Aggregation Functions: A Guide for Practitioners by Gleb Beliakov

By Gleb Beliakov

Aggregation of data is of fundamental value within the building of information dependent platforms in a variety of domain names, starting from drugs, economics, and engineering to decision-making techniques, man made intelligence, robotics, and computer studying. This ebook provides a huge creation into the subject of aggregation capabilities, and gives a concise account of the houses and the most periods of such features, together with classical potential, medians, ordered weighted averaging capabilities, Choquet and Sugeno integrals, triangular norms, conorms and copulas, uninorms, nullnorms, and symmetric sums. It additionally provides a few cutting-edge innovations, many graphical illustrations and new interpolatory aggregation services. a selected recognition is paid to identity and building of aggregation services from software particular necessities and empirical facts. This e-book offers scientists, IT experts and method architects with a self-contained easy-to-use advisor, in addition to examples of computing device code and a software program package deal. it's going to facilitate development of selection help, professional, recommender, keep an eye on and lots of different clever systems.

Show description

Read Online or Download Aggregation Functions: A Guide for Practitioners PDF

Similar intelligence & semantics books

Programming the Semantic Web

I stopped studying via bankruptcy 6 up to now. .. my total effect is, moderate, yet believe inadequate.

There are a few dialogue i admire: for instance, the easy triple shop implementation is illustrative, inspiration clever. even if, the dialogue on RDF serialization structure, the instance given, ontology, it simply feels the phrases are not easy to swallow. you are going to imagine a e-book approximately semantic must have very specified common sense and rationalization may be crystal transparent. in spite of the fact that, as I learn it, I frequently get the texture anything . .. "this might be this tough to provide an explanation for, what's he speaking approximately the following? " . .. probably i'm anticipating an excessive amount of.

Symbolic dynamics. One-sided, two-sided and countable state Markov shifts

This can be a thorough advent to the dynamics of one-sided and two-sided Markov shifts on a finite alphabet and to the elemental homes of Markov shifts on a countable alphabet. those are the symbolic dynamical platforms outlined via a finite transition rule. the elemental houses of those structures are validated utilizing straight forward tools.

Machine Learning: An Artificial Intelligence Approach

The power to benefit is without doubt one of the such a lot basic attributes of clever habit. for that reason, growth within the concept and computing device modeling of study­ ing procedures is of serious importance to fields enthusiastic about knowing in­ telligence. Such fields comprise cognitive technological know-how, man made intelligence, infor­ mation technological know-how, development acceptance, psychology, schooling, epistemology, philosophy, and similar disciplines.

Principles of Noology: Toward a Theory and Science of Intelligence

The belief of this bookis toestablish a brand new clinical self-discipline, “noology,” below which a collection of primary ideas are proposed for the characterization of either evidently happening and synthetic clever structures. The method followed in ideas of Noology for the characterization of clever platforms, or “noological systems,” is a computational one, very like that of AI.

Additional resources for Aggregation Functions: A Guide for Practitioners

Sample text

N ), input x we do not expect the output f (˜ x) to be substantially different from f (x). The Lipschitz constant M bounds the factor by which the noise is magnified. 59. Since f (0) = 0 and f (1) = 1, the Lipschitz √ constant of any aggregation function is M ≥ 1/||1||. For p-norms we have ||1|| = p n · 1 ≤ 1, that is M ≥ n−1/p , so in principle M can be smaller than 1. 60 (p-stable aggregation functions). Given p ≥ 1, an aggregation function is called p-stable if its Lipschitz constant in the p-norm || · ||p is 1.

3) Both the measure of orness and the average orness value are 12 for weighted arithmetic means, and later we will see that both quantities coincide for OWA functions. 2. 2 Classical means Means are often treated synonymously with averaging functions. , [40]) excludes certain types of averaging functions, which have been developed quite recently, in particular ordered weighted averaging and various integrals. , some Gini means) lack monotonicity, and therefore are not aggregation functions. Following the tradition, in this section we will concentrate on various classical means, and present other types of averaging, or mean-type functions in separate sections.

1 × 2 × 3 × . . × n possible permutations of (1, 2, . . , n). We will denote a vector whose components are arranged in the order given by a permutation P by xP = (xP (1) , xP (2) , . . , xP (n) ). In our example, xP = (x5 , x3 , x2 , x1 , x4 ). We will frequently use the following special permutations of the components of x. 18. We denote by x the vector obtained from x by arranging its components in non-decreasing order, that is, x = xP where P is the permutation such that xP (1) ≤ xP (2) ≤ .

Download PDF sample

Rated 4.02 of 5 – based on 32 votes