id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-3049	Kehayopulu, Niovi	Hypersemigroups and Fuzzy Hypersemigroups	2017	17	.pdf	application/pdf	8266	526	92	The aim is to show that the theory of hypersemigroups and the theory of fuzzy hyper- semigroups are parallel to each other, in the following sense: An hypersemigroup H is intra-regular, for example, if and only if A∩B ⊆ B∗A for every right ideal A and every left ideal B of H. And an hypersemigroup H is intra-regular if and only if f ∧g � g◦f for every fuzzy right ideal f and every fuzzy left ideal g of H. An hypersemigroup H is left quasi-regular if and only if A∩B ⊆ A ∗B for every ideal A and every nonempty subset B of H. And an hypersemigroup H is left quasi-regular if and only if f ∧ g � f ◦ g for every fuzzy ideal f and every fuzzy subset g of H. 2010 Mathematics Subject Classifications: AMS 20M99, 08A72 Key Words and Phrases: Hypersemigroup, right (left) ideal, bi-ideal, fuzzy right (left) ideal, fuzzy bi-ideal, regular, intra-regular, left (right) quasi-regular, semisimple 1. For two fuzzy subsets f and g of H, we denote by f ◦ g the fuzzy subset of H defined as follows: f ◦ g : H → [0, 1] a→  ∨ (y,z)∈Aa min{f(y), g(z)}	cache/ejpam-3049.pdf	txt/ejpam-3049.txt