Affiliations: [a] Department of Mathematics, Hazara University, Mansehra, Khyber Pakhtunkhwa, Pakistan | [b] Department of Basic Sciences, Riphah International University, Islamabad, Pakistan
Correspondence:
[*]
Correspondence to: Saleem Abdullah, Assistant Professorat
Department of Mathematics, Hazara University, Mansehra,Khyber Pakhtunkhwa, Pakistan.
E-mails: saleemabdullah81@yahoo.com, saleem@math.qau.edu.pk (S. Abdullah); afawada@gmail.com (Ahmad Fawad Ali).
Abstract: In this paper, we formulate the notion of N-fuzzy filters in a BE-algebras and discussed some connected assets. We define N-fuzzy filter, N-Level filters, N-fuzzy implicative filter and their results. We discuss a characterization of N-fuzzy implicative filters of a BE-algebras in terms of N-fuzzy level filters. We also observe that every N-fuzzy implicative filter of a BE-algebra is a N-fuzzy filter but the converse is not true in general. We give some equivalent conditions of N-fuzzy filter of a BE-algebra to become a N-fuzzy implicative filter. An extension property of N-fuzzy implicative filters is also studied. The properties of homomorphic images of N-fuzzy implicative filters are studied. Finally, we study some properties of the cartesian product of N-fuzzy implicative filters in BE-algebras.
