Document Type : Research Paper


1 PG and Research Department of Mathematics, Muthurangam Government Arts College (Autonomus), Vellore-632002, Tamilnadu, India.

2 Department of Applied Mathematics, Ayandegan Institute of Higher Education, Tonekabon, Iran.

3 Department of CIS, Stillman College, Tuscaloosa, Alabama, USA.


An effective and flexible method for encoding ambiguous data is using cubic sets. The concept of incline algebraic sub-structure is considered and is interlinked with the notation of the cubic set to define cubic subincline. The sense of cubic sub incline of algebra is established with relevant results. Additionally, the results such as homomorphic image, preimage, cartesian product and level sets of cubic sub incline are worked out in this study, and several of its associated findings were looked into.


Main Subjects

  • Ahn, S. S., Jun, Y. B., & Kim, H. S. (2001). Ideals and quotients of incline algebras. Communications-Korean mathematical society16(4), 573-584.
  • Ahn, S. S., Kim, Y. H., & Ko, J. M. (2014). Cubic subalgebras and filters of CI-algebras. Honam mathematical journal36(1), 43-54.
  • Cao, Z. Q., Roush, F. W., & Kim, K. H. (1984). Incline algebra and applications. Ellis Horwood, Ltd.
  • Jun, Y. B., Kim, C. S., & Yang, K. O. (2012). Cubic sets. Annals of fuzzy mathematics and informatics4(1), 83-98.
  • Jun, Y. B., Jung, S. T., & Kim, M. S. (2011). Cubic subgroups. Annals of fuzzy mathematics and informatics, 2(1), 9-15.
  • Jun, Y. B., Kim, C. S., & Kang, M. S. (2010). Cubic subalgebras and ideals of BCK/BCI-algebras. Far east journal of mathematical sciences44(2), 239-250.
  • Jun, Y. B., Ahn, S. S., & Kim, H. S. (2001). Fuzzy subinclines (ideals) of incline algebras. Fuzzy sets and systems123(2), 217-225.
  • Kim, K. H., & Roush, F. W. (1995). Inclines of algebraic structures. Fuzzy sets and systems72(2), 189-196.
  • Kim, K. H., Roush, F. W., & Markowsky, G. (1997). Representation of incline algebras. Algebra colloquium, 4(4), 461-470.
  • Prakasam, M., Saeid, A. B., Vinodkumar, R., & Palani, G. (2022). An overview of cubic intuitionistic β− subalgebras. Proyecciones journal of mathematics41(1), 23-44.
  • Prakasam, M., Davvaz, B., Vinodkumar, R., & Palani, G. (2020). Applications of cubic level set on β-subalgebras. Advances in mathematics: scientific journals9(3), 1359-1365.
  • Renugha, M., Sivasakthi, M., & Chellam, M. (2014). Cubic BF-algebra. International journal of innovative research in advanced engineering1(7), 48-52.
  • Prakasam, M. (2022). Application of MBJ-neutrosophic set on filters of incline algebra. International journal of neutrosophic science (IJNS)19(1), 60-67.
  • Arvinda Raju, V. (2017). A note on incline algebras. International journal of mathematical archive8(9), 154-157.
  • Wang, F. (2018). Intuitionistic anti-fuzzy subincline of incline. 2018 3rd international conference on communications, information management and network security (CIMNS 2018)(pp. 96-100). Atlantis Press.
  • Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353.
  • Rosenfeld, A. (1971). Fuzzy groups. Journal of mathematical analysis and applications35(3), 512-517.
  • Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy sets and systems, 20(1), 87-96.