C1 fuzzy manifolds

Mario Ferraro, David H. Foster

    Research output: Contribution to journalArticlepeer-review


    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 languageEnglish
    Pages (from-to)99-106
    Number of pages7
    JournalFuzzy Sets and Systems
    Issue number1
    Publication statusPublished - 25 Feb 1993


    • fuzzy differentiation
    • fuzzy manifold
    • Fuzzy topology
    • tangent vector space


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