Chaos in iterated fuzzy systems (Q1332226)

This paper can be considered as a natural continuation of previous works [e.g., the author and \textit{P. E. Kloeden}, Fuzzy Sets Syst. 29, No. 3, 341-348 (1989; Zbl 0661.54011); \textit{P. E. Kloeden} and \textit{A. I. Mees}, Bull. Math. Biol. 47, 697-738 (1985; Zbl 0586.92002)]. Using the well known principle of G. Darbo, the author gives a fixed point theorem in a suitable metric space of fuzzy sets. Sufficient conditions for chaos of fuzzy mappings are presented relaxing the hypothesis of compactness. Indeed an example of a noncompact chaotic mapping is given in the last section.