Ideal theory of BCK/BCI-algebras based on hybrid structures

Volume 23, Issue 2, pp 136--144 http://dx.doi.org/10.22436/jmcs.023.02.06

Publication Date: October 22, 2020 Submission Date: June 28, 2020 Revision Date: September 20, 2020 Accteptance Date: September 24, 2020

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Authors

G. Muhiuddin - Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia. D. Al-Kadi - Department of Mathematics and Statistic, Taif University, Taif 21974, Saudi Arabia. Ahsan Mahboob - Department of Mathematics, Madanapalle Institute of Technology (\&) Science, Madanapalle-517325, India.

Abstract

In this paper, the concept of hybrid ideals in BCK/BCI-algebras is introduced, and related properties are investigated. Further, it is proved that every hybrid ideal is hybrid sub-algebra in BCK/BCI-algebras, but the converse is not valid in general, and an example is provided in this regard. Some characterizations of hybrid ideals in BCK/BCI-algebras are given. Moreover, the notion of hybrid closed ideals in BCI-algebras is introduced, and some associated properties are studied. Furthermore, the hybrid intersection and hybrid union are also discussed.

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Keywords

• BCK/BCI-algebras
• hybrid sub-algebra
• hybrid ideal
• hybrid closed ideal

MSC

•  03E72
•  03G25
•  06F35
•  08A72
•  16D25
•  94D05

References

• [1] U. Acar, F. Koyuncu, B. Tanay, Soft sets and soft rings, Comput. Math. Appl., 59 (2010), 3458--3463
  • View Article
  • MathSciNet


• [2] A. Al-Masarwah, A. G. Ahmad, Novel concepts of doubt bipolar fuzzy H-ideals of BCK/BCI-algebras, Int. J. Innov. Comput. Inf. Control, 14 (2018), 2025--2041
  • Google Scholar


• [3] A. Al-Masarwah, A. G. Ahmad, On some properties of doubt bipolar fuzzy H-ideals in BCK/BCI-algebras, Eur. J. Pure Appl. Math., 11 (2018), 652--670
  • View Article
  • Google Scholar


• [4] A. Al-Masarwah, A. G. Ahmad, m-polar fuzzy ideals of BCK/BCI-algebras, J. King Saud Univ. Sci., 31 (2019), 1220--1226
  • View Article
  • Google Scholar


• [5] A. Al-Masarwah, A. G. Ahmad, A new form of generalized m-PF Ideals in BCK/BCI-algebras, Ann. Commun. Math., 2 (2019), 11--16
  • Google Scholar


• [6] A. Al-Masarwah, A. G. Ahmad, G. Muhiuddin, Doubt N-ideals theory in BCK-algebras based on N-structures, Ann. Commun. Math., 3 (2020), 54--62
  • View Article
  • Google Scholar


• [7] H. Aktaş, N. Çağman, Soft sets and soft groups, Inf. Sci., 177 (2007), 2726--2735
  • View Article
  • MathSciNet
  • Google Scholar


• [8] S. Anis, M. Khan, Y. B. Jun, Hybrid ideals in semigroups, Cogent Math., 4 (2017), 12 pages
  • View Article
  • MathSciNet


• [9] A. O. Atagün, A. Sezgin, Soft substructures of rings, fields and modules, Comput. Math. Appl., 61 (2011), 592--601
  • View Article
  • Google Scholar


• [10] N. Çağman, S. Enginoğlu, Soft set theory and uni-int decision making, Eur. J. Oper. Res., 207 (2010), 848--855
  • View Article
  • Google Scholar


• [11] N. Çağman, S. Enginoğlu, Soft matrix theory and its decision making, Comput. Math. Appl., 59 (2010), 3308--3314
  • View Article
  • Google Scholar


• [12] B. Elavarasan, Y. B. Jun, Regularity of semigroups in terms of hybrid ideals and hybrid bi-ideals, Kragujev. J. Math., 46 (2022), 857--564
  • View Article
  • Google Scholar


• [13] B. Elavarasan, K. Porselvi, Y. B. Jun, Hybrid generalized bi-ideals in semigroups, Int. J. Math. Comput. Sci., 14 (2019), 601--612
  • View Article
  • MathSciNet


• [14] F. Feng, Y. B. Jun, X. Zhao, Soft semirings, Comput. Math. Appl., 56 (2008), 2621--2628
  • View Article
  • MathSciNet


• [15] Y. Huang, BCI-algebra, Science Press, Beijing (2006)
  • Google Scholar


• [16] Y. Imai, K. Iséki, On Axiom Systems of Propositional Calculi. XIV, Proc. Japan Acad., 42 (1966), 19--22
  • View Article
  • MathSciNet
  • Google Scholar


• [17] K. Iséki, An algebra related with a propositional calculus, Proc. Japan Acad., 42 (1966), 26--29
  • View Article
  • MathSciNet


• [18] Y. B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl., 56 (2008), 1408--1413
  • View Article
  • MathSciNet


• [19] Y. B. Jun, K. J. Lee, A. Khan, Soft ordered semigroups, Math. Log. Q., 56 (2010), 42--50
  • View Article
  • MathSciNet


• [20] Y. B. Jun, K. J. Lee, C. H. Park, Soft set theory applied to ideals in d-algebras, Comput. Math. Appl., 57 (2009), 367--378
  • View Article
  • MathSciNet


• [21] Y. B. Jun, K. J. Lee, J. Zhan, Soft p-ideals of soft BCI-algebras, Comput. Math. Appl., 58 (2009), 2060--2068
  • View Article
  • MathSciNet


• [22] Y. B. Jun, G. Muhiuddin, M. A. Ozturk, E. H. Roh, Cubic soft ideals in BCK/BCI-algebras, J. Comput. Anal. Appl., 22 (2017), 929--940
  • View Article
  • MathSciNet
  • Google Scholar


• [23] Y. B. Jun, C. H. Park, Applications of soft sets in ideal theory of BCK/BCI-algebras, Inf. Sci., 178 (2008), 2466--2475
  • View Article
  • MathSciNet


• [24] Y. B. Jun, S.-Z. Song, G. Muhiuddin, Hybrid structures and applications, Ann. Commun. Math., 1 (2018), 11--25
  • View Article


• [25] K.-T. Kang, S.-Z. Song, E. H. Roh, Y. B. Jun, Hybrid Ideals of BCK/BCI-Algebras, Axioms, 9 (2020), 11 pages
  • View Article
  • Google Scholar


• [26] P. K. Maji, A. R. Roy, R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl., 44 (2002), 1077--1083
  • View Article
  • MathSciNet


• [27] J. Meng, Y. B. Jun, BCK-algebras, Kyungmoon Sa Co., Seoul (1994)
  • Google Scholar


• [28] D. Molodtsov, Soft set theory--First results, Comput. Math. Appl., 37 (1999), 19--31
  • View Article
  • MathSciNet


• [29] D. A. Molodtsov, The description of a dependence with the help of soft sets, J. Comput. Sys. Sc. Int., 40 (2001), 977--984
  • Google Scholar


• [30] D. Molodtsov, The theory of soft sets, URSS publishers, Moscow (2004)
  • Google Scholar


• [31] D. A. Molodtsov, V. Y. Leonov, D. V. Kovkov, Soft sets technique and its application, Nechetkie Sistemy i Myagkie Vychisleniya, 1 (2006), 8--39
  • View Article
  • Google Scholar


• [32] G. Muhiuddin, D. Al-Kadi, A. Mahboob, K. P. Shum, New types of bipolar fuzzy ideals of BCK-algebras, Int. J. Anal. Appl., 18 (2020), 859--875
  • View Article
  • Google Scholar


• [33] T. Senapati, Y. B. Jun, G. Muhiuddin, K. P. Shum, Cubic intuitionistic structures applied to ideals of BCI-algebras, An. Ştiinţ. Univ. "Ovidius'' Constanţa Ser. Mat., 27 (2019), 213--232
  • View Article
  • MathSciNet
  • Google Scholar


• [34] L. A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338--353
  • View Article
  • MathSciNet


• [35] J. Zhan, Y. B. Jun, Soft BL-algebras based on fuzzy sets, Comput. Math. Appl., 59 (2010), 2037--2046
  • View Article
  • MathSciNet