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Applications of double-framed soft ideals in BE-algebras

Year 2016, Volume: 4 Issue: 2, 285 - 295, 01.03.2016

Abstract

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.


References

  • 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.
Year 2016, Volume: 4 Issue: 2, 285 - 295, 01.03.2016

Abstract

References

  • 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.
There are 18 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Khizar Hayat

Bing-yuan Cao This is me

Tahir Mahmood This is me

Kalim Ul-haq Tariq This is me

Publication Date March 1, 2016
Published in Issue Year 2016 Volume: 4 Issue: 2

Cite

APA Hayat, K., Cao, B.-y., Mahmood, T., Tariq, K. U.-h. (2016). Applications of double-framed soft ideals in BE-algebras. New Trends in Mathematical Sciences, 4(2), 285-295.
AMA Hayat K, Cao By, Mahmood T, Tariq KUh. Applications of double-framed soft ideals in BE-algebras. New Trends in Mathematical Sciences. March 2016;4(2):285-295.
Chicago Hayat, Khizar, Bing-yuan Cao, Tahir Mahmood, and Kalim Ul-haq Tariq. “Applications of Double-Framed Soft Ideals in BE-Algebras”. New Trends in Mathematical Sciences 4, no. 2 (March 2016): 285-95.
EndNote Hayat K, Cao B-y, Mahmood T, Tariq KU-h (March 1, 2016) Applications of double-framed soft ideals in BE-algebras. New Trends in Mathematical Sciences 4 2 285–295.
IEEE K. Hayat, B.-y. Cao, T. Mahmood, and K. U.-h. Tariq, “Applications of double-framed soft ideals in BE-algebras”, New Trends in Mathematical Sciences, vol. 4, no. 2, pp. 285–295, 2016.
ISNAD Hayat, Khizar et al. “Applications of Double-Framed Soft Ideals in BE-Algebras”. New Trends in Mathematical Sciences 4/2 (March 2016), 285-295.
JAMA Hayat K, Cao B-y, Mahmood T, Tariq KU-h. Applications of double-framed soft ideals in BE-algebras. New Trends in Mathematical Sciences. 2016;4:285–295.
MLA Hayat, Khizar et al. “Applications of Double-Framed Soft Ideals in BE-Algebras”. New Trends in Mathematical Sciences, vol. 4, no. 2, 2016, pp. 285-9.
Vancouver Hayat K, Cao B-y, Mahmood T, Tariq KU-h. Applications of double-framed soft ideals in BE-algebras. New Trends in Mathematical Sciences. 2016;4(2):285-9.