、排序及属性约简等问题．然而在现实世界中，不完备序信息系统十分常见．为解决不完备序信息系统中现有优势关系要求过于严格或宽松的缺陷和目前不完备序信息系统粗糙集模型及性质、对象排序、属性约简等理论研究的不完整性，首先，结合先验的知识，从概率分布的角度分析未知属性值，提出α－先验概率优势关系，在此基础上研究其粗糙集模型及性质；其次，给出α－先验概率优势类结构差异度的概念，并提出一种新的对象排序方法；然后，给出一种由α－先验概率优势类结构差异度来寻找不完备序信息系统的启发式属性约简算法，该算法能有效地避免因新的优势关系不满足单调性引起的弊端；最后，用具体实例验证所提方法的正确性和有效性．该课题内容不仅丰富了粗糙集理论的研究，而且为不完备序信息系统理论提供了新的方法和思路．

Abstract: Comparing，ranking，and attribution reduction problems et al under multiple attributes are always involved in ordered information systems.In the real world，however，incomplete ordered information systems are very common.As a matter of fact，there are some defects and shortcomings in the existing dominance relations，and the research of rough set model including its properties，objects ranking，and attribute reduction in incomplete ordered information systems are imperfect yet.In order to solve these problems，the concept of αprior probability is proposed firstly，then the relevant properties of rough set model based on the new dominance relation are discussed.They are combined with the knowledge of prior probability，and the unknown values are analyzed from the perspective of the probability distribution.Secondly，a new definition of structure diversity on αprior probabilistic dominance classes is proposed，and then some theories and a new method of objects ranking are put forward.The new method of objects ranking is of great significance，and it can be applied in the practical ranking problems.Thirdly，although there are a lot of algorithms concerning attribute reduction，they can’t be applied to the ordered information systems under the new dominance relation because of its nonmonotonous，so the structure diversity on αprior probabilistic dominance classes as well as a novel heuristic algorithm of attribute reduction is put forward.The algorithm can effectively avoid the defect that the dominance relation can’t meet monotonicity.Finally，in order to verify the accuracy and validity of the theory，the concrete examples are presented.Most importantly，this study not only enriches the content of rough set model，but also provides a new method and a train of thought to the theoretical basis of knowledge discovery in incomplete ordered information systems.

施玉杰1*，杨宏志2，徐久成3. α－先验概率优势关系下的粗糙集模型研究[J]. 南京大学学报(自然科学版), 2016, 52(5): 899–.

Shi Yujie1*，Yang Hongzhi2，Xu Jiucheng3. The study of rough set model under αprior probability dominance relation[J]. Journal of Nanjing University(Natural Sciences), 2016, 52(5): 899–.

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