Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 910450, 13 pages
http://dx.doi.org/10.1155/2012/910450
Research Article

Ideal Theory in BCK/BCI-Algebras Based on Soft Sets and 𝒩 -Structures

Young Bae Jun,1 Kyoung Ja Lee,2 and Min Su Kang3

1Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea
2Department of Mathematics Education, Hannam University, Daejeon 306-791, Republic of Korea
3Department of Mathematics, Hanyang University, Seoul 133-791, Republic of Korea

Received 14 December 2011; Accepted 1 February 2012

Academic Editor: Lee-Chae Jang

Copyright © 2012 Young Bae Jun 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 soft sets and 𝒩 -structures, the notion of (closed) 𝒩 -ideal over a BCI-algebra is introduced, and related properties are investigated. Relations between 𝒩 -BCI-algebras and 𝒩 -ideals are established. Characterizations of a (closed) 𝒩 -ideal over a BCI-algebra are provided. Conditions for an 𝒩 -ideal to be an 𝒩 -BCI-algebra are considered.