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

Author

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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)

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.

Suggested Citation

  • Chiranjibe Jana & Madhumangal Pal, 2019. "On ( α , β )-US Sets in BCK / BCI -Algebras," Mathematics, MDPI, vol. 7(3), pages 1-18, March.
  • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:252-:d:212822
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    References listed on IDEAS

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    1. Çagman, Naim & Enginoglu, Serdar, 2010. "Soft set theory and uni-int decision making," European Journal of Operational Research, Elsevier, vol. 207(2), pages 848-855, December.
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