反优势函数实现属性约简的粒计算分析与证明  

Analysis and Proof for Attribute Reductions Completed by Anti-Dominance Function Based on Granular Computing

作　　者：魏雁天[1] 刘慧[1] 闫林[1] 庞善起[2] 

机构地区：[1]河南师范大学计算机与信息技术学院,河南新乡453007 [2]河南师范大学数学与信息科学学院,河南新乡453007

出　　处：《广西师范大学学报（自然科学版）》2008年第3期104-109,共6页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(10571045);河南省自然科学基金资助项目(0611055200)

摘　　要：把基于逻辑公式的粒计算方法用于优势关系下反优势函数的理论分析。首先证明反优势函数对应的粒等于所有反优势关系的并,然后对反优势函数以及等价转换成的最简合取范式两者所产生粒之间的运算进行讨论。特别通过对合取范式中合取项所生成粒的研究,证明了与反优势函数等价的最简合取范式中所有的合取项就是信息系统属性集的全部约简,从而以粒计算为工具完成优势关系下对反优势函数实现信息系统属性约简的理论证明。In order to conduct a theoretical proof on attribute reduction via anti-dominance function under dominance relation,a kind of logical formulas is defined in this paper so as to construct an anti-dominance function under dominance relation. Because some conclusions indicate that the logical formulas can be used as a tool of granular computing,the method of granular computing based on the logical formulas is adopted for theoretical analysis on the anti-dominance function under dominance relation. The conclusion proved that the granule corresponding to the anti-dominance function is equal to the union of all anti-dominance relations under dominance relation,and then,discussions are made by analyzing the operations of the granules produced by both of the anti-dominance function and its shortest conjunctive normal form which is equivalently transformed. Especially through the study on the granules corresponding to conjuncts of conjunctive normal forms,it is finall＇y proved that all conjuncts of the shortest conjunctive normal form are all reductions of the attribute set based on dominance relation in the information system. So based on granular computing,the theoretical proof on attribute reduction under dominance relation via the anti-dominance function has been completed.

关 键 词：优势关系 反优势函数 反优势属性子集 析取范式 合取范式 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]