On (α,β)-US Sets in BCK/BCI-Algebras
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, India
Author to whom correspondence should be addressed.
Received: 26 January 2019 / Revised: 4 March 2019 / Accepted: 6 March 2019 / Published: 11 March 2019
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
-algebras. Firstly, we introduce the notion of the
-US) set, with some supporting examples. Then, we discuss the soft
-algebras, which are called
-US closed ideals, and
-US commutative ideals. In particular, some related properties and relationships of the above algebraic structures are investigated. We also provide the condition of an
-US ideal to be an
-US closed ideal. Some conditions for a Union-Soft (US) ideal to be a US commutative ideal are given by means of
-unions. Moreover, several characterization theorems of (closed) US ideals and US commutative ideals are given in terms of
-unions. Finally, the extension property for an
-US commutative ideal is established.
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MDPI and ACS Style
Jana, C.; Pal, M. On (α,β)-US Sets in BCK/BCI-Algebras. Mathematics 2019, 7, 252.
Jana C, Pal M. On (α,β)-US Sets in BCK/BCI-Algebras. Mathematics. 2019; 7(3):252.
Jana, Chiranjibe; Pal, Madhumangal. 2019. "On (α,β)-US Sets in BCK/BCI-Algebras." Mathematics 7, no. 3: 252.
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