Fuzzy Measures and Integrals: Recent Developments

Michel Grabisch (1, 2)

1 CES - Centre d'économie de la Sorbonne
2 PSE - Paris School of Economics

This paper surveys the basic notions and most important results around fuzzy measures and integrals, as proposed independently by Choquet and Sugeno, as well as recent developments. The latter includes bases and transforms on set functions, fuzzy measures on set systems, the notion of horizontal additivity, basic Choquet calculus on the nonnegative real line introduced by Sugeno, the extension of the Choquet integral for nonmeasurable functions, and the notion of universal integral.

Mots clés: fuzzy measure; capacity; Choquet integral; Sugeno integral

Domaines: Mathématique discrète [cs.DM]; Economies et finances

Michel Grabisch. Fuzzy Measures and Integrals: Recent Developments. D. E. Tamir and D. Rishe and A. Kande. Fifty Years of Fuzzy Logic and its Applications, 2015, ⟨10.1007/978-3-319-19683-1_8⟩. ⟨hal-01302377⟩