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      Soft Translations and Soft Extensions of BCI/BCK-Algebras

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          Abstract

          The concept of soft translations of soft subalgebras and soft ideals over BCI/BCK-algebras is introduced and some related properties are studied. Notions of Soft extensions of soft subalgebras and soft ideals over BCI/BCK-algebras are also initiated. Relationships between soft translations and soft extensions are explored.

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          Most cited references48

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          A note on soft sets, rough soft sets and fuzzy soft sets

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            On axiom systems of propositional calculi, XIV

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              Subalgebras of BCK/BCI-Algebras Based on Cubic Soft Sets

              Operations of cubic soft sets including “AND” operation and “OR” operation based on P-orders and R-orders are introduced and some related properties are investigated. An example is presented to show that the R-union of two internal cubic soft sets might not be internal. A sufficient condition is provided, which ensure that the R-union of two internal cubic soft sets is also internal. Moreover, some properties of cubic soft subalgebras of BCK/BCI-algebras based on a given parameter are discussed.
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                Author and article information

                Journal
                ScientificWorldJournal
                ScientificWorldJournal
                TSWJ
                The Scientific World Journal
                Hindawi Publishing Corporation
                2356-6140
                1537-744X
                2014
                14 September 2014
                : 2014
                : 536709
                Affiliations
                1Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
                2Department of Mathematics, University of Sargodha, Women Campus, Faisalabad, Pakistan
                3Islamabad Model College for Girls F-6/2, Islamabad 44000, Pakistan
                Author notes

                Academic Editor: Feng Feng

                Author information
                http://orcid.org/0000-0003-4501-9269
                Article
                10.1155/2014/536709
                4179941
                e38adb47-227e-4908-9adf-919a4e1bce1c
                Copyright © 2014 Nazra Sultana et al.

                This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                History
                : 12 June 2014
                : 8 August 2014
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