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The Scientific World Journal
Volume 2014, Article ID 197403, 7 pages
Research Article

Vague Congruences and Quotient Lattice Implication Algebras

Xiaoyan Qin,1,2 Yi Liu,1,3 and Yang Xu1

1Intelligent Control Development Center, Southwest Jiaotong University, Chengdu, Sichuan 610031, China
2College of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, China
3Key Laboratory of Numerical Simulation, Sichuan Provincial College, Neijiang Normal University, Neijiang, Sichuan 641000, China

Received 24 April 2014; Accepted 24 June 2014; Published 14 July 2014

Academic Editor: Young B. Jun

Copyright © 2014 Xiaoyan Qin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.