Characterization of almost ternary subsemigroups and their fuzzifications

Volume 27, Issue 2, pp 97--104 http://dx.doi.org/10.22436/jmcs.027.02.01

Publication Date: April 13, 2022 Submission Date: January 09, 2022 Revision Date: January 28, 2022 Accteptance Date: February 01, 2022

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Authors

R. Chinram - Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand. S. Kaewchay - Division of Mathematics, School of Science, Walailak University, Nakhon Si Thammarat 80160, Thailand. A. Iampan - Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand. P. Singavananda - Program in Mathematics, Faculty of Science and Technology, Songkhla Rajabhat University, Songkhla 90000, Thailand.

Abstract

In this paper, we define almost ternary subsemigroups of ternary semigroups. Almost ternary subsemigroups is a one of generalizations of ternary subsemigroups. We show that the union of two almost ternary subsemigroups is also an almost ternary subsemigroup. However, the intersection of two almost ternary subsemigroups need not be an almost ternary subsemigroup. Moreover, we define their fuzzifications and provide the relationships between almost ternary subsemigroups and their fuzzifications.

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Keywords

• Almost ternary subsemigroups
• fuzzy almost ternary subsemigroup
• minimal
• prime
• semiprime

MSC

•  20M99
•  03E72

References

• [1] M. Akram, N. Yaqoob, Intuitionistic fuzzy soft ordered ternary semigroups, Int. J. Pure Appl. Math., 84 (2013), 93--107
  • View Article
  • Google Scholar


• [2] M. A. Ansari, N. Yaqoob, T-rough ideals in ternary semigroups, Int. J. Pure Appl. Math., 86 (2013), 411--424
  • View Article
  • Google Scholar


• [3] O. Grošek, L. Satko, A new notion in the theory of semigroup, Semigroup Forum, 20 (1980), 233--240
  • View Article
  • MathSciNet
  • Google Scholar


• [4] K. Hila, J. Dine, On hyperideals in left almost semihypergroups, ISRN Algebra, 2011 (2011), 8 pages
  • View Article
  • MathSciNet


• [5] A. Iampan, R. Chinram, P. Petchkaew, A note on almost subsemigroups of semigroups, Int. J. Math. Comput. Sci., 16 (2021), 1623--1629
  • View Article
  • MathSciNet


• [6] D. H. Lehmer, A ternary analogue of abelian groups, Amer. J. Math., 54 (1932), 329--338
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] J. Los, On the extending of models $(I)^*$, Fund. Math., 42 (1955), 38--54
  • View Article
  • MathSciNet
  • Google Scholar


• [8] J. N. Mordeson, D. S. Malik, N. Kuroki, Fuzzy semigroups, Springer-Verlag, Berlin (2012)
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] P. Muangdoo, T. Chuta, W. Nakkhasen, Almost bi-hyperideals and their fuzzification of semihypergroups, J. Math. Comput. Sci., 11 (2021), 2755--2767
  • View Article
  • Google Scholar


• [10] S. Nawaz, M. Gulistan, N. Kausar, Salahuddin, M. Munir, On the left and right almost hyperideals of LA-semihypergroups, Int. J. Fuzzy Logic Intel. Syst., 21 (2021), 86--92
  • View Article
  • Google Scholar


• [11] A. Simuen, A. Iampan, R. Chinram, A novel of ideals and fuzzy ideals of Gamma-semigroups, J. Math., 2021 (2021), 14 pages
  • View Article
  • MathSciNet


• [12] S. Suebsung, T. Kaewnoi, R. Chinram, A not on almost hyperideals in semihypergroups, Int. J. Math. Comput. Sci., 15 (2020), 127--133
  • View Article
  • Google Scholar


• [13] S. Suebsung, K. Wattanatripop, R. Chinram, A-ideals and fuzzy A-ideals of ternary semigroups, Songklanakarin J. Sci. Tech., 41 (2019), 299--304
  • View Article
  • Google Scholar


• [14] K. Wattanatripop, R. Chinram, T. Changphas, Quasi-$A$-ideals and fuzzy $A$-ideals in semigroups, J. Discrete Math. Sci. Cryptogr., 21 (2018), 1131--1138
  • View Article
  • MathSciNet
  • Google Scholar


• [15] N. Yaqoob, S. Abdullah, N. Rehman, M. Naeem, Roughness and fuzziness in ordered ternary semigroups, World Appl. Sci. J., 17 (2012), 1683--1693
  • View Article
  • Google Scholar


• [16] N. Yaqoob, M. A. Ansari, Bipolar $(\lambda,\delta)$-fuzzy ideals in ternary semigroups, Int. J. Math. Anal. (Ruse), 7 (2013), 1775--1782
  • View Article
  • MathSciNet


• [17] N. Yaqoob, P. Corsini, F. Yousafzai, On intra-regular left almost semihypergroups with pure left identity, J. Math., 2013 (2013), 10 pages
  • View Article
  • MathSciNet


• [18] N. Yaqoob, M. Gulistan, Partially ordered left almost semihypergroups, J. Egyptian Math. Soc., 23 (2015), 231--235
  • View Article
  • MathSciNet


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