Invariant Aggregation and Pre-aggregation Functions

In this contribution, we introduce special transformations of fusion functions closely related to ratio scale, difference scale and interval scale invariant fusion functions. In particular, we show that in the case of aggregation functions the obtained transforms need not be aggregation functions but they are always pre-aggregation functions. We also provide sufficient conditions for constructing aggregation functions which are ratio scale, difference scale or interval scale invariant. We illustrate the obtained results applying the introduced transformations to the basic fuzzy integrals. It is shown that only the Choquet integral is invariant with respect to all studied transformations.