• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1937-1956
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• 2013

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.

• Honam Mathematical Journal
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• v.40 no.3
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• pp.377-389
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• 2018

The notion of a uni-soft commutative ideal with thresholds is introduced, and related properties are investigated. Relations between a uni-soft ideal with thresholds and a uni-soft commutative ideal with thresholds are discussed. Conditions for a uni-soft ideal with thresholds to be a uni-soft commutative ideal with the same thresholds are provided. Characterizations of a uni-soft commutative ideal with thresholds are established.

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.361-369
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• 2017

A characterization of int-soft ideal is considered, and an int-soft ideal generated by a soft set is discussed. A new int-soft ideal from old one is constructed.

• The Pure and Applied Mathematics
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• v.21 no.2
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• pp.105-112
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• 2014

The notion of intersection-soft ideal of CI-algebras is introduced, and related properties are investigated. A characterization of an intersection-soft ideal is provided, and a new intersection-soft ideal from the old one is established.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.339-348
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• 2015

Using the notion of soft sets, the concepts of the soft transfer, support and soft algebraic extension of an int-soft subalgebra and ideal in BCK/BCI-algebras are introduced, and related properties are investigated. Conditions for a soft set to be an int-soft subalgebra and ideal are provided. Regarding the notion of support, conditions for the soft transfer of a soft set to be an int-soft subalgebra and ideal are considered.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.335-349
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• 2009

Soft set theory by Molodtsov is applied to ideals in BCC-algebras. The notion of soft BCC-ideals of soft BCC-algebras and idealistic soft BCC-algebras are introduced, and several examples are provided. Relations between a fuzzy BCC-ideal and an idealistic soft BCC-algebra are given, and the characterization of idealistic soft BCC-algebras is established.

• Annals of Fuzzy Mathematics and Informatics
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• v.16 no.3
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• pp.317-331
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• 2018

This paper aims to extend the notion of hesitant fuzzy sets on UP-algebras to hesitant fuzzy soft sets over UP-algebras by merging the notions of hesitant fuzzy sets and soft sets. Further, we discuss the notions of hesitant fuzzy soft strongly UP-ideals, hesitant fuzzy soft UP-ideals, hesitant fuzzy soft UP-filters, and hesitant fuzzy soft UP-subalgebras of UP-algebras, and provide some properties.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.671-686
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• 2015

The notion of soft α-ideals and α-idealistic soft BCI-algebras is introduced and their basic properties are discussed. Relations between soft ideals and soft α-ideals of soft BCI-algebras are provided. Also idealistic soft BCI-algebras and α-idealistic soft BCI-algebras are being related. The restricted intersection, union, restricted union, restricted difference and "AND" operation of soft α-ideals and α-idealistic soft BCI-algebras are established. The characterizations of (fuzzy) α-ideals in BCI-algebras are given by using the concept of soft sets. Relations between fuzzy α-ideals and α-idealistic soft BCI-algebras are discussed.

• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.183-196
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• 2011

Molodtsov [5] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to an implicative ideal of BCK-algebras. The notion of implicative soft ideals in BCK-algebras and implicative idealistic soft BCK-algebras is introduced, and related properties are investigated. Relations between implicative soft ideals and commutative (resp. positive implicative) soft ideals are discussed. Also, relations between implicative idealistic soft BCK-algebras and commutative (resp. positive implicative) idealistic soft BCK-algebras are provided.

• Korean Journal of Mathematics
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• v.28 no.1
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• pp.89-104
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• 2020

In this paper, we connect (α, β) union soft sets and their ideal related properties with KU-algebras. In particular, we will study (α, β)-union soft sets, (α, β)-union soft ideals, (α, β)-union soft commutative ideals and ideal relations in KU-algebras. Finally, a characterization of ideals in KU-algebras in terms of (α, β)-union soft sets have been provided.