Erich Klement, Radko Mesiar,
"Monotone measures-based integrals"
, in Janusz Kacprzyk, Witold Pedrycz: Springer Handbook of Computational Intelligence, Springer, Berlin, Heidelberg, Seite(n) 75-88, 2015, ISBN: 978-3-662-43504-5
Monotone measures-based integrals
Sprache des Titels:
Springer Handbook of Computational Intelligence
The theory of classical measures and integral reflects the genuine property of several quantities in standard physics and/or geometry, namely the ?-additivity. Though monotone measures not assuming
?-additivity appeared naturally in models
extending the classical ones (for example, inner and outer measures, where the related integral was considered by Vitali already in 1925), their intensive research was initiated in the past 40 years by the computer science applications in areas
reflecting human decisions, such as economy,
psychology, multicriteria decision support, etc. In this chapter, we summarize basic types of monotone measures together with the basic monotone measures-based integrals, including the Choquet and Sugeno integrals, and we introduce the concept of universal integrals proposed by Klement
et al. to give a common roof for all mentioned integrals. Benvenuti?s integrals linked to semicopulas are shown to be a special class of universal integrals. Up to several other integrals, we also introduce
decomposition integrals due to Even and
Lehrer, and show which decomposition integrals are inside the framework of universal integrals.