id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6327	Sarapuddin, Hulsen; Vilela, Jocelyn	On Quotient KS-semigroups Induced by Fuzzy KS-ideals	2025	23	.pdf	application/pdf	10780	813	92	Since (z ∗ x) ∗ (z ∗ y) ≤ y ∗ x and (z ∗ y) ∗ (z ∗ x) ≤ x ∗ y, we have µ((z ∗ x) ∗ (z ∗ y)) ≥ µ(y ∗ x) > 0 and µ((z ∗ y) ∗ (z ∗ x)) ≥ µ(x ∗ y) > 0 by Lemma 1(i). = y ∗ (y ∗ x) for all x, y ∈ X, (ii) positive implicative if (x ∗ y) ∗ z = (x ∗ z) ∗ (y ∗ z), or equivalently, x ∗ y = (x ∗ y) ∗ y for all x, y, z ∈ X, (iii) implicative if x∗ (y ∗x) = x for all x, y ∈ X, or if it is both commutative and positive implicative.	cache/ejpam-6327.pdf	txt/ejpam-6327.txt