Affiliations: [a]
School of Science, Xi’an Aeronautical University, Xi’an, China
| [b]
School of Mathematics, Northwest University, Xi’an, China
| [c] Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
| [d]
School of Science, Xi’an Shiyou University, Xi’an, China
Correspondence:
[*]
Corresponding author. Xiaolong Xin, School of Mathematics, Northwest University, Xi’an, 710127, China. E-mail: xlxin@nwu.edu.cn.
Abstract: In this paper, we introduce the co-annihilator ⊥A of a set A and the co-annihilator of (F : a) of a relative to a prefilter (filter) F in an EQ-algebra ɛ. We investigate related properties of them, and obtain that the lattice of all prefilters
PF(ɛ)
forms a pseudo-complemented lattice and the collection of all co-annihilators
COA(ɛ)
forms a Boolean algebra in a separated EQ-algebra ɛ. Moreover, we introduce the notion of Δ-co-annihilators in an EQΔ-algebra ɛΔ and conclude that the collection of all Δ-prefilters
PFΔ(ɛΔ)
in an ℓEQΔ-algebra ɛΔ constitutes a relative pseudo-complemented lattice. Finally, we introduce and investigate two types of fuzzy co-annihilators AnnR (μ) and Ann (μ, ν) in ɛ. We come to a conclusion that the set of all fuzzy filters
FF(ɛ)
in a residuated ℓEQ-algebra ɛ forms a relative pseudo-complemented lattice whence → is the Gödel residuated implication in Str (μ, ν).
