Constructive and axiomatic approaches of fuzzy approximation operators
Constructive and axiomatic approaches of fuzzy approximation operators
复制标题
DOI：
10.1016/j.ins.2003.08.005
复制
发表时间：
2004-02-15
影响因子：
8.1
通讯作者：
Zhang, WX
中科院分区：
文献类型：
--
作者：
Wu, WZ;Zhang, WX
本文提出了一个一般框架，用于研究模糊环境中使用建设性和公理方法的粗糙集近似算子。在建设性的方法中，首先定义了一对上下部和上部的模糊粗糙（分别和粗糙的模糊）近似算子。然后呈现模糊粗糙近似运算符和粗模糊近似操作员的表示。进一步建立了模糊（和脆弱）关系与模糊（和粗糙模糊）近似运算符之间的连接。在公理方法中，各种模糊近似算子的特征是不同的公理集。模糊近似运算符的最小公理集保证存在某些类型的模糊或清晰关系，从而产生相同的操作员。 （c）2003 Elsevier Inc.保留所有权利。
This paper presents a general framework for the study of rough set approximation operators in fuzzy environment in which both constructive and axiomatic approaches are used. In constructive approach, a pair of lower and upper generalized fuzzy rough (and rough fuzzy, respectively) approximation operators is first defined. The representations of both fuzzy rough approximation operators and rough fuzzy approximation operators are then presented. The connections between fuzzy (and crisp, respectively) relations and fuzzy rough (and rough fuzzy, respectively) approximation operators are further established. In axiomatic approach, various classes of fuzzy approximation operators are characterized by different sets of axioms. The minimal axiom sets of fuzzy approximation operators guarantee the existence of certain types of fuzzy or crisp relations producing the same operators. (C) 2003 Elsevier Inc. All rights reserved.