Applications of Fuzzy Sets on Essential Ideals of n-Ary Semigroups with Zero

Main Article Content

Pattarawan Singavananda, Ronnason Chinram

Abstract

An n-ary semigroup is an algebraic system that consists of a non-empty set and an associative n-ary operation. In this paper, we introduce the concepts of essential ideals and essential fuzzy ideals of n-ary semigroups. Furthermore, we investigate certain relationships between essential ideals and essential fuzzy almost ideals in n-ary semigroups.

Article Details

References

  1. S. Baupradist, B. Chemat, K. Palanivel, R. Chinram, Essential Ideals and Essential Fuzzy Ideals in Semigroups, J. Discret. Math. Sci. Cryptogr. 24 (2020), 223–233. https://doi.org/10.1080/09720529.2020.1816643.
  2. R. Chinram, T. Gaketem, Essential (m, n)-Ideal and Essential Fuzzy (m, n)-Ideals in Semigroups, ICIC Express Lett. 15 (2021), 1037–1044. https://doi.org/10.24507/icicel.15.10.1037.
  3. T. Gaketem, A. Iampan, On Essential Bi-Ideals and Essential Fuzzy Bi-Ideals in Semigroups, Int. J. Appl. Math. 36 (2023), 483–496. https://doi.org/10.12732/ijam.v36i4.4.
  4. R. Kasner, An Extension of the Group Concepts, Bull. Am. Math. Soc. 10 (1904), 290–291.
  5. N. Panpetch, T. Muangngao, T. Gaketem, Some Essential Bi-Ideals and Essential Fuzzy Bi-Ideals in a Semigroup, J. Math. Comput. Sci. 28 (2022), 326–334. https://doi.org/10.22436/jmcs.028.04.02.
  6. R. Rittichuai, A. Iampan, R. Chinram, P. Singavananda, Essential Ideals and Their Fuzzifications of Ternary Semigroups, ICIC Express Lett. 17 (2023), 191–199. http://doi.org/10.24507/icicel.17.02.191.
  7. L. A. Zadeh, L. Zadeh, Fuzzy Sets, Inf. Control. 8 (1965), 338–353. https://doi.org/10.1016/s0019-9958(65)90241-x.