A generalization of universal integrals by means of level dependent capacities

Authors:
Erich Peter Klement;Anna KolesáRová;Radko Mesiar;Andrea StupňAnová
Affiliations:
Department of Knowledge-Based Mathematical Systems, Johannes Kepler University, Linz, Austria;Institute of Information Engineering, Automation and Mathematics, Faculty of Chemical and Food Technology, Slovak University of Technology, Bratislava, Slovakia;Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovakia and Centre of Excellence IT4Innovations, Division University ...;Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovakia
Venue:
Knowledge-Based Systems
Year:
2013

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Abstract

An axiomatic approach to universal integrals based on level dependent capacities is presented. Based on a given semicopula, two corresponding extremal universal integrals based on level dependent capacities are given. If the underlying semicopula is even a copula, another class of universal integrals based on level dependent capacities is studied, generalizing, among others, both the Choquet and the Sugeno integral based on level dependent capacities which were introduced recently.