对象定向概念格的不协调决策约简

南京大学学报(自然科学版) ›› 2016, Vol. 52 ›› Issue (5): 853–.

对象定向概念格的不协调决策约简

李俊余1，2，王　霞1，2*

出版日期:2016-09-25 发布日期:2016-09-25
作者简介: 1.浙江海洋大学数理与信息学院，舟山，316022；2.浙江省海洋大数据挖掘与应用重点实验室，舟山，316022
基金资助:
国家自然科学基金(61202206，61573321，61602415)
收稿日期：2016－09－04
*通讯联系人，Email：bblylm@126.com

Inconsistent decision reduction of object oriented concept lattices

Li Junyu1，2，Wang Xia1，2*

Online:2016-09-25 Published:2016-09-25
About author: 1.School of Mathematics，Physics and Information Science，Zhejiang Ocean University，Zhoushan，316022，China；2．Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province，Zhoushan，316022，China

摘要/Abstract

摘要： 由于噪声、预测能力等因素的影响，实际问题中遇到的决策形式背景大多是不协调的．因为形式背景中不协调性的存在使得人们挖据有用的信息变得更加复杂和困难，而属性约简可以使决策形式背景的知识表示更为简洁，隐藏的知识更加清晰，因此研究不协调决策形式背景的属性约简具有重要的意义．针对不协调决策形式背景研究了对象定向概念格的属性约简的定义和方法．首先，利用对象幂集上的等价关系定义了对象定向概念格的两种属性约简：分布约简和最大分布约简．分布约简集保持每个对象子集在每个决策等价类的隶属程度不变，而最大分布约简集保持每个对象子集的最大决策等价类不变．其次，讨论了分布协调集和最大分布协调集之间的关系．最后，定义了分布辨识矩阵和最大分布辨识矩阵，给出了分布约简集和最大分布约简集的判定定理，提出了计算分布约简集和最大分布约简集的方法．

Abstract: In practice，most formal decision contexts are inconsistent because of various factors such as prediction capability，noise in data，and so on.Due to inconsistency，it is more complex and difficult to extract useful information from inconsistent formal decision contexts.Since attribute reduction of concept lattices makes knowledge representation of formal decision contexts more succinct，knowledge hiding in formal decision contexts clearer，and adaptability of rule sets for formal decision contexts better，it is necessary to research attribute reduction of concept lattices in the case of inconsistent formal decision contexts.The purpose of this paper is to investigate notions and methods of attribute reduction of object oriented concept lattices in the case of inconsistent decision formal contexts.Based on an equivalent relation defined on the object power set，two notions of attribute reduction of an object oriented concept lattice are presented for an inconsistent decision formal context，which are decision attribute reduct and maximum decision attribute reduct.It is shown that the distribution consistent set preserves the degrees in which the conditional equivalent class belongs to each decision equivalent class，and the maximum distribution consistent set preserves all maximum decision equivalent classes.Then relations between decision attribute consistent set and maximum decision attribute consistent are discussed in detail.And a distribution consistent set must be a maximum distribution consistent set，but the converse is not necessarily true.Finally，two notions of discernible matrix are introduced into an object oriented concept lattice，which are decision discernible matrix and maximum decision discernible matrix.By using decision discernible matrix and maximum decision discernible matrix，judgement theorems of decision attribute reduct and maximum decision attribute reduct are obtained respectively，and a method of discernible matrix is proposed to obtain all decision attribute reducts and maximum decision attribute reducts of the object oriented concept lattice.

李俊余1，2，王　霞1，2*. 对象定向概念格的不协调决策约简[J]. 南京大学学报(自然科学版), 2016, 52(5): 853–.

Li Junyu1，2，Wang Xia1，2*. Inconsistent decision reduction of object oriented concept lattices[J]. Journal of Nanjing University(Natural Sciences), 2016, 52(5): 853–.

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