Affiliations: [a] School of Mathematics and Statistics, Beibei, Chongqing, PR China | [b] Department of Mathematics, Yazd University, Yazd, Iran
Correspondence:
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Corresponding author. GuiYun Chen, School of Mathematics and Statistics, TianSheng Road, 400715, Beibei, Chongqing, PR China. E-mail: [email protected].
Abstract: We give the notion of fuzzy congruences in a non-associative semigroup briefly known as Abel-Grassmann’s groupoid. First, we study fuzzy full, fuzzy self-conjugate, fuzzy normal subgroupoids and show that fuzzy kernel κ and fuzzy trace τ of a congruence make up a congruence pair (κ, τ) . Then, we investigate fuzzy idempotent-separating congruence and show that μ(κ,τ) is a unique fuzzy congruence. Next, we study the lattice of fuzzy congruences, fuzzy congruence relations φmin and φmax and show a relation between fuzzy kernel and fuzzy trace of ρmax in a completely inverse AG**-groupoid.
Keywords: Completely inverse AG**-groupoid, fuzzy kernel of a congruence, fuzzy
trace of congruence, fuzzy congruence pair, lattice of fuzzy congruences
