On ( ?, ? )-US Sets in BCK / BCI -Algebras

Chiranjibe Jana and Madhumangal Pal
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Chiranjibe Jana: Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, India
Madhumangal Pal: Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, India

Mathematics, 2019, vol. 7, issue 3, 1-18

Abstract: Molodtsov originated soft set theory, which followed a general mathematical framework for handling uncertainties, in which we encounter the data by affixing the parameterized factor during the information analysis. The aim of this paper is to establish a bridge to connect a soft set and the union operations on sets, then applying it to B C K / B C I -algebras. Firstly, we introduce the notion of the ( α , β ) -Union-Soft ( ( α , β ) -US) set, with some supporting examples. Then, we discuss the soft B C K / B C I -algebras, which are called ( α , β ) -US algebras, ( α , β ) -US ideals, ( α , β ) -US closed ideals, and ( α , β ) -US commutative ideals. In particular, some related properties and relationships of the above algebraic structures are investigated. We also provide the condition of an ( α , β ) -US ideal to be an ( α , β ) -US closed ideal. Some conditions for a Union-Soft (US) ideal to be a US commutative ideal are given by means of ( α , β ) -unions. Moreover, several characterization theorems of (closed) US ideals and US commutative ideals are given in terms of ( α , β ) -unions. Finally, the extension property for an ( α , β ) -US commutative ideal is established.

Keywords: BCK/BCI-algebra; ( ? , ? )-US set; ( ? , ? )-US subalgebra; ( ? , ? )-US (closed) ideal; ( ? , ? )-US commutative ideal (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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