多尺度覆盖决策信息系统的布尔矩阵方法  

Boolean Matrix Approach for Multi-scale Covering Decision Information System

作　　者：陈应生 李进金 林荣德 陈东晓 CHEN Yingsheng;LI Jinjin;LIN Rongde;CHEN Dongxiao(Fujian Province University Key Laboratory of Computational Science,School of Mathematical Sciences,Huaqiao University,Quanzhou 362021;School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000)

机构地区：[1]华侨大学数学科学学院计算科学福建省高校重点实验室,泉州362021 [2]闽南师范大学数学与统计学院,漳州363000

出　　处：《模式识别与人工智能》2020年第9期776-785,共10页Pattern Recognition and Artificial Intelligence

基　　金：国家自然科学基金项目(No.11871259,11701258);福建省高校创新团队发展计划项目暨泉州市高层次人才团队项目(No.2017ZT012)资助。

摘　　要：在多尺度决策信息系统中,一个条件属性对应某个尺度构成论域的一个划分.文中把相应的划分推广为覆盖,并建立多尺度覆盖决策信息系统模型(MSCDS).为了简化系统复杂信息的表达,采用矩阵方法.首先,利用布尔矩阵描述覆盖决策信息系统,包括上下近似、协调性和广义决策函数等.再使用布尔矩阵建立多尺度覆盖决策信息系统的定义,研究该系统的粒描述、上下近似、协调性和广义决策不变性.最后,针对协调与不协调的情况,利用布尔矩阵定义尺度组合的重要度,给出多尺度覆盖决策信息系统最优尺度选择的矩阵方法,并给出相应的选择算法和具体算例.In multi-scale decision information system,one condition attribute corresponding to a certain scale forms a partition of the universe.A multi-scale covering decision information system(MSCDS)is proposed and the partition is generalized to a covering.A boolean matrix method is applied to simplify the complexity of information expression in this system.Firstly,boolean matrix is employed to describe the covering decision information system,including upper and lower approximations,consistency and generalized decision function.Secondly,the definitions of MSCDS,consistency and generalized decision invariant of the system are expressed in boolean matrix method.Finally,the boolean matrix method is utilized to define the significance of a combination scale with both consistency and inconsistency,and the relevant algorithms and examples of optimal granularity selection of MSCDS are presented.

关 键 词：粗糙集 覆盖信息系统 布尔矩阵 多尺度覆盖决策信息系统 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]