粗集模型的特征函数表示

粗糙集理论是处理不确定知识的一种工具,已在人工智能与知识发现、模式识别与分类、数据挖掘与故障检测等方面得到了较好应用。由于粗糙集在理论和应用两个方面的迅速发展,粗集模型得到拓广。本文研究粗集模型的特征函数表示形式,这种表示形式具有一般性,可以统一各种推广模型。粗集理论的核心是一对非数值型算子,即上下近似算子。粗集理论中的上下近似算子与证据理论中的一对数值算子——似然函数和信任函数有密切关系,为此作者研究了粗糙集与证据理论的关系。

Characteristic Function Representation of Rough Sets

Rough set theory is a new tool dealing with uncertainty.We have found its applications in many areas such as artificial intelligence(AI),knowledge discovery(KDD),pattern recognition and classification,and data mining and fault diagnostication.Various generalization of rough set in lower and upper approximation is given due to the development of the rough set theory and its application.The paper studies the characteristic function representation of rough set.This representation is universal.Unified characteristic function form of lower and upper approximation is given.The core of rough set theory is a pair of non-numerical operators,i.e.lower and upper approximation operators.Lower and upper approximation operators have close relation with likelihood functions and belief functions that are a pair of numerical operators in the Shafer's evidence theory.So it is necessary to investigate the relationship between rough set and Shafer's evidence theory.