Fuzzy Measures and Integrals: Recent Developments

Book section: 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.

Author(s)

Michel Grabisch

Scientific editor(s)
  • D. E. Tamir and D. Rishe and A. Kande
Title of the work
  • Fifty Years of Fuzzy Logic and its Applications
Date of publication
  • 2015
Keywords
  • Fuzzy measure
  • Capacity
  • Choquet integral
  • Sugeno integral
Version
  • 1