| Title of paper:
|
(α,β)-Interval-valued intuitionistic fuzzy subgroups
|
| Author(s):
|
|
| Published in:
|
Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 2, pages 195–206
|
| DOI:
|
https://doi.org/10.7546/nifs.2025.31.2.195-206
|
| Download:
|
PDF (787 Kb, File info)
|
| Abstract:
|
In this paper, (α,β)-interval-valued intuitionistic fuzzy subgroups are studied. The definition of these structures are given by using (α,β)-interval-valued intuitionistic fuzzy sets. The structural properties of these subgroups are studied. Some examples are given about these structures to satisfy the conditions of propositions.
|
| Keywords:
|
Interval-valued intuitionistic fuzzy sets, (α,β)-interval-valued intuitionistic fuzzy sets, (α,β)-interval-valued intuitionistic fuzzy subgroups
|
| AMS Classification:
|
03E72, 18B40, 08A72.
|
| References:
|
- Atanassov, K. T. (1983). Intuitionistic fuzzy sets. VII ITKR’s Session, Sofia, June, (deposed in Central Sci.-Techn. Library of Bulg. Acad. Of Sci. No. 1697/84 (in Bulgarian). Reprinted: International Journal Bioautomation, 20 (1), 2016, S1–S6.
- Atanassov, K. T., & Gargov, G. (1989). Interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 31(3), 343–349.
- Atanassov, K. T. (1994). Operators over interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 64(2), 159–174.
- Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications. Springer, Heidelberg.
- Atanassov, K. T. (2018). Intuitionistic fuzzy sets and interval valued intuitionistic fuzzy sets. Advanced Studies in Contemporary Mathematics, 28(2), 167–176.
- Atanassov, K. T. (2024). Intuitionistic fuzzy modal multi-topological structures and intuitionistic fuzzy multi-modal multi-topological structures. Mathematics, 12(3), Article 361.
- Aygünoğlu, A., Varol Pazar, B., Çetkin, V., & Aygün, H. (2012). Interval-valued intuitionistic fuzzy subgroups on interval-valued double t-norm. Neural Computing & Applications, 21(1), 207–214.
- Bal, A., Çuvalcıoğlu, G., & Tuğrul, F. (2022). On some fundamental properties of α-interval valued fuzzy subgroups. Thermal Science, 26(Spec. Issue 2), 681–693.
- Bal, A., Çuvalcıoğlu, G., & Altıncı, C. (2023). (α, β)-Interval valued intuitionistic fuzzy sets defined on (α, β)-interval valued set. Journal of Universal Mathematics, 6(1), 114–130.
- Biswas, R. (1994). Rosenfeld’s fuzzy subgroups with interval-valued membership functions. Fuzzy Sets and Systems, 63(1), 87–90.
- Çuvalcıoğlu, G., Bal, A., & Çitil, M. (2022). The α-interval valued fuzzy sets defined on α-interval valued set. Thermal Science, 26(Spec. Issue 2), 665–679.
- Grattan-Guiness, I. (1976). Fuzzy membership mapped onto interval and many-valued quantities. Mathematical Logic Quarterly, 22(1), 149–160.
- Gorzałczany, M. B. (1983). Approximate inference with interval-valued fuzzy sets: An outline. Proceedings of the Polish Symposium on Interval and Fuzzy Mathematics, Poznan, 26–29 August 1983, 89–95.
- Gorzałczany, M. B. (1987). A method of inference in approximate reasoning based on interval-valued fuzzy set. Fuzzy Sets and Systems, 21(1), 1–17.
- Jahn, K. U. (1975). Intervall-wertige Mengen. Mathematische Nachrichten, 68, 115–132.
- Kang, H.-W., & Hur, K. (2010). Interval-valued fuzzy subgroups and rings. Honam Mathematical Journal, 32(4), 593–617.
- Li, X., & Wang G. (1996). TH-interval valued fuzzy subgroups. Journal of Lanzhou University, 32, 96–99.
- Li, X., & Wang, G. (2000). The SH-interval-valued fuzzy subgroups. Fuzzy Sets and Systems, 112(2), 319–325.
- Mondal, T. K., & Samanta, S. K. (1999). Topology of interval-valued fuzzy sets. Indian Journal of Pure and Applied Mathematics, 30(1), 20–38.
- Mondal, T. K., & Samanta, S. K. (2001). Topology of interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 119(3), 483–494.
- Pal, M., & Rashmanlou, H. (2013). Irregular interval-valued fuzzy graphs. Annals of Pure and Applied Mathematics, 3(1), 56–66.
- Rosenfeld, A. (1971). Fuzzy groups. Journal of Mathematical Analysis and Applications, 35(3), 512–517.
- Sambuc, R. (1975). Fonctions φ-floues. Application L’aide au Diagnostic en Pathologie Thyroidienne. Ph. D. Thesis, University of Marseille, France.
- Sharma, P. K. (2024). Intuitionistic fuzzy lattice ordered G-modules. Journal of Fuzzy Extension and Applications, 5(1), 141–158.
- Tarsuslu (Yılmaz), S. (2023). A study on intuitionistic fuzzy topological operators. Italian Journal of Pure and Applied Mathematics, 49, 863–875.
- Tarsuslu (Yılmaz), S. (2022). Intuitionistic fuzzy quasi-interior ideals in ordered Γ-semigroups. Annals of Oradea University, 29(1), 71–80.
- Tarsuslu (Yılmaz), S. & Çuvalcıoğlu, G. (2021). Intuitionistic fuzzy quasi-interior ideals of semigroups. Notes on Intuitionistic Fuzzy Sets, 27(4), 36–43.
- Turksen, I. (1986). Interval valued fuzzy sets based on normal forms. Fuzzy Sets and Systems, 20(2), 191–210.
- Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353.
- Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning–I. Information Sciences, 8(3), 199–249.
- Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning–II. Information Sciences, 8(4), 301–357.
- Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning–III. Information Sciences, 9(1), 43–80.
|
| Citations:
|
The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.
|
|