M-fuzzifying normed vector spaces

In this paper, we introduce the concept of M-fuzzifying norm, which can be seen as a fuzzy co-norm. Fuzzy norm plays a key role in fuzzy functional analysis, which can be applied in theoretical computer science and information theory. We also present a characterization of M-fuzzifying norm using cut-sets. Furthermore, we prove that Morsi’s fuzzy norm and M-fuzzifying norm are equivalent when \(M=[0,1]\) $M=[0,1]$ . In addition, we show that an M-fuzzifying norm can induce an M-fuzzifying topology. Finally, we study an M-fuzzifying Banach space. We also study the boundedness of M-fuzzifying normed space. In particular, the mapping corresponding to the degree of fuzzifying boundedness is exactly an M-fuzzifying bornology.