Cubic Of Positive Implicative Ideals In KU- Semigroup
Main Article Content
Abstract
In this paper, we define a cubic positive implicative-ideal, a cubic implicative-ideal and a cubic commutative-ideal of a semigroup in KU-algebra as a generalization of a fuzzy (positive implicative-ideal, an implicative-ideal and a commutative-ideal) of a semigroup in KU-algebra. Some relations between these types of cubic ideals are discussed. Also, some important properties of these ideals are studied. Finally, some important theories are discussed. It is proved that every cubic commutative-ideal, cubic positive implicative-ideal, and cubic implicative-ideal are a cubic ideal, but not conversely. Also, we show that if Θ is a cubic positive implicative-ideal and a cubic commutative-ideal then Θ is a cubic implicative-ideal. Some examples of the opposite direction of the previous theories are obtained.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
licenseTerms
Publication Dates
References
Prabpayak, C. ; Leerawat, U. On ideals and congruence in KU-algebras. Scientia Magna(International Book Series). 2009,5,1, 54-57.
Prabpayak, C. ; Leerawat, On isomorphisms of KU-algebras, scientia magna (International Book Series). 2009,5,3, 25-31.
Zadeh, L. A. The concept of a linguistic variable and its application to Approximate reasoning. I, Information Sci. And Control. 1975, 8, 199-249. DOI: https://doi.org/10.1016/0020-0255(75)90036-5
Rosenfeld, A. Fuzzy groups, J. Math. Anal. Appl.1971, 35, 512-517. DOI: https://doi.org/10.1016/0022-247X(71)90199-5
Jun, Y. B.; Meng J. Fuzzy p-ideals in BCI-algebras. Math. Japonica. 1994, 40 ,2, 271–282.
Jun, Y. B.; Meng J ; Mostafa, S.M. On Fuzzy Implicative ideals of BCK- algebras. SOOCHW Journal of Mathematics. 1999 , 25, 1, 57-70.
Mostafa, S.M.; Abd-Elnaby, M.A.; Yousef, M.M.M. Fuzzy ideals of KU-Algebras. Int. Math, Forum. 2011, 6,63, 3139-3149.
Xin , X. L.; Ji ,W.; Hua, X. J .Fuzzy Filter Spectrum of a BCK Algebra. International Journal of Mathematics and Mathematical Sciences 2011, 13 pages. https://doi.org/10.1155/2011/795934 DOI: https://doi.org/10.1155/2011/795934
Satyanarayana, B. ; Madhavi , U .B. fuzzy positive implicative extension ideals in BCK-algebras. British Journal of Mathematics and Computer Science. 2016, 12,4, 1-9. DOI: https://doi.org/10.9734/BJMCS/2016/20217
Tawfiq, L. N.; Qa’aed, M. M. On Fuzzy Groups and Group Homomorphism. Ibn AL-Haitham Journal For Pure and Applied Sciences 2017, 25,2, 340-346. https://jih.uobaghdad.edu.iq/index.php/j/article/view/641
Mostafa, S.M.; Abd El-Baser, O.W. Fuzzy implicative ideals in KU-algebra. Journal of New Theory. 2018, 22, 82-91.
Megalai, K.; Tamilarasi, A. Fuzzy Subalgebras and Fuzzy T-ideals in TM-Algebras. J Math Stat. 2011, 7 , 2,107-111. https://doi.org/10.3844/jmssp.2011.107.111 DOI: https://doi.org/10.3844/jmssp.2011.107.111
Lee, K.M. Bipolar-valued fuzzy sets and their operations. Proc. Int. Conf. on Intelligent Technologies. 2000, 307-312.
Lee, K.M. Comparison of interval-valued fuzzy sets, intuitionistic fuzzy sets and bipolar-valued fuzzy sets. J. Fuzzy Logic intelligent Systems. 2004, 14, 125-129. DOI: https://doi.org/10.5391/JKIIS.2004.14.2.125
Yaqoob, N.; Ansari, M. A. Bipolar (λ,δ)- Fuzzy ideals in Ternary semigroups. Int. J. Math. Analysis. 2013, 7,361777-1782. DOI: https://doi.org/10.12988/ijma.2013.35127
Muhiuddin, G. Bipolar fuzzy KU-subalgebrasideals of KU-algebras. Ann. Fuzzy Math. Inform. 2014 ,8,3, 339-504.
Kareem, F.F. ; Talib, S. A. Interval value fuzzy k-ideals of KU-semigroup. Ibn Al-Haitham Journal for Pure and Applied Science. 2020,33,2, 95-106. https://doi.org/10.30526/33.2.2430 DOI: https://doi.org/10.30526/33.2.2430
Jun, Y. B.; Kim, C. S.; M. S. Kang. Cubic subalgebras and ideals of BCK/BCI-algebras. Far East Journal of Mathematical Sciences. 2010, 2,44, 239–250.
Jun, Y. B; Lee, K. J; Kang, M. S. Cubic structures applied to ideals of BCI-algebras. Comput Math Appl. 2011, 26,9, 3334-3342. https://doi.org/10.1016/j.camwa.2011.08.042 DOI: https://doi.org/10.1016/j.camwa.2011.08.042
Yaqoob, N.; Mostafa, S.M.; Ansari, M. A. On cubic KU-ideals of KU-algebras. ISRN Algebra. 2013 Article ID935905, 10 pages. DOI: https://doi.org/10.1155/2013/935905
Hasan, E. R.; Kareem, F.F. Fuzzy KU-Semi-Groups and Investigate Some Basic Properties. Journal of Engineering and Applied Science. 2018,13,18, 7739-7744.
Kareem, F.F.; Hasan, O.A. Cubic ideals of semigroup in KU-algebra. J. Phys.: Conf. Ser. 1804. 2021, 012018.
Senapati, T.; Shum, K.P. Cubic implicative ideals of BCK-algebras. Missouri J. of Math. Sci. 2017, 29, 2, 125-138.
Senapati, T.; Jun, Y. B.; Shum, K.P. Cubic Intuitionistic Implicative Ideals of BCK-Algebras. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 2021, 91, 2, 273-282.
Jun, Y. B.; Kim, C. S.; Kang; Kang, J. G. Cubic q -ideals of BCI-algebras. Annals of Fuzzy Mathematics and Informatics. 2011, 1, 1, 25- 34.
Akram, M. ; Yaqoob, N.; Gulistan, M. cubic KU-subalgebras. Int. J. Pure Appl. Math. 2013, 89 ,5, 659- 665. DOI: https://doi.org/10.12732/ijpam.v89i5.2
Muhiuddin, G.; Al-roqi, A. M. Cubic soft sets with applications in BCK/ BCI-algebras. Annals of Fuzzy Mathematics and Informatics. 2014, 8 , 291-304. DOI: https://doi.org/10.1155/2014/458638
Janaa, C.; Senapati, T. Cubic G-subalgebras of G-algebras. Annals of Pure and Applied Mathematics. 2015, 10, 1, 105-115.
Muhiuddin, G.; Ahn, S. S.; Kim, C. S.; Jun, Y .B . Stable Cubic Sets. Journal of Computational Analysis and Applications. 2017 , 23,5, 802–819 .
Lee, J. G.; Hur , K.; Mostafa, S. M. Cubic bipolar structures of BCC-ideal on BCC-algebras. Annals of Fuzzy Mathematics and Informatics.2020, 20,1, 89-103.