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The Scientific World Journal
Volume 2014, Article ID 951796, 11 pages
http://dx.doi.org/10.1155/2014/951796
Research Article

Characterizations of MV-Algebras Based on the Theory of Falling Shadows

1School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China
2School of Mathematics, Northwest University, Xi’an 710127, China

Received 24 June 2014; Accepted 28 July 2014; Published 28 August 2014

Academic Editor: Hee S. Kim

Copyright © 2014 Yongwei Yang 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.

Abstract

Based on the falling shadow theory, the concept of falling fuzzy (implicative) ideals as a generalization of that of a -fuzzy (implicative) ideal is proposed in MV-algebras. The relationships between falling fuzzy (implicative) ideals and -fuzzy (implicative) ideals are discussed, and conditions for a falling fuzzy (implicative) ideal to be a -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 -fuzzy ideals are investigated based on probability spaces.