Discrete Integrals and Axiomatically Defined Functionals

Abstract

Several discrete universal integrals on finite universes are discussed from an axiomatic point of view. We start from the first attempt due to B. Riemann and cover also most recent approaches based on level dependent capacities. Our survey includes, among others, the Choquet and the Sugeno integral and general copula-based integrals.

Keywords

• capacity
• Choquet integral
• copula
• fuzzy integral
• OWA operator
• OMA operator
• Sugeno integral