Ordinal sums of aggregation operators

Authors:
Bernard De Baets;Radko Mesiar
Affiliations:
Department of Applied Mathematics, Biometrics and Process Control, Faculty of Agricultural and Applied Biological Sciences, Ghent University, Coupure links 653, B-9000 Gent, Belgium;Department of Mathematics, Faculty of Applied Sciences, Slovak Technical University, Radlinského 11, SK-81368 Bratislava, Slovakia and Systems Research Institute, Polish Academy of Sciences, ...
Venue:
Technologies for constructing intelligent systems
Year:
2002

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Abstract

In this work, aggregation operators are to be understood in their most general sense, i.e. as families of operators, one for each arity. We characterize the smallest and greatest aggregation operators with a predefined behaviour in case all arguments are taken from the same interval (belonging to a system of pairwise disjoint open intervals). Similarly, we characterize the smallest and greatest idempotent aggregation operators with a predefined idempotent behaviour. Relationships with classical ordinal sum constructions are investigated.