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INTUITIONISTIC FUZZY IDEAL OF PARTIALLY ORDERED NEAR-RING

Year 2026, Volume: 16 Issue: 2, 236 - 248, 03.02.2026

Abstract

In this paper, we introduce the concept of intuitionistic fuzzy ideals ($IFI$) within the framework of partially ordered near-rings ($PONR$). We explore the fundamental properties and characterizations of $IFI$ in $PONR$, providing a comprehensive theoretical foundation for their study. Our work extends the existing literature on fuzzy algebraic structures, aligning with advancements in intuitionistic fuzzy sets and their applications in near-ring theory.

References

  • Abou-Zaid, S., (1991), On fuzzy subnear-ring and ideals, Fuzzy Sets and Systems, 44, 139–146.
  • Atanasov, K. T., (1986), Intuitionistic fuzzy sets, J. Fuzzy Math., 20, 87-96.
  • Atanasov, K. T., (1994), New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems, 61, 137–142.
  • Biswas, R., (1987), Intuitionistic fuzzy subgroups, Math. Forum., 10, 37–46.
  • Cho, Y. U., and Jun, Y. B., (2005), On intuitionistic fuzzy R-subgroups of near-rings, J. Appl. Math. Comput., 18, 665-677.
  • Kim, K. H., and Lee, J. G., (2008), Intuitionistic (T,S)-normed fuzzy ideals of -rings, International Mathematical Forum, 3(3), 115–123.
  • Kim, K., and Jun, Y. B., (2002), Intuitionistic fuzzy ideals of semigroups, Indian Journal of Pure and Applied Mathematics, 33(4), 443–449.
  • Kim, K. H., and Lee, J. G., (2005), On intuitionistic fuzzy bi-ideals of semigroups, Turkish Journal of Mathematics, 29(2), 202–210.
  • Kuroki, N., (1979), Fuzzy bi-ideals in semigroups, Commentarii Mathematici Universitatis Sancti Pauli, 28, 17–21.
  • Kuroki, N., (1981), On fuzzy ideals and fuzzy bi-ideals in semigroups, Fuzzy Sets and Systems, 5(2), 203–215.
  • Mordeson, J. N., Malik, D. S., et al., (2003), Fuzzy semigroups, Springer-Verlag Berlin Heidelberg, 307.
  • Murugadas, P., and Vetrivel, V., (2019), (T,S)-Intuitionistic fuzzy ideals in near-rings, Malaya Journal of Matematik, Vol. S, No. 1, 321-326.
  • Radhakrishna, A., and Bhandari, M., (1977), On lattice ordered near-rings, Pure Appl. Math. Sci.
  • Rosenfeld, A., (1971), Fuzzy groups, Journal of Mathematical Analysis and Application, 35, 512–517.
  • Zadeh, L. A., (1965), Fuzzy Sets, Information and Control, 8, 338-353.
  • Zhan, J., and Ma, X., (2004), Intuitionistic fuzzy ideals of near-rings, Scientae Math Japonicae, 61(2), 219–223.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Logic, Set Theory, Lattices and Universal Algebra
Journal Section Research Article
Authors

Saravanakumar Gurusamy 0000-0003-1309-7609

K. A. Venkatesan This is me 0009-0001-5574-2170

A. Arulselvam This is me 0000-0001-8383-2889

Tharmalingam Gunasekar 0000-0002-7268-1613

Submission Date February 21, 2025
Acceptance Date June 25, 2025
Publication Date February 3, 2026
Published in Issue Year 2026 Volume: 16 Issue: 2

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