Some Basic Properties of QIFSN(G)
Abstract
In this paper, as using norms (T and C), we introduce the concepts of strongest relations, cosets and middle cosets of Q-intuitionistic fuzzy subgroups and prove some simple but elegant results about them. Also we discuss few results of them under homomorphism as well as anti homomorphism.
References
Abu Osman, M. T. (1987). On some products of fuzzy subgroups. Fuzzy Sets and Systems, 24(1), 79-86. https://doi.org/10.1016/0165-0114(87)90115-1
Anthony, J. M., & Sherwood, H. (1977). Fuzzy groups redefined. Journal of Mathematical Analysis and Application, 69(1), 124-130. https://doi.org/10.1016/0022-247x(79)90182-3
Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87-96. https://doi.org/10.1016/s0165-0114(86)80034-3
Atanassov, K. T. (1994). New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets and Systems, 61(2), 137-142. https://doi.org/10.1016/0165-0114(94)90229-1
Buckley, J. J., & Eslami, E. (2002). An introduction to fuzzy logic and fuzzy sets. Springer-Verlag Berlin Heidelberg GmbH.
Rasuli, R., & Narghi, H. (2019). T-norms over Q-fuzzy subgroups of groups. Jordan Journal of Mathematics and Statistics (JJMS), 12(1), 1-13.
Rasuli, R. (2020). Anti Q-fuzzy subgroups under T-conorms. Earthline Journal of Mathematical Sciences, 4(1), 13-28. https://doi.org/10.34198/ejms.4120.1328
Rasuli, R. (2021). Conorms over conjugates and generalized characteristics of anti Q-fuzzy subgroups. In The Third national Conference on Management and Fuzzy Systems. University of Eyvanekey, Iran, Eyvanekey.
Rasuli, R. (2021). Conorms over level subsets and translations of anti Q-fuzzy subgroups. International Journal of Mathematics and Computation, 32(2), 55-67.
Rasuli, R. (2022). Fuzzy d-algebras under t-norms. Eng. Appl. Sci. Lett. (EASL), 5(1), 27-36.
Rasuli, R. (2022). T-fuzzy subgroups and normal T-fuzzy subgroups of bigroups. Journal of Ramannujan Society of Mathematics and Mathematical Sciences, 9(2), 165-184.
Rasuli, R. (2022). Intuitionistic fuzzy BCI-algebras (implicative ideals, closed implicative ideals, commutative ideals) under norms. Mathematical Analysis and its Contemporary Applications, 4(3), 17-34. https://doi.org/10.1109/icsai57119.2022.10005393
Rasuli, R. (2022). T-conorms over anti-fuzzy subgroups on direct product of groups. Annals of Mathematics and Computer Science, 10, 8-18.
Rasuli, R. (2023). Norms over intuitionistic fuzzy subgroups on direct product of groups. Communications in Combinatorics, Cryptography, and Computer Science, 1, 39-54.
Rasuli, R. (2023). T-norms over complex fuzzy subgroups. Mathematical Analysis and its Contemporary Applications, 5(1), 33-49.
Rasuli, R. (2023). Norms over Q-intuitionistic fuzzy subgroups of a group. Notes on Intuitionistic Fuzzy Sets, 29(1), 30-45. https://doi.org/10.7546/nifs.2023.29.1.30-45
Rasuli, R. (2023). Anti fuzzy multigroups and t-conorms. In 2nd National Conference on Soft Computing and Cognitive Science, Conbad Kavous University, Minudasht, Iran.
Rasuli, R. (2023). T-fuzzy subalgebras of BCI-algebras. International Journal of Open Problems in Computer Mathematics, 16(1), 55-72.
Rasuli, R. (2023). Norms over Q-intuitionistic fuzzy subgroups of a group. Notes on Intuitionistic Fuzzy Sets, 29(1), 30-45. https://doi.org/10.7546/nifs.2023.29.1.30-45
Rasuli, R. (2023). Fuzzy ideals of BCI-algebras with respect to t-norm. Mathematical Analysis and its Contemporary Applications, 5(5), 39-50.
Rasuli, R. (2023). Intuitionistic fuzzy complex subgroups with respect to norms (T and S). Journal of Fuzzy Extension and Application, 4(2), 92-114.
Rasuli, R. (2023). Anti fuzzy d-algebras and t-conorms. In 2nd National Conference on Soft Computing and Cognitive Science, Conbad Kavous University, Minudasht, Iran.
Rasuli, R. (2023). Normality and translation of $IFS(G times Q)$ under norms. In 26th International Conference on Intuitionistic Fuzzy Sets, Sofia, Bulgaria. https://doi.org/10.7546/nifs.2023.29.2.114-132
Rasuli, R. (2023). Some properties of fuzzy algebraic structures of $QIFSN (G)$. In 4th International Conference on Computational Algebra, Computational Number Theory and Applications, CACNA2023, University of Kashan, Iran.
Solairaju, A., & Nagarajan, R. (2009). A new structure and constructions of Q-fuzzy group. Advances in Fuzzy Mathematics, 4, 23-29.
Yuan, X. H., & Lee, E. S. (1977). A fuzzy algebraic system based on the theory of falling shadows. Journal of Mathematical Analysis and Application, 208(1), 243-251. https://doi.org/10.1006/jmaa.1997.5331
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353.
This work is licensed under a Creative Commons Attribution 4.0 International License.
.jpg){kind=logo}
