(2009-6152) 2-set-based extended functions

We generalize set-based extended functions, recently introduced by Mesiar et al., into 2-set-based extended functions. In both cases, an efficient reduction of repeated  data to be fused is considered which prepares a sound background for big data processing. We discuss and study several types of 2-set-based extended functions, in particular,  2-set-based extended aggregation functions, including t-norms, t-conorms, uninorms, nullnorms and OWA operators.