## 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.

### MSC:

 2.8e+11 Fuzzy measure theory

### Keywords:

aggregation operator; Choquet integral
Full Text:

### References:

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