Ternary Semigroups Characterized by Spherical Fuzzy Bi-ideals
Article Sidebar
Main Article Content
Abstract
The concept of spherical fuzzy sets, was introduced by Ashraf et al. in 2019, and is a generalization of the concepts of intuitionistic fuzzy sets, picture fuzzy sets and Pythagorean fuzzy sets. In this paper, we introduce the concepts of spherical fuzzy quasi-ideals and spherical fuzzy bi-ideals of ternary semigroups and investigate some of their properties. Then, we characterize regular ternary semigroups in terms of spherical fuzzy left (resp., lateral, right) ideals, spherical fuzzy quasi-ideals and spherical fuzzy bi-ideals of ternary semigroups. Moreover, some characterizations of weakly regular ternary semigroups by the concepts of many types of spherical fuzzy ideals in ternary semigroups are discussed.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
References
Zadeh, L.Z. Fuzzy sets. Information and Control. 1965; 8: 338–353.
Rosenfeld, A. Fuzzy groups. Journal of Mathematical Analysis and Applications. 1971; 35: 512-517.
Kuroki, N. On fuzzy ideals and fuzzy bi- ideals in semigroups. Fuzzy Sets and Sys- tems. 1981; 5: 203-215.
Kuroki, N. On fuzzy semigroups. Infor- mation Sciences. 1991; 53: 203-236.
Kuroki, N. Fuzzy generalized bi-ideals in semigroups. Information Sciences. 1992; 66: 235-243.
Lehmer, D.H. A ternary analogue of abelian groups. American Journal of Mathematics. 1932. 54: 329–338.
Shabir, M. and Rehman, N. Characteriza- tions of ternary semigroups by their anti fuzzy ideals. Annals of Fuzzy Mathemat- ics and Informatics. 2011; 2: 227-238.
Kar, S. and Sarkar, P. Fuzzy ideals of ternary semigroups. Fuzzy Information and Engineering. 2012; 2: 181-193.
Atanassov, K.T. Intuitionistic fuzzy sets. Fuzzy Sets and Systems. 1986; 20: 87-96.
Akram, M. Intuitionistic fuzzy points and ideals of ternary semigroups. Inter- national Journal of Algebra and Statistics. 2012; 1: 74-82.
Lekkoksung, S. Intuitionistic fuzzy bi- ideals of ternary semigroups. Interna- tional Mathematical Forum. 2012. 7: 385- 389.
Lalithamani, N., Prabakaran, K. and Remesh, R. Intuitionistic fuzzy ideals and intuitionistic fuzzy filters of ternary semi- groups. Advances in Mathematics: Scien- tific Journal. 2020: 9: 9535-9540.
Yager, R.R. and Abbasov, A.M. Pythagorean membership grades, com-plex numbers, and decision making. International Journal of Intelligent Systems. 2013; 28: 436-452.
Chinram, R. and Paniyakul, T. Rough Pythagorean fuzzy ideals in ternary semi- groups. Journal of Mathematics and Com- puter Science. 2020; 20: 302-312.
Cuong, B.C. and Kreinovich, V. Picture fuzzy sets - a new concept for computa- tional intelligence problems. Proceedings of the Third World Congress on Infor- mation and Communication Technologies WIICT. 2013; 1-6.
Nakkhasen, W. Characterizing regular and intra-regular semigroups in terms of picture fuzzy bi-ideals. International Jour- nal of Innovative Computing, Information and Control. 2021; 17: 2115-2135.
Yiarayong, P. Semigroups characterized by picture fuzzy sets. International Jour- nal of Innovative Computing, Information and Control. 2020; 16: 2121-2130.
Yiarayong, P. Characterizations of semi- groups by the properties of their picture fuzzy bi-ideals. Journal of Control and Decision. 2022; 9: 111-116.
Nakkhasen, W. On picture fuzzy ideals of semigroups. IAENG Interna- tional Journal of Applied Mathematics. 2022; 52: 4.
Ashraf, S., Abdullah, S., Mahmood, T., Gahni, F. and Mahmood, T. Spherical fuzzy sets and their applications in multi- attribute decision making problems. Jour- nal of Intelligent & Fuzzy Systems. 2019; 36: 2829-2844.
Veerappan, C. and Venkatesan, S. Spher- ical interval-valued fuzzy bi-ideals of gamma near-rings. Journal of Fuzzy Ex- tension and Applications. 2020; 1: 314- 324.
Subha, V.S., Lavanya, S. and Aswini, C.B. Characterizations of semi-ring by rough spherical fuzzy ideals. Turkish On- line Journal of Qualitative Inquiry (TO- JQI). 2021; 12: 6103-6116.
Chinnadurai, V., Bobin, A. and Arulsel- vam, A. A study on spherical fuzzy ideals of semigroups. TWMS Journal of Applied and Engineering Mathematics. 2022; 12: 1202-1212.
Krailoet, W., Chinram, R., Petapirak, M. and Iampan, A. Application of spherical fuzzy sets in ternary semigroups. Interna- tional Journal of Analysis and Applica- tions. 2022; 20: 29.
Dutta, T.K., Kar, S. and Maity, B.K. On ideals in regular ternary semigroups. Dis- cussiones Mathematicae General Algebra and Applications. 2008; 28: 147-159.
Sioson, F.M. Ideal theory in ternary semi- groups. Mathematica Japonica. 1965; 10: 63-84.
Dixit, V.N. and Dewan, S. A note on quasi and bi-ideals in ternary semigroups. In- ternational Journal of Mathematics and Mathematical Sciences. 2995; 18: 501- 508.
Kar, S. and Sarkar, P. Fuzzy quasi-ideals and fuzzy bi-ideals of ternary semigroups. Annals of Fuzzy Mathematics and Infor- matics. 2012; 4: 407-423.
Shabir, M. and Bano, M. Prime bi-ideals in ternary semigroups. Quasigroups and Related Systems. 2008; 16: 239-256.
Lekkoksung, N. and Jampachon, P. On right weakly regular ordered ternary semi- groups. Quasigroups and Related Sys- tems. 2014; 22: 257-266.
Bashir, S. and Du, X. Intra-regular and weakly regular ordered ternary semi- groups. Annals of Fuzzy Mathematics and Informatics. 2017; 13: 539-551.