2016/06/17 by Niovi Kehayopulu, Kehayopulu, Niovi
Biochemistry, Genetics and Molecular Biology · Decision Sciences · #08A72) #20N99 (20M99 #FOS: Mathematics #Fuzzy and Soft Set Theory #General Mathematics (math.GM) #Peroxisome Proliferator-Activated Receptors
paper · pdf · doi:10.48550/arxiv.1606.06079
openalex publication_date 2016/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that an hypersemigroup H is regular if and only, for any fuzzy\nsubset f of H, we have f preceq f\∘ 1\∘ f and it is intra-regular\nif and only if, for any fuzzy subset f of H, we have f preceq 1\∘\nf\∘ f\∘ 1. An hypersemigroup H is left (resp. right) quasi-regular if\nand only if, for any fuzzy subset f of S we have f preceq 1\∘ f\∘\n1\∘ f (resp. f preceq f\∘ 1\∘ f\∘ 1) and it is semisimple if and\nonly if, for any fuzzy subset f of S we have f preceq 1\∘ f\∘ 1\∘\nf\∘ 1. The characterization of regular and intra-regular hypersemigroups in\nterms of fuzzy subsets are very useful for applications.\n