title: The interaction between fuzzy subsets and groupoids.
abstract: We discuss properties of a class of real-valued functions on a set X (2) constructed as finite (real) linear combinations of functions denoted as [(X, ∗); μ ], where (X, ∗) is a groupoid (binary system) and μ is a fuzzy subset of X and where [(X, ∗); μ ](x, y): = μ (x ∗ y) - min{μ (x), μ (y)}. Many properties, for example, μ being a fuzzy subgroupoid of X, ∗), can be restated as some properties of [(X, ∗); μ]. Thus, the context provided opens up ways to consider well-known concepts in a new light, with new ways to prove known results as well as to provide new questions and new results. Among these are identifications of many subsemigroups and left ideals of (Bin(X), □) for example.
authors.affiliation: Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA.
authors.forename: Seung Joon
authors.initials: SJ
authors.lastname: Shin
authors.affiliation: Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Republic of Korea.
authors.forename: Hee Sik
authors.identifier: 0000-0001-5321-5919
authors.initials: HS
authors.lastname: Kim
authors.affiliation: Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA.
authors.forename: J
authors.initials: J
authors.lastname: Neggers
mesh_terms: D017143:Fuzzy Logic; D008962:Models, Theoretical