<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper, we present an approach to data aggregation based on a generalization of the discrete Choquet integral by means of fusion functions. Inspired by Mesiar, R.-Kolesárová, A.-Bustince, G.-Pereira Dimuro, G.-Bedregal, B.: Fusion functions based discrete Choquet-like integrals, European J. Oper. Res. 252 (2016), 601-609, we merge information contained in capacities m of criteria sets and values of score vectors by a fusion function F instead of the product operator. We give the conditions under which fusion functions F yield well-defined functionals CFm and we also discuss properties of these functionals. Some examples for particular capacities m and particular fusion functions F are given.</abstract>

In this paper, we present an approach to data aggregation based on a generalization of the discrete Choquet integral by means of fusion functions. Inspired by Mesiar, R.-Kolesárová, A.-Bustince, G.-Pereira Dimuro, G.-Bedregal, B.: Fusion functions based discrete Choquet-like integrals, European J. Oper. Res. 252 (2016), 601-609, we merge information contained in capacities m of criteria sets and values of score vectors by a fusion function F instead of the product operator. We give the conditions under which fusion functions F yield well-defined functionals CFm and we also discuss properties of these functionals. Some examples for particular capacities m and particular fusion functions F are given.

Integration Based on Fusion Functions

Institute of Information Engineering, Automation and Mathematics Faculty of Chemical and Food Technology Slovak University of Technology in Bratislava, Radlinsk´eho 9 SK–812-37 Bratislava,

Department of Mathematics and Descriptive Geometry Faculty of Civil Engineering Slovak University of Technology in Bratislava Radlinského 11 SK–810-05 Bratislava,

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Integration Based on Fusion Functions"}

In this paper, we present an approach to data aggregation based on a generalization of the discrete Choquet integral by means of fusion functions. Inspired by...

Integration Based on Fusion Functions

Published Online: Jan 20, 2017

Page range: 51 - 66

Received: Jul 15, 2016

DOI: https://doi.org/10.1515/tmmp-2016-0019

Keywords
Choquet integral, capacity, fusion function, aggregation function, decision making

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Integration Based on Fusion Functions

Published Online: Jan 20, 2017

Page range: 51 - 66

Received: Jul 15, 2016

DOI: https://doi.org/10.1515/tmmp-2016-0019

KeywordsChoquet integral, capacity, fusion function, aggregation function, decision making

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Choquet integral, capacity, fusion function, aggregation function, decision making