2014/04/22 by Niovi Kehayopulu, Kehayopulu, Niovi, Michael Tsingelis +1
Computer Science · Decision Sciences · Mathematics · #06F05 (08A72 #20M10) #20N02 #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #General Mathematics (math.GM) #Multi-Criteria Decision Making #math.GM #msc:06F05 #msc:20N02
paper · pdf · doi:10.48550/arxiv.1404.5875
arxiv created 2014/04/22 · openalex publication_date 2014/04/22 · arxiv updated 2014/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A fuzzy subset f of an ordered semigroup (or semigroup) S is called fuzzy semiprime if f(x)≥ f(x2) for every x∈ S (Definition 1). Following the terminology of semiprime subsets of ordered semigroups (semigroups), the terminology of ideal elements of poe-semigroups (: ordered semigroups possessing a greatest element), and the terminology of ordered semigroups, in general, a fuzzy subset f of an ordered semigroups (semigroup) should be called fuzzy semiprime if for every fuzzy subset g of S such that g2:=g∘ g\preceq f, we have g\preceq f (Definition 2). And this is because if S is a semigroup or ordered semigroup, then the set of all fuzzy subsets of S is a semigroup (ordered semigroup) as well. What is the relation between these two definitions? that is between the usual definition (Definition 1) we always use and the definition we give in the present paper (Definition 2) saying that that definition should actually be the correct one? The present paper gives the related answer.