Choquet-like integrals with respect to level-dependent capacities and ϕ -ordinal sums of aggregation function

Radko Mesiar; Peter Smrek

Kybernetika (2015)

  • Volume: 51, Issue: 3, page 420-432
  • ISSN: 0023-5954

Abstract

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In this study we merge the concepts of Choquet-like integrals and the Choquet integral with respect to level dependent capacities. For finite spaces and piece-wise constant level-dependent capacities our approach can be represented as a ϕ -ordinal sum of Choquet-like integrals acting on subdomains of the considered scale, and thus it can be regarded as extension method. The approach is illustrated by several examples.

How to cite

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Mesiar, Radko, and Smrek, Peter. "Choquet-like integrals with respect to level-dependent capacities and $\varphi $-ordinal sums of aggregation function." Kybernetika 51.3 (2015): 420-432. <http://eudml.org/doc/271612>.

@article{Mesiar2015,
abstract = {In this study we merge the concepts of Choquet-like integrals and the Choquet integral with respect to level dependent capacities. For finite spaces and piece-wise constant level-dependent capacities our approach can be represented as a $\varphi $-ordinal sum of Choquet-like integrals acting on subdomains of the considered scale, and thus it can be regarded as extension method. The approach is illustrated by several examples.},
author = {Mesiar, Radko, Smrek, Peter},
journal = {Kybernetika},
keywords = {Choquet integral; Choquet-like integral; level-dependent capacity; $\varphi $-ordinal sum of aggregation functions; Choquet integral; Choquet-like integral; level-dependent capacity; $\varphi $-ordinal sum of aggregation functions},
language = {eng},
number = {3},
pages = {420-432},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Choquet-like integrals with respect to level-dependent capacities and $\varphi $-ordinal sums of aggregation function},
url = {http://eudml.org/doc/271612},
volume = {51},
year = {2015},
}

TY - JOUR
AU - Mesiar, Radko
AU - Smrek, Peter
TI - Choquet-like integrals with respect to level-dependent capacities and $\varphi $-ordinal sums of aggregation function
JO - Kybernetika
PY - 2015
PB - Institute of Information Theory and Automation AS CR
VL - 51
IS - 3
SP - 420
EP - 432
AB - In this study we merge the concepts of Choquet-like integrals and the Choquet integral with respect to level dependent capacities. For finite spaces and piece-wise constant level-dependent capacities our approach can be represented as a $\varphi $-ordinal sum of Choquet-like integrals acting on subdomains of the considered scale, and thus it can be regarded as extension method. The approach is illustrated by several examples.
LA - eng
KW - Choquet integral; Choquet-like integral; level-dependent capacity; $\varphi $-ordinal sum of aggregation functions; Choquet integral; Choquet-like integral; level-dependent capacity; $\varphi $-ordinal sum of aggregation functions
UR - http://eudml.org/doc/271612
ER -

References

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