Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지
DOI QR코드

DOI QR Code

ON KU-ALGEBRAS CONTAINING (α, β)-US SOFT SETS

  • Ansari, Moin A. (Department of Mathematics, College of Science, Post Box 2097 New Campus, Jazan University) ;
  • Koam, Ali N.A. (Department of Mathematics, College of Science, Post Box 2097 New Campus, Jazan University) ;
  • Haider, Azeem (Department of Mathematics, College of Science, Post Box 2097 New Campus, Jazan University)
  • Received : 2019.11.21
  • Accepted : 2020.03.03
  • Published : 2020.03.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we connect (α, β) union soft sets and their ideal related properties with KU-algebras. In particular, we will study (α, β)-union soft sets, (α, β)-union soft ideals, (α, β)-union soft commutative ideals and ideal relations in KU-algebras. Finally, a characterization of ideals in KU-algebras in terms of (α, β)-union soft sets have been provided.

Keywords

References

  1. H. Aktas and Cagmass N, soft sets and soft groups, Inf. Sci. 177 (13) (2007), 2726-2735. https://doi.org/10.1016/j.ins.2006.12.008
  2. Moin A. Ansari and Ali N. A. Koam, Rough approximations in KU-algebras, Italian Journal of Pure and Applied Mathematics, N. 40-2018 (679-691).
  3. Muhammad Gulistan and Muhammad Shahzad, Soft KU-algebras, Journal of Algebra, Number Theory: Advances and Applications 11 (1) (2014), pg 1-20.
  4. Mohammad Gulistan, Mohammad Shahzad, and Sarfaraz A., On (${\alpha},{\beta}$) fuzzy KU-ideals of KU-algebras, Afrika Matematika 26 (2015), 651-661. https://doi.org/10.1007/s13370-014-0234-2
  5. Y. B. Jun, KyoungJa Lee and Min Su Kang, Ideal theory in BCK/BCI-algebras based on soft sets and N-structures, Discrete Dynamics in Nature and Society, Volume 2012, Article ID 910450, 13 pages.
  6. Chiranjibe Jana and Madhumangal Pal, On (${\alpha},{\beta}$)-US sets in BCK/BCI-Algebras, Mathematics 7 (3) (2019), 252. https://doi.org/10.3390/math7030252
  7. Ali N. A. Koam, Azeem Haider and Moin A. Ansari, Pseudo-metric on KU-algebras, The Korean J. Math. 27 (1) (2019), 131-140. https://doi.org/10.11568/KJM.2019.27.1.131
  8. Ali N. A. Koam, Moin A. Ansari and Azeem Haider, n-ary block codes related to KU-algebras, Journal of Taibah University for Science 14 (1) (2020), 172-176. https://doi.org/10.1080/16583655.2020.1713585
  9. P. K. Maji, R. Biswas and A. R. Roy, An application of soft sets in a decision making problems, Computers and Mathematics with applications 44 (2002), 1077-1083. https://doi.org/10.1016/S0898-1221(02)00216-X
  10. D. Molodotsov, Soft Set Theory-First Results, Computers and Mathematics with Applications 37 (1999), 19-31. https://doi.org/10.1016/S0898-1221(99)00056-5
  11. S. M. Mostafa, M.A. Abd-Elnaby and M.M.M. Yousef, Fuzzy ideals of KU-Algebras, Int. Math. Forum. 6 (63), (2011), 3139-3149.
  12. Cagman N. and Enginoglu S. Soft set theory and uni-int decision making, Eur. J. Oper. Res. 207 (2010), 848-855. https://doi.org/10.1016/j.ejor.2010.05.004
  13. C. Prabpayak and U. Leerawat, On ideals and congruences in KU-algebras, Scientia Magna J. 5 (1) (2009), 54-57.
  14. C. Prabpayak and U. Leerawat, On isomorphism of KU-algebras, Scientia Magna J. 5 (3) (2009), 25-31.
  15. Daneshpayeh, Roohallah, Arsham Saeid Borumand and Saeed Mirvakili, A representation for radicals in pseudo BL-algebras, Journal of Intelligent & Fuzzy Systems 36 (2) (2019), 1443-1454. https://doi.org/10.3233/JIFS-181039
  16. Tapan Senapati, and K.P. Shum, Atanassov's intuitionistic fuzzy bi-normed KU-ideals of a KU-algebra, Journal of Intelligent & Fuzzy Systems 30 (2016), 1169-1180. https://doi.org/10.3233/IFS-151841
  17. Xi Y., Liao Z.H. and Chen X.M., A new type of soft ideal of KU-algebras, Fuzzy Syst. Math. 31 (2) (2017), 13-21.
  18. Yue Xi., Zu-hua Liao, Xiao-hao, Xin-meng chen, wei Song, Shu-zhong Wu, Yong Li, A new type of soft prime ideals of KU-algebras, ICFIE 2017: Fuzzy sets and Operation Research pp 81-90.
  19. Xiaohong Zhang, Choonkil Park and Supeng Wu, Soft set theoretical approach to pseudo-BCI algebras, Journal of Intelligent & Fuzzy Systems 34 (1) (2018), 559-568. https://doi.org/10.3233/JIFS-17777