可换双剩余格上的广义模糊粗糙集及其公理化

General Fuzzy Rough Sets Based on Commutative Double Residuated Lattices with Axiomatic Systems

双剩余格是t-模、t-余模、模糊剩余蕴涵及其对偶算子的代数抽象,基于格的L-模糊关系是普通模糊关系的推广。作为Pawlak经典粗糙集及多种模糊粗糙集模型的共同推广,提出了一种基于可换双剩余格及L-模糊关系的广义模糊粗糙集模型,引入了正则可换双剩余格的概念,并给出了基于正则可换双剩余格的广义模糊粗糙上、下近似算子的公理系统,推广了多个文献中已有的结果。

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.