多尺度覆盖决策信息系统的布尔矩阵方法

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.

Boolean Matrix Approach for Multi-scale Covering Decision Information System

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.