Aggregation functions are generally defined and used to combine several numerical values into a single one, so that the final result of the aggregation takes into account all the individual values in a given manner. Such functions are widely used in many well-known disciplines such as statistics, economics, finance, and computer science. For general background, see Grabisch et al. [52]. For ins...

This article studies a large class of averaging aggregation functions based on minimizing a distance from the vector of inputs, or equivalently, minimizing a penalty imposed for deviations of individual inputs from the aggregated value. We provide a systematization of various ty es of penalty based aggregation functions, and show how many special cases arise as the result. We show how new aggre...

The aim of this contribution is to find a common framework for parametric characterization of aggregation functions exploiting the notions of unipolar and bipolar parametric characterization, and also unify the ideas of global and local parametric characterization. We revise the known approaches to classification of aggregation functions in special classes in this framework, and also propose so...

Aggregation functions are mathematical operators that merge given data in order to obtain a global value that preserves the information given by the data as much as possible. In most practical applications, this value is expected to be between the infimum and the supremum of the given data, which is guaranteed only when the aggregation functions are idempotent. Ordered weighted averaging (OWA) ...

The two-parts state-of-art overview of aggregation theory summarizes the essential information concerning aggregation issues. Overview of aggregation properties is given, including the basic classification of aggregation functions. In this first part, the stress is put on means, i.e., averaging aggregation functions, both with fixed arity (n-ary means) and with open arity (extended means).

A new method to construct aggregation functions is introduced. These aggregation functions are called biconic aggregation functions with a given diagonal (resp. opposite diagonal) section and their construction method is based on linear interpolation on segments connecting the diagonal (resp. opposite diagonal) of the unit square and the points (0, 1) and (1, 0) (resp. (0, 0) and (1, 1)). Speci...

In face recognition, one of the most important problems to tackle is a large amount of data and the redundancy of information contained in facial images. There are numerous approaches attempting to reduce this redundancy. One of them is information aggregation based on the results of classifiers built on selected facial areas being the most salient regions from the point of view of classificati...

the traditional fuzzy operators, such as t-norms, t-conorms and averaging operators have been used for soil suitability evaluation to aggregate criteria as an overall suitability index. however, such operators do not account for the degree of compensation common to human aggregation criteria, especially in the presence of conflicting criteria. fuzzy integrals are powerful and flexible aggregati...