基于决策规则的形式背景属性约简*

在经典形式背景中,利用对象和属性间的二元关系定义一对粗糙模糊上、下近似算子,讨论算子的基本性质,指出算子与已有粗糙近似算子的关系.利用定义的粗糙模糊上、下近似算子,得到两类决策规则,即确定性决策规则和可能性决策规则.针对两类决策规则,提出下近似约简和上近似约简的概念,关于上近似约简,得到可约属性和属性协调集的判别条件,给出属性约简方法,并举例说明方法的可行性.

Attribute Reduction of Formal Contexts Based on Decision Rules

By using the binary relation between objects and attributes, one pair of lower and upper rough fuzzy approximation operators is defined in formal contexts, properties of the approximation operators are explored, and the relationship between the defined approximation operators and the existing rough approximation operators is revealed. By using the defined approximation operators, two types of decision rules can be extracted, i.e., the certainty rules and the possibility rules. Subsequently, with respect to two types of decision rules, notions of lower and upper approximation reductions are proposed. For the upper approximation reduction, some necessary and sufficient conditions for reducible attributes and consistent subsets of attributes are obtained. An approach for attribute reduction is presented, and some illustration examples are given to show its reliability.