title: Characterizations of MV-algebras based on the theory of falling shadows.
abstract: Based on the falling shadow theory, the concept of falling fuzzy (implicative) ideals as a generalization of that of a T ∧-fuzzy (implicative) ideal is proposed in MV-algebras. The relationships between falling fuzzy (implicative) ideals and T-fuzzy (implicative) ideals are discussed, and conditions for a falling fuzzy (implicative) ideal to be a T ∧-fuzzy (implicative) ideal are provided. Some characterizations of falling fuzzy (implicative) ideals are presented by studying proprieties of them. The product ⊛ and the up product ⊚ operations on falling shadows and the upset of a falling shadow are established, by which T-fuzzy ideals are investigated based on probability spaces.
authors.affiliation: School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China ; School of Mathematics, Northwest University, Xi'an 710127, China.
authors.forename: Yongwei
authors.initials: Y
authors.lastname: Yang
authors.affiliation: School of Mathematics, Northwest University, Xi'an 710127, China.
authors.forename: Xiaolong
authors.initials: X
authors.lastname: Xin
authors.affiliation: School of Mathematics, Northwest University, Xi'an 710127, China.
authors.forename: Pengfei
authors.initials: P
authors.lastname: He
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D017143:Fuzzy Logic; D008432:Mathematical Computing; D008433:Mathematics / Q000379:methods; D008962:Models, Theoretical