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Mohtashamnia, Neda; Torkzadeh, Lida

The lattice of prefilters of an EQ-algebra. (English) Zbl 1393.03055

Fuzzy Sets Syst. 311, 86-98 (2017).
Summary: 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 \(\ell\)EQ-algebra. Furthermore, it is shown that the set of all principal prefilters of an \(\ell\)EQ-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 \(\ell\)EQ-algebra. Finally, the EQ-algebras for which the lattice of prefilters is a Boolean algebra are given.

Cited in 1 Review
Cited in 5 Documents

MSC:

03G25 Other algebras related to logic
06F35 BCK-algebras, BCI-algebras

Keywords:

EQ-algebra; Boolean algebra; Heyting algebra
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\textit{N. Mohtashamnia} and \textit{L. Torkzadeh}, Fuzzy Sets Syst. 311, 86--98 (2017; Zbl 1393.03055)
Full Text: DOI

References:

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