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On the fuzzy initial value problem. (English) Zbl 0643.34005
The paper deals with the initial value problem $x'(t)=f(t,x(t)),$ $x(0)=x\sb 0$ with fuzzy initial value and with deterministic or fuzzy function f. The discussion refers to two different approaches (the extension principle and the use of extremal solutions, respectively), and includes also generalizations to fuzzy integral equations and fuzzy functional differential equations.
Reviewer: V.C.Boffi

34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
Full Text: DOI
[1] Dubois, D.; Prade, H.: Towards fuzzy differential calculus. Part 1: integration of fuzzy mappings. Fuzzy sets and systems 8, 1-17 (1982) · Zbl 0493.28002
[2] Dubois, D.; Prade, H.: Towards fuzzy differential calculus. Part 2: integration on fuzzy intervals. Fuzzy sets and systems 8, 105-116 (1982) · Zbl 0493.28003
[3] Dubois, D.; Prade, H.: Towards fuzzy differential calculus. Part 3: differentiation. Fuzzy sets and systems 8, 225-233 (1982) · Zbl 0499.28009
[4] Ladas, G. E.; Lakshmikantham, V.: Differential equations in abstract spaces. (1972) · Zbl 0257.34002
[5] Mizumoto, M.; Tanaka, K.: The four operations of arithmetic on fuzzy numbers. Systems comput. Controls 7, 73-81 (1976)
[6] Piccinini, L. C.; Stampacchia, G.; Vidossich, G.: Ordinary differential equations in rn. (1984) · Zbl 0535.34001
[7] Puri, M.; Ralescu, D.: Differentials of fuzzy functions. J. math. Anal. appl. 91, 552-558 (1983) · Zbl 0528.54009
[8] Ralescu, D.: A survey of the representation of fuzzy concepts and its applications. Advances in fuzzy set theory and applications, 77-91 (1979)