1 Affiliation : Research Department of Mathethematics, Muthurangam Govt. Arts College (A), Vellore. TN, India
Email : firstname.lastname@example.org
2 Affiliation : Research Department of Mathethematics, Muthurangam Govt. Arts College (A), Vellore. TN, India
Email : email@example.com
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.
Incline algebra; Filter , MBJ - neutrosophic set; MBJ - neutrosophic filter; the level; projection and
product on MBJ - neutrosophic filter.
 Ahn, S.S., Jun, Y.B., Kim, H.S., Ideals and Quotients of Incline Algebras, Comm. Koren Math. Soc.,
16(4), 573 - 583, 2001.
 Arvinda Raju, V., A Note on Incline Algebras, International Journal of Mathematical Archive, 8(9), 154
- 157, 2017.
 Atanassov, K.T., Intuitionistic fuzzy sets, Fuzzy sets and systems, 20(1), 87 - 96, 1986.
 Jun, Y.B., Ahn, S.S, Kim, Fuzzy Subincline(Ideals) of Incline Algebras, Fuzzy Sets and Systems, 123,
217 - 255, 2001.
 Kim, K.H., Roush, F.W., Inclines of algebraic structures, Fuzzy Sets and Systems, 72, 189 - 196, 1995.
 Kim, K.H., Roush, F.W., Markowsky, G., Representation of Incline Algebras, Algebra Coll, 4 , 461 -
 Muralikrishna, P., Surya, M., MBJ- Neutrosophic β - Ideal of β - algebra, Neutrosophic Sets and Systems,
University of New Mexico, 35, 100 - 118, 2020.
 Smarandache, F., Neutrosophic Set, A generalization of Intuitionistic fuzzy sets, International Journal of
Pure and Applied Mathematics, 24(5), 287 - 297, 2005.
 Surya, M., Muralikrishna, P., On MBJ – Neutrosophic β – subalgebra, Neutrosophic Sets and Systems,
28, 216 – 227, 2019.
 Talkalloo, M.M., Jun, Y.B., MBJ – Neutrosophic Structures and its applications in BCK /BCI – algebra,
Neutrosophic Sets and System, 23, 72 – 84, 2018.
 Volety, V.S., Ramachandram, On some properties of Inclines, Journal of Science & Arts, 1(18), 13 - 16,
 Wang, F.X., Interval - valued subincline of Incline Algebras, Mathematics in Pratice and Theory, 47(24),
289 - 293, 2018.
 Yao, W. and Song - Chol Han, On Ideals, filters and congruences in inclines, Bull Korean Math. Soc.,
46(3), 591 - 598, 2009.
 Zadeh, L.A., Fuzzy Sets, Information and Control, 8(3), 338 - 353, 1965.
 Zhan, J., Xueling, Ma., Intuitionistic fuzzy ideals of Incline algebras, Scientiae Mathematicae Japonicae
online, 85 - 90, e - 2005.
 Zhan, J., Xueling, MA., Doubt Fuzzy Subincline(ideals) of Incline algebras, Scientiae Mathematicae
Japonicae Online, 193 - 198, e - 2004.