A survey on generalized measures

The authors present a unified approach to several concepts on generalized measures with various domains and ranges, which are: σ-additive measures; probability measures of fuzzy events; fuzzy probability measures; fuzzy-valued fuzzy measures; (σ-) ⊥-decomposable measures; measures of fuzzy sets; and ⊥´-decomposable measures, where ⊥´ is the extension of an Archimedean t-conorm on [0,M] to D_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