Applications of double-framed soft ideals in BE-algebras

Yıl 2016, Cilt: 4 Sayı: 2, 285 - 295, 01.03.2016

Khizar Hayat , Bing-yuan Cao Tahir Mahmood Kalim Ul-haq Tariq

Öz

In this study, the notion of a double-framed soft ideal (DFS-ideal) in BE-algebras is introduced and discussed related properties by means of R-inclusive set and S-exclusive set. We presented DFS-int-uni ideal of two DFS-ideals in BE-algebras. We characterized the properties of the image and pre-image of DFS-ideals by homomorphism of BE-algebras.

Anahtar Kelimeler

BE-Algebra, soft set, DFS-set, DFS-ideals, R-inclusive set

Kaynakça

• D. Molodtsov, Soft set theory-first results. Computers and Mathematics with Applications, 37 (1999), 19-31.
• P. K. Maji, R. Biswas, A. R. Roy, Soft set theory. Comput. Math. Appl. 45 (2003) 555-562.
• H. Aktas, N. Cagman, Soft sets and soft groups. Inform. Sci. 177 (2007) 2726-2735.
• A. Sezgin, A. O. Atagun, N. Cagman, Union soft substructures of near-rings and N-groups. Neural Comput. & Applic. 20 (2012) 133-143.
• N. Cagman, F. Citak, H. Aktas, Soft int-group and its applications to group theory. Neural Comput. & Applic. 21 (2012) 151-158.
• M. I. Ali, F. Feng, X. Liu, W. K. Min, M. Shabir, On some new operations in soft set theory. Comput. Math. Appl. 57 (2009) 1547-1553.
• H. S. Kim and Y. H. Kim, “On BE-algebras,” Scientiae Mathematicae Japonicae, 66 (2007), 113–116.
• A. Rezaei, and A. B. Saeid, Commutative ideals in BE-algebras. Kyungpook Math. J. 52 (2012), 483-494.
• A. Rezaei, A. B. Saeid, and R. A. Borzooei, Relation between Hilbert algebras and BE-algebras. Appl. Appl. Math. 8 (2013), 573-584.
• S. S. Ahn and K. S. So, On ideals and upper sets in BE-algebras, Sci. Math. Jpn. 68 (2008) 279–285.
• S. S. Ahn, Y. H. Kim and K. S. So, Fuzzy BE-algebras, J. Appl. Math. & Informatics, 29 (2011), 1049 - 1057.
• Y. B. Jun, K. J. Lee and S. Z. Song. Fuzzy ideals in BE-algebra, Bull. Malays. Math. Sci. Soc. 33 (2010) 147–153.
• Y. B. Jun, and S. S. Ahn, Applications of soft sets in BE-algebras, Hind. Pub. Corp. Algebra, (2013), Article ID 368962, 1-8.
• A. R. Hadipour, Double-framed soft BF-algebras, Indian J. of Sci. and Tech., 7 (2014) 491–496.
• Y. B. Jun and S. S. Ahn, Double-framed soft sets with applications in BCK/BCI-algebras, J. Appl. Math., 2012, Article ID 178159, 1-15.
• S. Abdullaha, A. F. Ali, Applications of N-structures in implicative filters of BE-algebras, J. of Int. & Fuzzy Syst. 29 (2015) 517–524.
• K. Hayat, T.Mahmood, Some Applications of Bipolar Soft Set: Characterizations of Two Isomorphic Hemi-Rings via BSI-h-Ideals, BJMCS, 13 (2016) 1-22.
• Y. B. Jun, Soft BCK/BCI-algebras, Comp. Math, with Appli., 56 (2008) 1408–1413.