The lattice of prefilters of an EQ-algebra
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- 作者：Neda Mohtashamnia nmohtashamniya@yahoo.com ; Lida Torkzadeh ; ltorkzadeh@yahoo.com
- 关键词：EQ-algebra ; Boolean algebra ; Heyting algebra
- 刊名：Fuzzy Sets and Systems
- 出版年：2017
- 出版时间：15 March 2017
- 年：2017
- 卷：311
- 期：Complete
- 页码：86-98
- 全文大小：302 K
- 卷排序：311
文摘
In this paper, the notion of a prefilter generated by a nonempty subset of an EQ-algebra is introduced and a characterization of it is obtained. It is proved that the set of all prefilters of an EQ-algebra is an algebraic lattice and it is a Brouwerian lattice for an ℓEQ-algebra. Furthermore, it is shown that the set of all principal prefilters of an ℓEQ-algebra is a sublattice of the lattice of prefilters. Then by defining an implication between two prefilters, it is determined that the lattice of prefilters is a Heyting algebra, for an ℓEQ-algebra. Finally, the EQ-algebras for which the lattice of prefilters is a Boolean algebra are given.