Abstract
An overview of various integrals is given which can be defined on arbitrary monotone set functions vanishing in the empty set (called here monotone measures). Our survey not only includes the Choquet integral [G. Choquet, Ann. Inst. Fourier (Grenoble) 5 (1954)], the Shilkret integral [N. Shilkret, Indag. Math. 33 (1971)] and the Sugeno integral [M. Sugeno, PhD thesis, Tokyo Institute of Technology (1974)] and some of their properties, but also some more general and more recent concepts as universal integrals [E. P. Klement, R. Mesiar, and E. Pap, IEEE Trans. Fuzzy Systems 18 (2010)] and decomposition integrals [Y. Even and E. Lehrer, Econom. Theory 56 (2014)], together with some of their properties, such as integral inequalities and convergence theorems.
| Original language | English |
|---|---|
| Pages (from-to) | 88-102 |
| Number of pages | 15 |
| Journal | Fuzzy Sets and Systems |
| Volume | 281 |
| DOIs | |
| Publication status | Published - 15 Dec 2015 |
Fields of science
- 101 Mathematics
- 101013 Mathematical logic
- 101024 Probability theory
- 102001 Artificial intelligence
- 102003 Image processing
- 102019 Machine learning
- 603109 Logic
- 202027 Mechatronics
JKU Focus areas
- Computation in Informatics and Mathematics
- Mechatronics and Information Processing
- Nano-, Bio- and Polymer-Systems: From Structure to Function