Fuzzy preorder and fuzzy topology

被引:208
作者
Lai, Hongliang [1 ]
Zhang, Dexue [1 ]
机构
[1] Sichuan Univ, Yangtze Ctr Math, Chengdu 610064, Peoples R China
关键词
fuzzy preorder; upper set; Alexandrov topology; specialization order; fuzzy topology;
D O I
10.1016/j.fss.2006.02.013
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
This paper presents, by means of Alexandrov topology for fuzzy preordered sets and specialization order for fuzzy topological spaces, a systematic investigation of the interrelationship between fuzzy preordered sets, topological spaces, and fuzzy topological spaces. (C) 2006 Elsevier B.V. All rights reserved.
引用
收藏
页码:1865 / 1885
页数:21
相关论文
共 31 条
[1]  
Adamek J., 1990, ABSTRACT CONCRETE CA
[2]  
[Anonymous], 1999, Mathematical Principles of Fuzzy Logic, DOI DOI 10.1007/978-1-4615-5217-8
[3]   Representations and constructions of similarity-based fuzzy orderings [J].
Bodenhofer, U .
FUZZY SETS AND SYSTEMS, 2003, 137 (01) :113-136
[4]   Openings and closures of fuzzy preorderings: Theoretical basics and applications to fuzzy rule-based systems [J].
Bodenhofer, U ;
De Cock, M ;
Kerre, EE .
INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, 2003, 32 (04) :343-360
[5]   Upper and lower approximations of fuzzy sets [J].
Boixader, D ;
Jacas, J ;
Recasens, J .
INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, 2000, 29 (04) :555-568
[6]  
Borceux F., 1994, HDB CATEGORICAL ALGE, V2
[7]  
Castro J. L, 1995, MATHWARE SOFT COMPUT, V2, P197
[8]   INDUCING IMPLICATION RELATIONS [J].
CASTRO, JL ;
DELGADO, M ;
TRILLAS, E .
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 1994, 10 (03) :235-250
[9]   Metrics and T-equalities [J].
De Baets, B ;
Mesiar, R .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 267 (02) :531-547
[10]   On (un)suitable fuzzy relations to model approximate equality [J].
De Cock, M ;
Kerre, E .
FUZZY SETS AND SYSTEMS, 2003, 133 (02) :137-153