用模糊Galois联络对L-模糊粗糙集进行公理化刻画(英文)  

Axiomatic Characterizations of L-fuzzy Rough Sets Using Fuzzy Galois Connections

作　　者：折延宏[1] 王国俊[2] 

机构地区：[1]西安石油大学理学院,陕西西安710065 [2]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《模糊系统与数学》2010年第5期96-104,共9页Fuzzy Systems and Mathematics

基　　金：Project supported by the NSF of China under Grant 10771129

摘　　要：粗糙集理论是由Pawlak提出的一种表示与处理数据表中信息的形式化工具。作为粗糙集概念的推广,一种基于完备剩余格的L-模糊粗糙集已由Radzikowska与Kerre提出,在本文中,我们第一次借助于L-模糊Galois联络对L-模糊粗糙集进行了公理化刻画。由于L-模糊粗糙集及L-模糊Galois联络均为相应经典情形的推广,故本文的结论对于经典粗糙集来说也是成立的,这就意味着通过Galois联络可将经典粗糙集乃至L-模糊粗糙集的公理化统一起来。Rough sets were proposed by Pawlak as a formal tool for representing and processing information in data tables.As a generalization of the notion of rough sets,L-fuzzy rough sets which take a complete residuated lattice as their basic structure,were introduced by Radzikowska and Kerre.In this paper,we present the axiomatic characterizations of L-fuzzy rough sets by usingL-fuzzy Galois connections for the first time.Since L-fuzzy rough sets and L-fuzzy Galois connections are the both generalizations of their classical counterparts,the results obtained in the present paper also hold for crisp rough sets.This means that the axiomatic approach of crisp rough sets and L-fuzzy rough sets can be unified by using Galois connections.

关 键 词：L-模糊Galois联络 L-模糊关系 L-模糊集 L-模糊粗糙集 剩余格 

分 类 号：O159[理学—数学]