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On fuzzy differential equations. (English) Zbl 0719.54007
This paper is just an extension of another work by the first author [J. Math. Anal. Appl. 129, 346-361 (1988; Zbl 0645.54009)] where the authors equipped the space of regular fuzzy sets on a Banach space with uniform topology, embedded it into a locally convex topological vector space and then introduced a calculus for fuzzy mappings. Here, the authors present an existence and uniqueness theorem for the solution of fuzzy differential equations satisfying certain Lipschitz condition.
Reviewer: S.Saha

54A40Fuzzy topology
34G99ODE in abstract spaces
Full Text: DOI
[1] Jr., S. B. Nadler: Hyperspaces of sets. (1978)
[2] Ouyang, He: Topological properties of the spaces of regular fuzzy sets. J. math. Anal. appl. 129, 346-361 (1988) · Zbl 0645.54009
[3] Radstrom, H.: An embedding theorem for spaces of convex sets. Proc. amer. Math. soc. 3, 165-169 (1952) · Zbl 0046.33304
[4] Rudin, W.: Functional analysis. (1973) · Zbl 0253.46001
[5] Peizhuang, Wang; Sanchez, E.: Treating a fuzzy subset as a projectable random subset. Fuzzy information and decision processes (1982) · Zbl 0516.94035