Korean J. Math. Vol. 28 No. 1 (2020) pp.89-104
DOI: https://doi.org/10.11568/kjm.2020.28.1.89

On $KU$-Algebras containing $(\alpha, \beta)$-US soft sets

Main Article Content

Moin A. Ansari
Ali N. A. Koam
Azeem Haider


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

Article Details


[1] H. Aktas and Cagmass N, soft sets and soft groups, Inf. Sci. 177 (13) (2007), 2726–2735. Google Scholar

[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). Google Scholar

[3] Muhammad Gulistan and Muhammad Shahzad, Soft KU-algebras, Journal of Algebra, Number Theory: Advances and Applications 11 (1) (2014), pg 1–20. Google Scholar

[4] Mohammad Gulistan, Mohammad Shahzad, and Sarfaraz A., On (α,β) fuzzy KU-ideals of KU-algebras, Afrika Matematika 26 (2015), 651–661. Google Scholar

[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. Google Scholar

[6] Chiranjibe Jana and Madhumangal Pal, On (α, β)-US sets in BCK/BCI-Algebras, Mathematics 7 (3) (2019), 252. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[10] D. Molodotsov, Soft Set Theory-First Results, Computers and Mathematics with Applications 37 (1999), 19–31. Google Scholar

[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. Google Scholar

[12] Cagman N. and Enginoglu S. Soft set theory and uni-int decision making, Eur. J. Oper. Res. 207 (2010), 848–855. Google Scholar

[13] C. Prabpayak and U. Leerawat, On ideals and congruences in KU-algebras, Scientia Magna J. 5 (1) (2009), 54–57. Google Scholar

[14] C. Prabpayak and U. Leerawat, On isomorphism of KU-algebras, Scientia Magna J. 5 (3) (2009), 25–31. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar