Abstract
This paper introduces the notion of a C1 fuzzy manifold as a natural development of the notions of a fuzzy topological vector space and of a fuzzy derivative of a fuzzy continuous mapping between fuzzy topological vector spaces. First, a fuzzy atlas of class C1 on a set is constructed and shown to yield a fuzzy topology that is compatible with the fuzzy atlas. The structure of a C1 fuzzy manifold on the set then follows. Next, it is shown that the product of two fuzzy manifolds is a fuzzy manifold, and that the composition of two fuzzy differentiable mappings between fuzzy manifolds is fuzzy differentiable. Finally, the notions of a tangent vector and of a tangent space at a point in a fuzzy manifold are formulated, and the tangent space is shown to be a vector space. © 1993.
| Original language | English |
|---|---|
| Pages (from-to) | 99-106 |
| Number of pages | 7 |
| Journal | Fuzzy Sets and Systems |
| Volume | 54 |
| Issue number | 1 |
| Publication status | Published - 25 Feb 1993 |
Keywords
- fuzzy differentiation
- fuzzy manifold
- Fuzzy topology
- tangent vector space