title: Vague congruences and quotient lattice implication algebras.
abstract: The aim of this paper is to further develop the congruence theory on lattice implication algebras. Firstly, we introduce the notions of vague similarity relations based on vague relations and vague congruence relations. Secondly, the equivalent characterizations of vague congruence relations are investigated. Thirdly, the relation between the set of vague filters and the set of vague congruences is studied. Finally, we construct a new lattice implication algebra induced by a vague congruence, and the homomorphism theorem is given.
authors.affiliation: Intelligent Control Development Center, Southwest Jiaotong University, Chengdu, Sichuan 610031, China ; College of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, China.
authors.forename: Xiaoyan
authors.initials: X
authors.lastname: Qin
authors.affiliation: Intelligent Control Development Center, Southwest Jiaotong University, Chengdu, Sichuan 610031, China ; Key Laboratory of Numerical Simulation, Sichuan Provincial College, Neijiang Normal University, Neijiang, Sichuan 641000, China.
authors.forename: Yi
authors.identifier: 0000-0001-5304-235X
authors.initials: Y
authors.lastname: Liu
authors.affiliation: Intelligent Control Development Center, Southwest Jiaotong University, Chengdu, Sichuan 610031, China.
authors.forename: Yang
authors.initials: Y
authors.lastname: Xu
mesh_terms: D055641:Mathematical Concepts