Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2013; 50(6): 1937-1956

Printed November 1, 2013

https://doi.org/10.4134/BKMS.2013.50.6.1937

Copyright © The Korean Mathematical Society.

Union-soft sets with applications in $BCK/BCI$-algebras

Young Bae Jun

Gyeongsang National University

Abstract

The aim of this article 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 union-soft sets is introduced, and its application to $BCK/BCI$-algebras is considered. The notions of union-soft algebras, union-soft (commutative) ideals and closed union-soft ideals are introduced, and related properties and relations are investigated. Conditions for a union-soft ideal to be closed are provided. Conditions for a union-soft ideal to be a union-soft commutative ideal are also provided. Characterizations of (closed) union-soft ideals and union-soft commutative ideals are established. Extension property for a union-soft commutative ideal is established.

Keywords: exclusive set, union-soft algebra, (closed) union-soft ideal, union-soft commutative ideal

MSC numbers: 06F35, 03G25, 06D72

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