## International Journal of Neutrosophic Science

##### Journal DOI

https://doi.org/10.54216/IJNS

2690-6805ISSN (Online) 2692-6148ISSN (Print)

Volume 19 , Issue 1 , PP: 60-67, 2022 | Cite this article as | XML | Html | PDF | Full Length Article

### Application of MBJ - Neutrosophic Set on Filters of Incline Algebra

Surya M. 1 * , P. Muralikrishna 2

• 1 Research Department of Mathethematics, Muthurangam Govt. Arts College (A), Vellore. TN, India - (suryamano95@gmail.com)
• 2 Research Department of Mathethematics, Muthurangam Govt. Arts College (A), Vellore. TN, India - (pmkrishna@rocketmail.com)
• Doi: https://doi.org/10.54216/IJNS.190104

Received: March 29, 2022 Accepted: September 02, 2022
##### Abstract

The concept of fuzzy set has been generalized to many kinds and one among them is neutrosophic set which is

a developed from intuitionistic fuzzy set by adding a components called indeterminate function between truth

and falsity membership function. This neutrosophic set also moved a step forward and shows a variation in

indeterminate function alone as an interval valued indeterminate function and other functions remains same

and this is named as MBJ - neutrosophic set. Here, this work on the MBJ - neutrosophic set merged with

incline algbera and introduces the idea of MBJ - neutrosophic filter of an incline algebraic structure and is

engrossing with several results. Also, the level, cartesian product, projection, characteristic function and chain

conditions are also disputed.

##### Keywords :

Incline algebra , Filter, MBJ - neutrosophic set , MBJ - neutrosophic filter , the level , projection and

product on MBJ - neutrosophic filter.

##### References

[1] Ahn, S.S., Jun, Y.B., Kim, H.S., Ideals and Quotients of Incline Algebras, Comm. Koren Math. Soc.,

16(4), 573 - 583, 2001.

[2] Arvinda Raju, V., A Note on Incline Algebras, International Journal of Mathematical Archive, 8(9), 154

- 157, 2017.

[3] Atanassov, K.T., Intuitionistic fuzzy sets, Fuzzy sets and systems, 20(1), 87 - 96, 1986.

[4] Jun, Y.B., Ahn, S.S, Kim, Fuzzy Subincline(Ideals) of Incline Algebras, Fuzzy Sets and Systems, 123,

217 - 255, 2001.

[5] Kim, K.H., Roush, F.W., Inclines of algebraic structures, Fuzzy Sets and Systems, 72, 189 - 196, 1995.

[6] Kim, K.H., Roush, F.W., Markowsky, G., Representation of Incline Algebras, Algebra Coll, 4 , 461 -

470, 1997.

[7] Muralikrishna, P., Surya, M., MBJ- Neutrosophic β - Ideal of β - algebra, Neutrosophic Sets and Systems,

University of New Mexico, 35, 100 - 118, 2020.

[8] Smarandache, F., Neutrosophic Set, A generalization of Intuitionistic fuzzy sets, International Journal of

Pure and Applied Mathematics, 24(5), 287 - 297, 2005.

[9] Surya, M., Muralikrishna, P., On MBJ – Neutrosophic β – subalgebra, Neutrosophic Sets and Systems,

28, 216 – 227, 2019.

[10] Talkalloo, M.M., Jun, Y.B., MBJ – Neutrosophic Structures and its applications in BCK /BCI – algebra,

Neutrosophic Sets and System, 23, 72 – 84, 2018.

[11] Volety, V.S., Ramachandram, On some properties of Inclines, Journal of Science & Arts, 1(18), 13 - 16,

2012.

[12] Wang, F.X., Interval - valued subincline of Incline Algebras, Mathematics in Pratice and Theory, 47(24),

289 - 293, 2018.

[13] Yao, W. and Song - Chol Han, On Ideals, filters and congruences in inclines, Bull Korean Math. Soc.,

46(3), 591 - 598, 2009.

[14] Zadeh, L.A., Fuzzy Sets, Information and Control, 8(3), 338 - 353, 1965.

[15] Zhan, J., Xueling, Ma., Intuitionistic fuzzy ideals of Incline algebras, Scientiae Mathematicae Japonicae

online, 85 - 90, e - 2005.

[16] Zhan, J., Xueling, MA., Doubt Fuzzy Subincline(ideals) of Incline algebras, Scientiae Mathematicae

Japonicae Online, 193 - 198, e - 2004.