Download Aggregation Functions: A Guide for Practitioners by Gleb Beliakov PDF

By Gleb Beliakov

Aggregation of data is of basic value within the development of information established structures in quite a few domain names, starting from drugs, economics, and engineering to decision-making strategies, synthetic intelligence, robotics, and desktop studying. This ebook offers a extensive creation into the subject of aggregation features, and offers a concise account of the homes and the most periods of such services, together with classical capacity, medians, ordered weighted averaging services, 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 features. a specific awareness is paid to identity and development of aggregation capabilities from program particular requisites and empirical facts. This booklet presents scientists, IT experts and approach architects with a self-contained easy-to-use consultant, in addition to examples of computing device code and a software program package deal. it's going to facilitate building of determination aid, specialist, recommender, regulate and plenty of different clever systems.

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Xm ), y1 , . . , yn ). */ // Recursive method double fn(int n, double[] x, (double)f(double x, double y)) { if(n==2) return f(x[0],x[1]); else return f(fn(n-1,x,f),x[n-1]); } // Non-recursive method double fn(int n, double[] x, (double)f(double x, double y)) { double s=f(x[0],x[1]); for(i=2;i

2xn − 1) + 1 . 15) f [−1,1] (x1 , . . 6 How to choose an aggregation function There are infinitely many aggregation functions. They are grouped in various families, such as means, triangular norms and conorms, Choquet and Sugeno integrals, and many others. The question is how to choose the most suitable aggregation function for a specific application. Is one aggregation function 32 1 Introduction enough, or should different aggregation functions be used in different parts of the application? There are two components to the answer.

5 Continuity and stability We will be mostly interested in continuous aggregation functions, which intuitively are such functions that a small change in the input results in a small change in the output. 13 There are some interesting aggregation functions that are discontinuous, but from the practical point of view continuity is very important for producing a stable output. The next definition is an even stronger continuity requirement. The reason is that simple, or even uniform continuity is not sufficient to distinguish functions that produce a “small” change in value due to a small change of the argument 14 .

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