Fuzzy Interior Ideals in Ternary Semigroups: Structural Properties and Characterizations
Acceptance: 04/05/2026
Published: 29/05/2026
Abstract
A ternary semigroup is an algebraic structure equipped with a ternary associative operation, and interior ideals play a crucial role in understanding its substructures. By introducing fuzzy sets into this framework, we define fuzzy interior ideals and investigate their fundamental properties. In this paper we introduce the notion of fuzzy interior ideals in Ternary semigroups and investigated relations between fuzzy ideals and fuzzy interior ideals in ternary of regularity. We finally introduce the concept of a fuzzy simple ordered semigroup, we proved that an ordered ternary semigroup is simple if and only if it is fuzzy simple, and we characterize the simple ordered ternary semigroups in terms of fuzzy interior ideals.
Author Name:
Dr.Thiriveedi Sunitha
Pages:
235-239
DOI Number:
10.5281/zenodo.20437712
Reference
1 .Zadeh, L.A.Fuzzy sets, Inform. Control, 8, pp. 338 – 353.
1. Sison, F.M. Ideal theory in ternary semigroups”, Math.Japon,10(1965),63-84
2. Kehayopulu N. and Tsingelis, M. Regular oerderd semigroups in terms of fuzzy subsets. information science, 176 (2006) 3675 – 3693.
3. Dixit V.N. and Dewan S.A note on quasi and bi ideals in ternary semigroups, international journal of Mathematical Society, 18(3) (199), 501-508.
4. T Sunitha, Dr. U. Nagi Reddy, Dr. G. Shobhalatha,.and C. Meena Kumari.:Ternary semigroups T Satisfying the identity b aba for all T aba T, , Journal of Computer and Mathematical 11 Sciences, Vol 10(4),780-786April 2019, ISSN 2319 8133.
5. Sunitha T., Shobhalatha G. and Nagi Reddy U., Some Properties Of Simple Ternary Semigroups,International Journal of Mathematics Trends and Technology (IJMTT) Ȃ Volume 65 Issue 6, ISSN:2231-5373, June 2019.
6. T. Sunitha, Dr, G, Shobhalatha ,Strongly Regular Ternary semigroups, Mathematical Sciences International Research Journal Volume 9 Issue 2,61-68,Aug 2020. ISSN 2278- 8697
7. U. Nagi Reddy and G. Shobhalatha, Some Characterizations Of Ternary Semigroups, September –2015, ISSN 2229-5518 IJSER © 2015 .http://www.ijser.org.
8. U. Nagi Reddy, U. Meena Kumari, C.and Shobhalatha, G. Some Properties of Fuzzy Quasi ideals in Ternary Semigroups, International Journal of Development Research, Volume 7 Issue 12 Pages 17512-17518, December – 2017.
9. T Sunitha1, U Nagi Reddy, G Shobhalatha, A Note on Full k-Ideals in Ternary Semirings, Indian Journal of Science and Technology 2021;14(21):1786–1790
Writer Name
Dr.Thiriveedi Sunitha
Pages
235-239
DOI Numbers
10.5281/zenodo.20437712
Our Social Networks
AD EDUXIAN Publication is dedicated to advancing educational research and providing innovative learning solutions. We offer a wide range of services including publishing, editing, design, and marketing to support authors and researchers in their academic and professional endeavors.
Never miss any important news. Subscribe to our newsletter.