Aggregation functions on [0,1]

Abstract

After a brief presentation of the history of aggregation, we recall the concept of aggregation functions on [0; 1] and on a general interval /⊆ [—∞, ∞]. We give a list of basic examples as well as some peculiar examples of aggregation functions. After discussing the classification of aggregation functions on [0; 1] and presenting the prototypical examples for each introduced class, we also recall several construction methods for aggregation functions, including optimization methods, extension methods, constructions based on given aggregation functions, and introduction of weights. Finally, a remark on aggregation of more general inputs, such as intervals, distribution functions, or fuzzy sets, is added.