α-filters and prime α-filter spaces in residuated lattices

被引：0
|
作者：
Dong, Yan Yan [1 ]
Xin, Xiao Long [1 ]
机构：
[1] Northwest Univ, Sch Math, Xian 710127, Shaanxi, Peoples R China
来源：
SOFT COMPUTING | 2019年 / 23卷 / 10期
基金：
中国国家自然科学基金;
关键词：
Residuated lattice; alpha-filter; Co-annihilator; Heyting algebra; Prime alpha-filter space;
D O I：
10.1007/s00500-018-3195-9
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
The main goal of this paper is to introduce and research co-annihilators and alpha-filters in residuated lattices. We characterize alpha-filters in terms of co-annihilators. Also, we answer the open problem which appeared in Haveshki and Mohamadhasani (J Intell Fuzzy Syst 28:373-382, 2015). We prove that the lattice of all alpha-filters in a residuated lattice forms a complete Heyting algebra. Finally, we investigate some topological properties of space of prime alpha-filters and give necessary and sufficient conditions for the space to become a T-1 space and Hausdorff space.
引用
收藏
页码：3207 / 3216
页数：10
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