Integrals of random fuzzy sets (Q882938)

The paper presents a unified and systematic investigation of integration of random fuzzy sets. The mostly accepted approach is the so called Aumann-integral introduced by \textit{M. L. Puri} and \textit{D. A. Ralescu} [J. Math. Anal. Appl. 114, 409--422 (1986; Zbl 0592.60004)]. Another approach has been initialized by \textit{P. Diamond} and \textit{P. Kloeden} [Fuzzy Sets Syst. 35, No. 2, 241--249 (1990; Zbl 0704.54006)] which allows an embedding of random fuzzy sets into the general probability theory in Banach spaces. Therefore, as an alternative to Aumann-integral, an adaption of Bochner- and Pettis-integration can be considered. The author discusses mutual relationships of these competing concepts. He completes and improves former results from literature and presents, as a by product, strong laws of large numbers and central limit theorems for random fuzzy sets which are based on weaker assumptions than previous versions from literature.