Abstract
This study considers four means of defining differential operators for extracting local aspects of shape in ill-specified environments: fuzzy differentiation as kernel smoothing; differentiation in the sense of weak or generalized derivatives; differentiation for fuzzy functions between normed spaces; and fuzzy differentiation for mappings between fuzzy manifolds. More consideration is given to the last, norm-free approach, which involves the notions of an abstract fuzzy topological vector space, fuzzy differentiation between fuzzy topological vector spaces, fuzzy atlases, and tangent vectors of fuzzy manifolds.
| Original language | English |
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| Title of host publication | Shape in Picture: Mathematical Description of Shape in Grey-level Images |
| Place of Publication | Berlin |
| Publisher | Springer Nature |
| Pages | 319-332 |
| Number of pages | 14 |
| Publication status | Published - 1994 |