Pythagorean模糊信息系统属性约简的图论方法  

A Graph Approach for Attribute Reduction of Pythagorean Fuzzy Information Systems

作　　者：张少谱 孙品 冯涛[2] ZHANG Shaopu;SUN Pin;FENG Tao(Department of Mathematics and Physics,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;School of Sciences,Hebei University of Science and Technology,Shijiazhuang 050018,China)

机构地区：[1]石家庄铁道大学数理系,河北石家庄050043 [2]河北科技大学理学院,河北石家庄050018

出　　处：《郑州大学学报（理学版）》2020年第1期79-86,113,共9页Journal of Zhengzhou University:Natural Science Edition

基　　金：国家自然科学基金项目(61573127);河北省自然科学基金项目(A2018210120);河北省人才工程培养资助项目(A2017002112,A201901049);河北省优秀专家出国培训项目

摘　　要：信息系统中,属性约简是知识发现问题的一个研究热点,能达到发掘并简化知识的目的。目前已有很多利用辨识矩阵来进行属性约简的研究,但是当数据维数较大时,算法复杂度往往很大。利用加权欧几里得距离来定义二元关系及辨识矩阵,利用信息系统的约简与生成图的最小顶点覆盖等价的关系,将辨识矩阵求解约简的问题转化为求解生成图中最小顶点覆盖的问题,并给出了Pythagorean模糊信息系统中属性约简的算法;在此基础上,利用基于加权欧几里得距离的相似关系,定义了Pythagorean模糊决策信息系统的辨识矩阵,并给出了用最小顶点覆盖的方法求约简算法,最后利用实例验证了算法的有效性。Attribute reduction was a hot spot of knowledge discovery in information systems.It helped us to discover and simplify knowledge.There were many studies on attribute reduction using discernibility matrix.However,when the data dimension increased,the complexity of the algorithm also increased.Weighted Euclidean distance was used to define the binary relation and the discernibility matrix.Using the equivalence relationship between attribute reduction of a given information system and minimum vertex cover of a graph induced from this information system,the problem of solving reduction of discernibility matrix was transformed into the calculation of minimum vertex cover of the induced graph.Then a new algorithm of attribute reduction in Pythagorean fuzzy information system was proposed.Reduction algorithm based on the method of minimum vertex cover of Pythagorean fuzzy decision information system was constructed by the same way.Then,the effectiveness of the proposed algorithms was demonstrated by examples.Finally,the comparative analysis was given.

关 键 词：Pythagorean模糊信息系统 属性约简 辨识矩阵 最小顶点覆盖 

分 类 号：O236[理学—运筹学与控制论]