Characterizations of Some Regularities in Ordered Ternary Semigroups in Terms of Fuzzy Subsets

Authors

  • Nareupanat Lekkoksung Division of Mathematics, Faculty of Engineering, Rajamangala University of Technology Isan, Khon Kaen Campus, Khon Kaen 40000
  • Hataikhan Sanpan Division of Mathematics, Faculty of Engineering, Rajamangala University of Technology Isan, Khon Kaen Campus, Khon Kaen 40000
  • Somsak Lekkoksung Division of Mathematics, Faculty of Engineering, Rajamangala University of Technology Isan, Khon Kaen Campus, Khon Kaen 40000

DOI:

https://doi.org/10.26713/cma.v12i2.1489

Keywords:

Fuzzy left ideal, Fuzzy lateral ideal, Fuzzy right ideal, Ordered ternary semigroup

Abstract

Characterizations of some classes of ordered ternary semigroups; left (resp., right) lightly regular and generalized regular are given in terms of fuzzy left ideals, fuzzy right ideals, fuzzy lateral ideals, and fuzzy ideals of ordered ternary semigroups.

Downloads

Download data is not yet available.

References

M. Akram and N. Yaqoob, Intuitionistic fuzzy soft ordered ternary semigroups, International Journal of Pure and Applied Mathematics 84 (2013), 93 – 107, DOI: 10.12732/ijpam.v84i2.8.

S. Bashir and X. Du, Intra-regular and weakly regular ordered ternary semigroups, Annals of Fuzzy Mathematics and Informatics, 13 (2017), 539 – 551, http://www.afmi.or.kr/papers/2017/Vol-13-No-04/PDF/AFMI-13-4(539-551)-H-160823-1.pdf.

R. Bˇelohlávek, Fuzzy equational logic, Archive for Mathematical Logic 41 (2002), 83 – 90, DOI: 10.1007/s001530200006.

R. Chinram and S. Saelee, Fuzzy ideals and fuzzy filters of ordered ternary semigroups, Journal of Mathematics Research 2 (2010), 93 – 97, DOI: 10.5539/jmr.v2n1p93.

V.R. Daddi and Y.S. Pawar, On ordered ternary semigroups, Kyungpook Mathematical Journal 52 (2012), 375 – 381, DOI: 10.5666/KMJ.2012.52.4.375.

A. Iampan, Characterizing the minimality and maximality of ordered lateral ideals in ordered ternary semigroups, Journal of the Korean mathematical society 46 (2009), 775 – 784, DOI: 10.4134/JKMS.2009.46.4.775.

D.H. Lehmer, A ternary analogue of Abelian groups, American Journal of Mathematical Society 59 (1932), 329 – 338, DOI: 10.2307/2370997.

N. Lekkoksung and P. Jampachon, Characterizations of regular ordered ternary semigroups in term of fuzzy subsets, Southeast-Asian Journal of Sciences 2 (2013), 141 – 153, http://sajs.ntt.edu.vn/index.php/jst/article/view/34.

N. Lekkoksung and P. Jampachon, On right weakly regular ordered ternary semigroups, Quasigroups and Related Systems 22 (2014), 257 – 266, http://www.quasigroups.eu/contents/download/2014/22_25.pdf.

J. Åos, On the extending of models (I), Fundamenta Mathematicae 42 (1955), 38 – 54, https://eudml.org/doc/213372.

J. Sanborisoot and T. Changphas, On pure ideals in ordered ternary semigroups, Thai Journal of Mathematics 12 (2014), 455 – 464, http://thaijmath.in.cmu.ac.th/index.php/thaijmath/article/view/892.

M.L. Santiago and S. Sri Bala, Ternary semigroups, Semigroup Forum 81 (2010), 380 – 388, DOI: 10.1007/s00233-010-9254-x.

P. Pornsurat and B. Pibaljommee, Regularities in ordered ternary semigroups, Quasigroups and Related Systems 27 (2019), 107 – 118, http://www.quasigroups.eu/contents/download/2019/27_11.pdf.

N. Yaqoob, S. Abdullah, N. Rehman and M. Naeem, Roughness and fuzziness in ordered ternary semigroups, World Applied Sciences Journal 17 (2012), 1683 – 1693, https://www.idosi.org/wasj/wasj17(12)12/21.pdf.

L.A. Zadeh, Fuzzy sets, Information and Control 8 (1065), 338 – 353, DOI: 10.1016/S0019-9958(65)90241-X.

Downloads

Published

30-06-2021
CITATION

How to Cite

Lekkoksung, N., Sanpan, H., & Lekkoksung, S. (2021). Characterizations of Some Regularities in Ordered Ternary Semigroups in Terms of Fuzzy Subsets. Communications in Mathematics and Applications, 12(2), 325–333. https://doi.org/10.26713/cma.v12i2.1489

Issue

Vol. 12 No. 2 (2021)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.