On filter theory of residuated lattices

被引：141
作者：
Zhu, Yiquan [1 ]
Xu, Yang [2 ]
机构：
[1] Guangzhou Maritime Univ, Div Basic Sci, Guangzhou 510725, Guangdong, Peoples R China
[2] SW Jiaotong Univ, Sch Math, Chengdu 610031, Peoples R China
来源：
INFORMATION SCIENCES | 2010年 / 180卷 / 19期
关键词：
(Regular) residuated lattice; (Fuzzy) filter; Regular (fuzzy) filter; (Fuzzy) Boolean (implicative positive implicative and fantastic) filter; GENERALIZED FUZZY FILTERS; IMPLICATIVE FILTERS; SYSTEMS;
D O I：
10.1016/j.ins.2010.05.034
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
The aim of this paper is to develop the filter theory of general residuated lattices. First, we extend some particular types of filters and fuzzy filters in BL-algebras and MTL-algebras naturally to general residuated lattices, and further enumerate some relative results obtained in BL-algebras or MTL-algebras, which still hold in general residuated lattices. Next, we introduce the concepts of regular filters and fuzzy regular filters to general residuated lattices, which are two new types of filters and fuzzy filters, and derive some of their characterizations. Finally, we discuss the relations between (fuzzy) regular filters and several other special (fuzzy) filters, and also characterize some special classes of residuated lattices by filters or fuzzy filters. (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：3614 / 3632
页数：19
相关论文
共 41 条
[1]  
[Anonymous], 2003, STUD FUZZINESS SOFT
[2]  
Chang C. C., 1958, Trans. Amer. Math. Soc., V88, P467, DOI [DOI 10.1090/S0002-9947-1958-0094302-9, 10.1090/S0002-9947-1958-0094302-9]
[3]  
Hajek P., 1998, METAMATHEMATICS FUZZ
[4]   Some types of filters in BL algebras [J].
Haveshki, M ;
Saeid, AB ;
Eslami, E .
SOFT COMPUTING, 2006, 10 (08) :657-664
[5]   FUZZY IMPLICATIVE AND BOOLEAN IDEALS OF MV-ALGEBRAS [J].
HOO, CS .
FUZZY SETS AND SYSTEMS, 1994, 66 (03) :315-327
[6]  
Jun Y.B., 2002, J FUZZY MATH, V10, P893
[7]   Fuzzy filters of MTL-algebras [J].
Jun, YB ;
Xu, Y ;
Zhang, XH .
INFORMATION SCIENCES, 2005, 175 (1-2) :120-138
[8]   Fuzzy positive implicative and fuzzy associative filters of lattice implication algebras [J].
Jun, YB .
FUZZY SETS AND SYSTEMS, 2001, 121 (02) :353-357
[9]  
Jun Young Bae, 2004, [Communications of the KMS, 대한수학회논문집], V19, P11
[10]  
Jun Young Bae, 2004, Journal of Applied Mathematics and Informatics, V14, P137
12345