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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 178159, 15 pages
http://dx.doi.org/10.1155/2012/178159
Research Article

Double-Framed Soft Sets with Applications in BCK/BCI-Algebras

1Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea
2Department of Mathematics Education, Dongguk University, Seoul 100-715, Republic of Korea

Received 26 August 2012; Revised 23 October 2012; Accepted 23 October 2012

Academic Editor: Morteza Rafei

Copyright © 2012 Young Bae Jun and Sun Shin Ahn. 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

In order to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties, the notion of double-framed soft sets is introduced, and applications in BCK/BCI-algebras are discussed. The notions of double-framed soft algebras in BCK/BCI-algebras are introduced, and related properties are investigated. Characterizations of double-framed soft algebras are considered. Product and int-uni structure of double-framed soft algebras are discussed, and several examples are provided.