The authors present a unified approach to several concepts on generalized measures with various domains and ranges, which are: sigma -additive measures; probability measures of fuzzy events; fuzzy probability measures; fuzzy-valued fuzzy measures; ( sigma -) perpendicular to -decomposable measures; measures of fuzzy sets; and perpendicular to '-decomposable measures, where perpendicular to ' is the extension of an Archimedean t-conorm on (0,M) to D/sub M/ via the extension principle. All these measures are handled in a unified way. The main emphasis is on integral representations of such measures if they are defined on a collection of fuzzy sets.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
