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

By Gleb Beliakov

ISBN-10: 3540737200

ISBN-13: 9783540737209

A wide creation to the subject of aggregation features is to be present in this booklet. It additionally presents a concise account of the houses and the most periods of such capabilities. a few cutting-edge innovations are offered, besides many graphical illustrations and new interpolatory aggregation services. specific realization is paid to identity and building of aggregation features from program particular standards and empirical information.

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Extra resources for Aggregation Functions: A Guide for Practitioners

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Xn ). Thus bivariate associative aggregation functions univocally define extended aggregation functions. 39. The product, minimum and maximum are associative aggregation functions. The arithmetic mean is not associative. Associativity simplifies calculation of aggregation functions, and it effectively allows one to easily aggregate any number of inputs, as the following code on Fig. 2 illustrates. It is not the only way of doing this (for instance the arithmetic or geometric means are also easily computed for any number of inputs).

The following definition puts a bound on the actual change in value due to changes in the input. 13 A real function of n arguments is continuous if for any sequences {xij }, i = 1, . . , n such that lim xij = yi it holds lim f (x1j , . . xnj ) = f (y1 , . . , yn ). Bej→∞ 14 j→∞ cause the domain [0, 1]n is a compact set, continuity is equivalent to its stronger version, uniform continuity. , we can check continuity by fixing all variables but one, and checking continuity of each univariate function.

75 (Sugeno integral). 11) where x = (x(1) , x(2) , . . , x(n) ) is a non-decreasing permutation of the input x, and Hi = {(i), . . , (n)}. , when v(Hi ) = v(|Hi |) depends only on the cardinality of the set Hi ), Sugeno integral becomes the median Sv (x) = M ed(x1 , . . , xn , 1, v(n − 1), v(n − 2), . . , v(1)). 6 Conjunctive and disjunctive functions The prototypical examples of conjunctive and disjunctive aggregation functions are so-called triangular norms and conorms respectively (t-norms and t-conorms).

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