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The Scientific World Journal
Volume 2014, Article ID 542846, 9 pages
Research Article

Roughness in Lattice Ordered Effect Algebras

1Department of Mathematics, Northwest University, Xi’an 710127, China
2Faculty of Science, Xi’an University of Technology, Xi’an 710048, China
3Department of Basic Courses, Xi’an Aeronautical University, Xi’an 710048, China

Received 4 February 2014; Revised 1 July 2014; Accepted 2 July 2014; Published 24 July 2014

Academic Editor: Bijan Davvaz

Copyright © 2014 Xiao Long Xin 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.


Many authors have studied roughness on various algebraic systems. In this paper, we consider a lattice ordered effect algebra and discuss its roughness in this context. Moreover, we introduce the notions of the interior and the closure of a subset and give some of their properties in effect algebras. Finally, we use a Riesz ideal induced congruence and define a function in a lattice ordered effect algebra and build a relationship between it and congruence classes. Then we study some properties about approximation of lattice ordered effect algebras.