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Journal of Applied Mathematics
Volume 2013, Article ID 853907, 9 pages
http://dx.doi.org/10.1155/2013/853907
Research Article

Positive Implicative Ideals of BCK-Algebras Based on Intersectional Soft Sets

1Department of Mathematics Education, Chinju National University of Education, Jinju 660-756, Republic of Korea
2Department of Mathematics Education (and RINS), Gyeongsang National University, Jinju 660-701, Republic of Korea

Received 14 September 2012; Revised 17 March 2013; Accepted 8 May 2013

Academic Editor: Mina Abd-El-Malek

Copyright © 2013 Eun Hwan Roh and Young Bae Jun. 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

The aim of this paper is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of int-soft positive implicative ideals is introduced, and related properties are investigated. Relations between an int-soft ideal and an int-soft positive implicative ideal are established. Characterizations of an int-soft positive implicative ideal are obtained. Extension property for an int-soft positive implicative ideal is constructed. The -product and -product of int-soft positive implicative ideals are considered, and the soft intersection (resp., union) of int-soft positive implicative ideals is discussed.