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M-fuzzifying normed vector spaces.
- Source :
- Computational & Applied Mathematics; Jun2024, Vol. 43 Issue 4, p1-15, 15p
- Publication Year :
- 2024
-
Abstract
- 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 ] . 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01018205
- Volume :
- 43
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Computational & Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 177312507
- Full Text :
- https://doi.org/10.1007/s40314-024-02697-4