title: Concave soft sets, critical soft points, and union-soft ideals of ordered semigroups.
abstract: The notions of union-soft semigroups, union-soft l-ideals, and union-soft r-ideals are introduced, and related properties are investigated. Characterizations of a union-soft semigroup, a union-soft l-ideal, and a union-soft r-ideal are provided. The concepts of union-soft products and union-soft semiprime soft sets are introduced, and their properties related to union-soft l-ideals and union-soft r-ideals are investigated. Using the notions of union-soft l-ideals and union-soft r-ideals, conditions for an ordered semigroup to be regular are considered. The concepts of concave soft sets and critical soft points are introduced, and their properties are discussed.
authors.affiliation: Department of Mathematics Education, Gyeongsang National University, Jinju 660-701, Republic of Korea.
authors.forename: Young Bae
authors.initials: YB
authors.lastname: Jun
authors.affiliation: Department of Mathematics, Jeju National University, Jeju 690-756, Republic of Korea.
authors.forename: Seok Zun
authors.initials: SZ
authors.lastname: Song
authors.affiliation: Department of Mathematics, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia.
authors.forename: G
authors.identifier: 0000-0002-5596-5841
authors.initials: G
authors.lastname: Muhiuddin
mesh_terms: D017143:Fuzzy Logic; D015233:Models, Statistical; D035501:Uncertainty