Interval-valued intuitionistic (T, S)-fuzzy filters theory on residuated lattices

被引：12
|
作者：
Liu, Yi [1 ,2 ]
Qin, Xiaoyan [3 ]
Xu, Yang [2 ]
机构：
[1] Neijiang Normal Univ, Coll Math & Informat Sci, Neijiang 641000, Sichuan, Peoples R China
[2] Southwest Jiaotong Univ, Intelligent Control Dev Ctr, Chengdu 610031, Sichuan, Peoples R China
[3] Shanxi Norm Univ, Coll Math & Comp Sci, Linfen 041000, Shanxi, Peoples R China
来源：
INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS | 2014年 / 5卷 / 05期
关键词：
Residuated lattices; Interval valued intuitionistic fuzzy set; t-norm; s-norm(t-conorm); Interval valued intuitionistic (T; S)-fuzzy; (implication; positive implicative; Boolean; G; MV); filters; FUZZY-SET-THEORY; ALGEBRAS;
D O I：
10.1007/s13042-013-0213-1
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
The aim of this paper is further to develop the filter theory on residuated lattices. Firstly, the notion of interval valued intuitionistic (T, S)-fuzzy filter(IVI (T, S)-fuzzy filter for short) on residuated lattices is introduced by linking the interval valued intuitionistic fuzzy set, t-norm, s-norm and filter theory of residuated lattices; the properties and equivalent characterizations of interval valued intuitionistic (T, S)-fuzzy filter are investigated; the relation between IVI (T, S)-fuzzy filter and filter is studied. Secondly, the notions of interval valued intuitionistic (T, S)-fuzzy implicative filter and interval valued intuitionistic (T, S)-fuzzy Boolean filter are introduced; the properties and equivalent characterizations of them are investigated; the intuitionistic (T, S)-fuzzy implicative filter is proved to be equivalent to the intuitionistic (T, S)-fuzzy Boolean filter in residuated lattices. Finally, the intuitionistic (T, S)-fuzzy positive implicative filter and intuitionistic (T, S)-fuzzy G (MV) filter are introduced; some equivalent characterizations of them are obtained and the relations among these fuzzy filters are investigated.
引用
收藏
页码：683 / 696
页数：14
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