基于等价关系逻辑“与”“或”的粗糙集

Rough Set Based on Logical AND and OR of Equivalence Relations

摘要: 本文从关系逻辑运算的角度研究粗糙集，对经典的粗糙集进行了推广。对多个等价关系进行逻辑“与”和逻辑“或”运算，提出了逻辑“与”粗糙集模型和逻辑“或”粗糙集模型。说明了逻辑“与”粗糙集模型和Pawlak经典粗糙集的关系，并详细研究了逻辑“或”粗糙集模型的重要性质，定义了逻辑“或”粗糙集模型中的若干度量，举例验证了该模型。

Abstract: We popularize the classical rough set model in this paper and study rough set in the view of logical operation of equivalence relations. The logical AND rough set model and the logical OR rough set model are proposed on the basis of the operations logical AND and logical OR of equivalence relations. Furthermore, the connection between the logical AND rough set model and Pawlak’s classical rough set model is illustrated. Important properties are discussed in depth and several measures are defined in OR-RS. An example is em-ployed to explain OR-RS.