Aggregation of preferences, criteria or similarities happens at various stages in recommender systems. Typically such aggregation is done by using either the arithmetic mean or maximum/minimum functions. Many other aggregation functions which would deliver flexibility and adaptability towards more relevant recommendations are often overlooked. In this chapter we will review the basics of aggreg...

The aim of this contribution is to present the concept of unipolar parametric evaluation of aggregation functions, and unify the ideas of global and local unipolar parametric evaluations. We show that several well–known parameters introduced in special classes of aggregation functions are included in this framework, and we also propose some new parameters for aggregation functions.

This paper presents the role of copula functions in the theory of aggregation operators and an axiomatic characterization of Archimedean aggregation functions. In this context we are focusing our attention about several properties of aggregation functions, like supermodularity and Schur-concavity.

This paper offers a comprehensive study of information aggregation in intelligent systems prompted by common engineering interest. After a motivating introduction we consider aggregation functions and their fundamental properties as a basis for further development. Four main classes of aggregation functions are identified, and important subclasses are described and characterized as prototypes. ...

Given a finite set F of functions and a learning sample, the aim of an aggregation procedure is to have a risk as close as possible to risk of the best function in F . Up to now, optimal aggregation procedures are convex combinations of every elements of F . In this paper, we prove that optimal aggregation procedures combining only two functions in F exist. Such algorithms are of particular int...

Current SQL aggregation functions have evident limitations for computing percentages, for which this paper proposes two SQL aggregation functions. The two novel aggregation functions are easy to use, which have wide applicability and can be efficiently evaluated. They may be used as a framework to study percentage queries and to generate efficient SQL code. Experiments compare our proposed perc...

Aggregation functions and utility functions belong to very interesting parts of modern decision making theory. We develop basic concept of the connection of aggregation functions theory and utility theory to determine gross annual premium in general insurance. We introduce specific values of the gross annual premium on the basis of aggregation of the person’s utility functions which were determ...

This paper investigates the optimisation of aggregation functions in the context of computationally complete database programming languages and aims to generalise and provide a unifying formal foundation for previous work. We deene a `fold' operator over collection types in terms of which operations such as selection, projection, join and group-by can be deened, as well as aggregation functions...

The choice of an aggregation function is a common problem in Multi Attribute Decision Making (MADM) systems. The Method of Imprecision (MoI) is a formal theory for the manipulation of preliminary design information that represents preferences among design alternatives with the mathematics of fuzzy sets. The MoI formulates the preliminary design problem as a MADM problem. To date, two aggregatio...