Abstract
Abstract The main goal of this paper is to introduce the notion of stabilizers in EQ-algebras and develop stabilizer theory in EQ-algebras. In the paper, we introduce (fuzzy) left and right stabilizers and investigate some related properties of them. Then, we discuss the relations among (fuzzy) stabilizers, (fuzzy) prefilters (filters) and (fuzzy) co-annihilators. Also, we obtain that the set of all prefilters in a good EQ-algebra forms a relative pseudo-complemented lattice, where Str(F, G) is the relative pseudo-complemented of F with respect to G. These results will provide a solid algebraic foundation for the consequence connectives in higher fuzzy logic.
Highlights
EQ-algebra was proposed by Novak in [1]
The main goal of this paper is to introduce the notion of stabilizers in EQ-algebras and develop stabilizer theory in EQ-algebras
We obtain that the set of all pre lters in a good EQ-algebra forms a relative pseudo-complemented lattice, where Str(F, G) is the relative pseudo-complemented of F with respect to G
Summary
EQ-algebra was proposed by Novak in [1]. One of the motivations was to introduce a special algebra as the correspondence of truth values for high-order fuzzy type theory (FTT). ([6]) Let μ be a fuzzy pre lter of an EQ-algebra E. The following theorem provides a method for determining the fuzzy pre lter of an good EQ-algebra. Let F(x) = {y ∈ E : x ≤ y} be a normal pre lter of a good EQ-algebra E for all x ∈ E.
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