The characterization of regular ordered Gamma semigroups in terms of (E,EVq_k)-fuzzy Gamma ideals

Authors

  • Ibrahim Gambo Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor, Malaysia.
  • Nor Haniza Sarmin Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor, Malaysia.
  • Hidayat Ullah Khan Department of Mathematics, University of Malakand, Khyber Pukhtunkhwa, 18800 Pakistan.
  • Muhammad Faiz Khan Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhwa, 19130 Pakistan.

DOI:

https://doi.org/10.11113/mjfas.v0n0.608

Abstract

The advancement in the fascinating area of fuzzy set theory has become area of much interest, generalization of the existing fuzzy subsystems of other algebraic structures is very important to tackle more current real life problems. In this paper, we give more generalized form of regular ordered gamma semigroups in terms of (E,EVq_k)-fuzzy gamma ideals. Particularly, we characterized left regular, right regular, simple and completely regular ordered gamma semigroups in terms of this new notion. Some necessary and sufficient conditions for ordered gamma semigroup to be completely regular are provided in this paper.

Author Biographies

Ibrahim Gambo, Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor, Malaysia.

PhD Student,
Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia,
81310 UTM Johor, Malaysia.

Nor Haniza Sarmin, Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor, Malaysia.

A Professor of Mathematics,
Department of Mathematical Sciences,
Faculty of Science, Universiti Teknologi Malaysia,
81310 UTM Johor, Malaysia.

Hidayat Ullah Khan, Department of Mathematics, University of Malakand, Khyber Pukhtunkhwa, 18800 Pakistan.

Assistant Professor,
Department of Mathematics,
University of Malakand,
Khyber Pukhtunkhwa, 18800 Pakistan.

Muhammad Faiz Khan, Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhwa, 19130 Pakistan.

Assistant Professor and In charge,
Department of Mathematics and Statistics,
University of Swat,
Khyber Pakhtunkhwa, 19130 Pakistan.

References

Abbasi, M. Y., & Basar, A. (2013). On ordered quasi-gamma-ideals of regular ordered gamma-semigroups. Algebra, 1-7.

Bhakat, S. K., & Das, P. (1992). On the definition of a fuzzy subgroup. Fuzzy sets and Systems, 51(2), 235-241.

Bhakat, S. K., & Das, P. (1996). (∈,∈∨q)-fuzzy subgroups. Fuzzy sets and Systems, 80, 359-368.

Changphas, T. (2012). On Intra-regular Γ-semigroups. International Journal of Contemporary Mathematical Sciences, 7(6), 273-277.

Gambo, I., Sarmin, N. H., Khan, H. U., & Khan, F. M. (2017). New form of fuzzy bi Γ-ideals in ordered Γ-semigroup. 4th International Conference of Mathematics and Statistic (ICMS4 2016) AIP Conference Proceedings 1830, 070019.

Gambo, I., Sarmin, N. H., Khan, H. U., & Khan, F. M. (2017). On the characterization of bi Γ− ideals of the type (∈,∈∨ qk) in ordered Γ− semigroups. Paper presented at the 4th Biennial International Group Theory Conference 2017 (4BIGTC2017), 23rd-26th January, UTM Kuala Lampur, Malaysia, 111-114.

Good, R. A., & Hughes, D. R. (1952). Associated groups for a semi-group. Bulletin of the American Mathematical Society, 58(6), 624-625.

Jun, Y. B., Khan, A., & Shabir, M. (2009). Ordered semigroups characterized by their (∈,∈∨ q)-fuzzy bi-ideals. Bulletin of the Malaysian Mathematical Sciences Society, (2), 32(3), 391-408.

Kazancı, O., & Yamak, S. (2008). Generalized fuzzy bi-ideals of semigroups. Soft computing, 12(11), 1119-1124.

Khan, F. M., Sarmin, N. H., & Khan, A. (2013). Fuzzy Generalized Bi–Γ–Ideals of Type (λ, θ) In Ordered Γ–Semigroups. Jurnal Teknologi, 62(3), 1-6.

Khan, F. M., Sarmin, N. H., & Khan, A. (2014). A novel approach towards fuzzy Γ-ideals in ordered Γ-semigroups. Indian Journal of Pure and Applied Mathematics, 45(3), 343-362.

Ma, X., Zhan, J., Davvaz, B., & Jun, Y. B. (2008). Some kinds of (∈,∈∨q)-interval-valued fuzzy ideals of BCI-algebras. Information Sciences, 178(19), 3738-3754.

Sen, M. K. (1981). On Γ semigroups Lecture Notes in Pure and Appl. Math., Dekker, New York. Algebra and its Applications, 91, 301-308.

Sen, M. K., & Saha, N. K. (1986). Orthodox Γ-semigroup. I. Bulletin of Calcutta Mathematical Society, 78(3), 180-186.

Tang, J., & Xie, X.-Y. (2013). On (∈, ∈ ∨q k )-fuzzy ideals of ordered semigroups. Fuzzy Information and Engineering, 5(1), 57-67.

Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353.

Downloads

Published

26-12-2017