Extension of fuzzy measures through the monotone expectation.
ISSN: 0210-7821
Année de publication: 1987
Volumen: 11
Número: 2-3
Pages: 75-92
Type: Article
D'autres publications dans: Stochastica: revista de matemática pura y aplicada
Résumé
The monotone expectation is defined as a functional over fuzzy measures on finite sets. The functional is based on Choquet functional over capacities and its more relevant properties are proved, including the generalization of classical mathematical expectation and Dempster's upper and lower expectations of an evidence. In second place, the monotone expectation is used to define measures of fuzzy sets. Such measures are compared with the ones based on Sugeno integral. Finally, we prove a generalization of the Sugeno bound for probabilities to the whole body of fuzzy measures.