Möbius fitting aggregation operators. (English) Zbl 1265.28042

Summary: Standard Möbius transform evaluation formula for the Choquet integral is associated with the \(\min \)-aggregation. However, several other aggregation operators replacing \(\min \) operator can be applied, which leads to a new construction method for aggregation operators. All binary operators applicable in this approach are characterized by the 1-Lipschitz property. Among ternary aggregation operators all 3-copulas are shown to be fitting and moreover, all fitting weighted means are characterized. This new method allows to construct aggregation operators from simpler ones.


28E10 Fuzzy measure theory
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