Intuitionistic fuzzy (bifuzzy) BCK-algebras under norms
*Rasul RasuliCorresponding authorRasuli@pnu.ac.irDepartment of Mathematics Payame Noor University (PNU) P. O. Box 19395-3697Tehran, Iran0000-0003-3755-5790View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 16 May 2023
- Published Online:
- 20 May 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1780
- Pages:
- 1315–1334
Abstract
Keywords
Subject Classifications
References
[1] Mohammad Tairab Abu Osman, On some products of fuzzy subgroups, Fuzzy Sets and Systems, vol. 24, pp. 79–86, 1987.
[2] Krassimir T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol. 20, pp. 87–96, 1986.
[3] Krassimir T. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol. 61, pp. 137–142, 1994.
[4] James J. Buckley and Esfandiar Eslami, An Introduction to Fuzzy Logic and Fuzzy Sets, Berlin, Germany: Springer-Verlag, 2002.
[5] Yosiyuki Imai and Katsumi Iseki, On axioms of proportional calculi XIV, Proceedings of the Japan Academy, vol. 42, pp. 19–22, 1966.
[6] Young Bae Jun, A note on fuzzy ideals in BCK-algebras, Mathematica Japonica, vol. 42, no. 2, pp. 233–235, 1995.
[7] Young Bae Jun, Finite valued fuzzy ideals in BCK-algebras, Journal of Fuzzy Mathematics, vol. 5, no. 1, pp. 111–114, 1997.
[8] Young Bae Jun, Characterizations of Noetherian BCK-algebras via fuzzy ideals, Fuzzy Sets and Systems, vol. 108, no. 2, pp. 231–234, 1997.
[9] Young Bae Jun, Seong Min Hong, Seong Joo Kim, and Sang Zi Song, Fuzzy ideals and fuzzy subalgebras of BCK-algebras, Journal of Fuzzy Mathematics, vol. 7, no. 2, pp. 411–418, 1999.
[10] Young Bae Jun and Eun Hee Roh, Fuzzy commutative ideals of BCK-algebras, Fuzzy Sets and Systems, vol. 64, no. 3, pp. 401–405, 1994.
[11] Young Bae Jun and Kyung Hoon Kim, Intuitionistic fuzzy ideals of a BCK-algebras, International Journal of Mathematics and Mathematical Sciences, vol. 24, no. 12, pp. 839–849, 2000.
[12] Dharam S. Malik and John N. Mordeson, Fuzzy Commutative Algebra, Singapore: World Scientific Publishing Co. Pte. Ltd., 1995.
[13] Jian Meng, Young Bae Jun, and Hyeon Sook Kim, Fuzzy implicative ideals of BCK-algebras, Fuzzy Sets and Systems, vol. 89, no. 2, pp. 243–248, 1997.
[14] Rahim Rasuli, Norms over intuitionistic fuzzy subrings and ideals of a ring, Notes on Intuitionistic Fuzzy Sets, vol. 22, no. 5, pp. 72–83, 2016.
[15] Rahim Rasuli, Characterization of Q-fuzzy subrings (Anti Q-fuzzy subrings) with respect to a T-norm (T-conorm), Journal of Information and Optimization Sciences, vol. 39, no. 4, pp. 1–12, 2018.
[16] Rahim Rasuli, Fuzzy subgroups over a T-norm, Journal of Information and Optimization Sciences, vol. 39, pp. 1757–1765, 2018.
[17] Rahim Rasuli, Fuzzy congruence on product lattices under T-norms, Journal of Information and Optimization Sciences, vol. 42, no. 2, pp. 333–343, 2021.
[18] Rahim Rasuli, Intuitionistic fuzzy congruences on product lattices under norms, Journal of Interdisciplinary Mathematics, vol. 24, no. 5, pp. 1281–1304, 2021.
[19] Rahim Rasuli, Normalization, commutativity and centralization of TFSM(G), Journal of Discrete Mathematical Sciences and Cryptography, vol. 26, no. 5, pp. 1027–1050, 2023.
[20] Rahim Rasuli, Intuitionistic fuzzy G-modules with respect to norms (T and S), Notes on Intuitionistic Fuzzy Sets, vol. 29, no. 3, pp. 277–291, 2023.
[21] Rahim Rasuli, Intuitionistic fuzzy complex subgroups with respect to norms (T and S), Journal of Fuzzy Extension and Application, vol. 4, no. 2, pp. 92–114, 2023.
[22] B. Satyanarayana and R. Durga Prasad, Some results on intuitionistic fuzzy ideals in BCK-algebras, General Mathematics Notes, vol. 4, no. 1, pp. 1–15, 2011.
[23] B. Satyanarayana, U. B. Madhavi, and R. Durga Prasad, On intuitionistic fuzzy H-ideals in BCK-algebras, International Journal of Algebra, vol. 4, no. 15, pp. 743–749, 2010.
[24] B. Satyanarayana, E. V. Koteswara Rao, and L. Krishna, On intuitionistic fuzzy BCK-algebras, ANU Journal of Physical Sciences, vol. 1, no. 2, pp. 21–32, 2009.
[25] Seyed Mohammad Seyedjoula, Ali Gilani, and Ebrahim Arfa, Exact BCK-sequence in BCK-algebra, Journal of Information and Optimization Sciences, vol. 41, no. 4, pp. 1153–1162, 2020.
[26] Lotfi A. Zadeh, Fuzzy sets, Information and Control, vol. 8, pp. 338–353, 1965.
