Approximate evaluations based on aggregation functions

Aggregation of real-valued evaluations of elements x, y from a set U is investigated in order to find an approximate evaluation of the composition of x and y performed by a binary operation defined on U. The notions of a lower bound and an upper bound of an evaluation function with respect to a binary operation are introduced and illustrated with examples. Approximate evaluations of composite concepts described by the union of granules of a finite fuzzy set are studied in detail.