# zbMATH — the first resource for mathematics

On the fuzzy initial value problem. (English) Zbl 0643.34005
The paper deals with the initial value problem $$x'(t)=f(t,x(t)),$$ $$x(0)=x_ 0$$ 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

##### MSC:
 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
Full Text:
##### References:
  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  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  Dubois, D.; Prade, H., Towards fuzzy differential calculus. part 3: differentiation, Fuzzy sets and systems, 8, 225-233, (1982) · Zbl 0499.28009  Ladas, G.E.; Lakshmikantham, V., Differential equations in abstract spaces, (1972), Academic Press New York · Zbl 0257.34002  Mizumoto, M.; Tanaka, K., The four operations of arithmetic on fuzzy numbers, Systems comput. controls, 7, 73-81, (1976)  Piccinini, L.C.; Stampacchia, G.; Vidossich, G., Ordinary differential equations in $$R$$^n, (1984), Springer New York-Berlin · Zbl 0535.34001  Puri, M.; Ralescu, D., Differentials of fuzzy functions, J. math. anal. appl., 91, 552-558, (1983) · Zbl 0528.54009  Ralescu, D., A survey of the representation of fuzzy concepts and its applications, (), 77-91
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.