关键词: 模糊粗糙集, 双剩余格, 正则可换双剩余格, 公理系统

Abstract: The notion of double residuated lattice is an algebraic abstract of triangular norm, triangular co-norm, residuated implication and its dual operator, and the notion of L-fuzzy relation is a generalization of fuzzy relation based on lattices. As a generalization of Pawlak classical rough sets and some fuzzy rough sets, this paper proposes a new generalized fuzzy rough set model based on commutative double residuated lattices and L-fuzzy relations. It also introduces the notion of regular commutative double residuated lattice, and investigates the axiomatic systems of fuzzy rough upper and lower approximation operators based on regular commutative double residuated lattices, which are generalizations of some results in many literatures.