The extension theorem of F-measure spaces
A fuzzy \(\sigma\)-algebra of fuzzy subsets is a special \(\sigma\)-complete, distributive lattice equipped with an order reversing involution, and a fuzzy measure is a positive \(\sigma\)-continuous valuation on a given fuzzy \(\sigma\)-algebra. The author proves two different extension theorems: The first theorem is a generalization of the Caratheodory extension of ordinary masure spaces to fuzzy measure spaces, the second one is an extension theorem of fuzzy measures from a fuzzy \(\sigma\)- algebra \({\mathcal A}\) to the normal extension of \({\mathcal A}\) which uses in a crucial way a representation theorem of fuzzy probability measures due to \textit{E. P. Klement, R. Lowen} and \textit{W. Schwyhla} [cf. Fuzzy Sets Syst. 5, 21-30 (1981; Zbl 0447.28005)].
fuzzy \(\sigma\)-algebra of fuzzy subsets
scientific article; zbMATH DE number 3863525