An existence theorem for a fuzzy functional integral equation. (English) Zbl 0888.45006

The paper deals with an integral equation for multivalued transformations using the Aumann integral [cf. R. J. Aumann, J. Math. Anal. Appl. 12, 1-12 (1965; Zbl 0163.06301)] and Krasnoselskij’s fixed point theorem [cf. D. R. Smart, Fixed point theorems (1974; Zbl 0297.47042)]. Results are formulated in the setting of fuzzy functions [cf. D. Dubois and H. Prade, Fuzzy sets and systems (1980; Zbl 0444.94049)].
The proof of Theorem 3.1 contains many irritating misprints.


45G10 Other nonlinear integral equations
03E72 Theory of fuzzy sets, etc.
28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections
46S40 Fuzzy functional analysis