Acknowledgement
The authors would like to thank the anonymous reviewers for their constructive suggestion and helpful comments, which enabled us to improve the presentation of our work.
References
- Akram M.: Spherical fuzzy K-algebras. Journal of Algebraic Hyperstructures and Logical Algebras 2 (2021), no. 3, 85-98. DOI:10.52547/HATEF.JAHLA.2.3.7
- Akram M., Davvaz B. & Feng F.: Intutionistic fuzzy soft K-algebras. Mathematics in Computer science 7 (2013), no. 3, 353-365. DOI:10.1007/s11786-013-0158-5
- A. Borumand Saeid, M. Murali Krishna Rao & K.R. Kumar: Γ-BCK Algebras. J. of Mahani Mathematical Research 11 (2022), no. 3, 133-145. DOI:10.22103/JMMR.2022.19322.1234
- Dar K.H. & Akram M.: On K-homomorphisms of K-algebras. International Mathematical Forum 2 (2007), no. 46, 2283-2293. https://doi.org/10.12988/imf.2007.07203
- Huang Y.S.: BCI-Algebra. Science Press, Beijing, China, (2006).
- K. Iseki: On BCI-algebras. Kobe University, Mathematics Seminar Notes 8 (1980), no. 1, 125-130 .
- K. Iseki & S. Tanaka: An introduction to the theory of BCK-algebras. Mathematica Japonica 23 (1978), no. 1, 1-26.
- Y. Imai & K. Iseki: On axiom systems of propositional calculi, XIV. Proceedings of the Japan Academy 42 (1966) 19-22. DOI:10.3792/pja/1195522169
- K. Iseki: An algebra related with a propositional calculus. Proceedings of the Japan Academy 42 (1966) 26-29. DOI:10.3792/pja/1195522171
- J.M. Jie & Y.B. Jun: BCK-Algebras. Kyung Moon Sa Co., Seoul, Republic of Korea, (1994).
- J. Meng & X.E. Guo: On fuzzy ideals in BCK/BCI-algebras. Fuzzy sets and Systems 149 (2005), no. 3, 509-525. https://doi.org/10.1016/j.fss.2003.11.014
- M. Murali Krishna Rao: Γ-semirings-I. Southeast Asian Bull. of Math. 19 (1995), no. 1, 49-54.
- M. Murali Krishna Rao: Γ-Field. Disc. Math. General Alg. and Appli. 39 (2019), 125-133. https://doi.org/10.7151/dmgaa.1303
- M. Murali Krishna Rao: Γ-Inclines. Bulletin Int. Math. Virtual Inst. 10 (2020), no. 2, 305-314. DOI:10.7251/BIMVI2002305R
- M. Murali Krishna Rao: Γ-Group. Bulletin Int. Math. Virtual Inst. 10 (2020), no. 1, 51-58. DOI:10.7251/BIMVI2001051R
- M. Murali Krishna Rao: A study of Γ-semiring as a generalization of soft semiring (F, Γ) over M. Bulletin Int. Math. Virtual Inst. 8 (2018), 533-541. DOI:10.7251/BIMVI1803533R
- A. Rosenfeld: Fuzzy groups. J. Math. Anal. Appl. 35 (1971), no. 3, 512-517. https://doi.org/10.1016/0022-247X(71)90199-5
- M.K. Sen: On Γ-semigroup. Proc. of Inter. Con. of Alg. and its Appl., Decker Publicaiton, New York (1981) 301-308.
- L.A. Zadeh: Fuzzy sets. Information and control 8 (1965), no. 3, 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X