基于模糊包含度的集值决策系统的局部约简算法

Local reduct algorithm for set-valued information systems based on fuzzy inclusion degree

集值信息系统用来描述有不确定信息和缺省信息的信息系统.针对集值决策系统,提出一种新的模糊集合包含度,并用新的模糊集合包含度定义模糊粗糙集的变精度上下近似.给出了基于模糊包含度局部约简的定义,基于模糊包含度定义了属性的相对重要度,并基于这种重要度给出了一种模糊粗糙集局部约简的启发式算法.为模糊粗糙集的研究提供了一种新的工具.

A set-valued information system has some objects which are with more than one value.It is a generalized model of single-valued information system,and a special data table with uncertainty and default information for the development of decision support systems.Inclusion degree is practically a measure on partially ordered relation.However,the classical inclusion degree is not suitable for measuring the fuzzy sets.In this paper,the classical inclusion degree is extended to fuzzy inclusion degree in fuzzy environment for defining fuzzy lower and upper approximations.Based on the new defined fuzzy inclusion degree,the variable precision fuzzy lower and upper approximations are defined.Moreover,a kind of local reduction for fuzzy inclusion rough sets is defined to maintain the approximation ability of the set-valued information system.Since obtaining all of the reducts for an information system is a NP-hard problem,the heuristic reduct algorithm is widely used in practice.In the end of this paper,a new heuristic local reduct algorithm is designed based on the new attribute inclusion significance.The main objective of this paper is to introduce a fuzzy rough set local reduct method based on the new fuzzy inclusion degree.The new proposed method opens a new door for the study of fuzzy rough sets and set-valued information systems.In the further work,we will continue to extract and simplify the decision rules in the set-valued information systems.