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See detailAn axiomatic approach of the discrete Sugeno integral as a tool to aggregate interacting criteria in a qualitative framework
Marichal, Jean-Luc UL

in IEEE Transactions on Fuzzy Systems (2001), 9(1), 164-172

We present a model allowing to aggregate decision criteria when the available information is of a qualitative nature. The use of the Sugeno integral as an aggregation function is justified by an axiomatic ... [more ▼]

We present a model allowing to aggregate decision criteria when the available information is of a qualitative nature. The use of the Sugeno integral as an aggregation function is justified by an axiomatic approach. It is also shown that the mutual preferential independence of criteria reduces the Sugeno integral to a dictatorial aggregation. [less ▲]

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See detailAn axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria
Marichal, Jean-Luc UL

in IEEE Transactions on Fuzzy Systems (2000), 8(6), 800-807

The most often used operator to aggregate criteria in decision making problems is the classical weighted arithmetic mean. In many problems however, the criteria considered interact, and a substitute to ... [more ▼]

The most often used operator to aggregate criteria in decision making problems is the classical weighted arithmetic mean. In many problems however, the criteria considered interact, and a substitute to the weighted arithmetic mean has to be adopted. We show that, under rather natural conditions, the discrete Choquet integral is an adequate aggregation operator that extends the weighted arithmetic mean by the taking into consideration of the interaction among criteria. The axiomatic that supports the Choquet integral is presented and an intuitive approach is proposed as well. [less ▲]

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See detailA characterization of the ordered weighted averaging functions based on the ordered bisymmetry property
Marichal, Jean-Luc UL; Mathonet, Pierre UL

in IEEE Transactions on Fuzzy Systems (1999), 7(1), 93-96

This paper deals with a characterization of a class of aggregation operators. This class concerns operators which are symmetric, increasing, stable for the same positive linear transformations and present ... [more ▼]

This paper deals with a characterization of a class of aggregation operators. This class concerns operators which are symmetric, increasing, stable for the same positive linear transformations and present a property close to the bisymmetry property: the ordered bisymmetry property. It is proved that the class investigated contains exactly the ordered weighted averaging operators (OWA) introduced by Yager in 1988. [less ▲]

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See detailCharacterization of the ordered weighted averaging operators
Fodor, Janos; Marichal, Jean-Luc UL; Roubens, Marc

in IEEE Transactions on Fuzzy Systems (1995), 3(2), 236-240

This paper deals with the characterization of two classes of monotonic and neutral (MN) aggregation operators. The first class corresponds to (MN) aggregators which are stable for the same positive linear ... [more ▼]

This paper deals with the characterization of two classes of monotonic and neutral (MN) aggregation operators. The first class corresponds to (MN) aggregators which are stable for the same positive linear transformations and presents the ordered linkage property. The second class deals with (MN)-idempotent aggregators which are stable for positive linear transformations with the same unit, independent zeroes and ordered values. These two classes correspond to the weighted ordered averaging operator (OWA) introduced by Yager in 1988. It is also shown that the OWA aggregator can be expressed as a Choquet integral. [less ▲]

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