Download Aggregation Functions by Grabisch M., Marichal J.-L., Mesiar R., Pap E. PDF

By Grabisch M., Marichal J.-L., Mesiar R., Pap E.

Aggregation is the method of mixing numerous numerical values right into a unmarried consultant price, and an aggregation functionality plays this operation. those capabilities come up anywhere aggregating info is critical: utilized and natural arithmetic (probability, information, selection concept, sensible equations), operations learn, laptop technological know-how, and plenty of utilized fields (economics and finance, development acceptance and photograph processing, info fusion, etc.). it is a complete, rigorous and self-contained exposition of aggregation capabilities. sessions of aggregation services lined contain triangular norms and conorms, copulas, ability and averages, and people in response to nonadditive integrals. The homes of every approach, in addition to their interpretation and research, are studied intensive, including building equipment and functional id tools. unique consciousness is given to the character of scales on which values to be aggregated are outlined (ordinal, period, ratio, bipolar). it's an excellent creation for graduate scholars and a special source for researchers

Show description

Read Online or Download Aggregation Functions PDF

Best nonfiction_11 books

Macroscopic Ocular Pathology: An Atlas Including Correlations with Standardized Echography

At the present time, ophthalmic pathology bargains increasingly more with pathogenesis utilizing hugely refined ideas. In contemporary many years, it has ex­ panded to such an volume that it now fills numerous volumes of a contemporary complete atlas or textbook. Black and white prints of the macroscopic visual appeal of dissected eyes are typical in smooth textbooks.

Applications of Liquid Crystals

Over the last ten years liquid crystals have attracted a lot curiosity and huge development has been made with admire to our wisdom during this box. the new improvement was once initiated frequently through the paintings of J. L. Fergason and G. H. Heilmeier, who mentioned the significance of liquid crystals for thermographic and electro­ optic purposes.

Copper and Silver Halates

Copper and Silver Halates is the 3rd in a sequence of 4 volumes on inorganic steel halates. This quantity provides serious reviews and compilations for halate solubilities of the gang II metals. The solubility information integrated during this quantity are these for the 5 compounds, copper chlorate and iodate, and silver chlorate, bromate and iodate

Models of Neural Networks: Temporal Aspects of Coding and Information Processing in Biological Systems

Because the visual appeal of Vol. 1 of types of Neural Networks in 1991, the speculation of neural nets has excited about paradigms: details coding via coherent firing of the neurons and useful suggestions. details coding via coherent neuronal firing exploits time as a cardinal measure of freedom.

Extra resources for Aggregation Functions

Example text

In this latter setting, strong bisymmetry seems very natural as well. Obviously, for any strongly bisymmetric extended function F : ∪n∈N In → I, each n-ary function F(n) is bisymmetric. Moreover, we have the following result [284]. 84. If F : ∪n∈N In → I is strongly decomposable and idempotent then it is strongly bisymmetric. In particular F(2) is bisymmetric. Proof. For the sake of understanding, let us first prove that F(2) is bisymmetric. 76) = F F(x1 , x3 ), F(x2 , x4 ), F(x1 , x3 ), F(x2 , x4 ) = F F(x1 , x3 ), F(x2 , x4 ) (strong decomposability) (strong idempotency).

For any countable set K, we let SK denote the set of all permutations on K. For any A ⊆ K and any σ ∈ SK , we set σ(A) := {σ(a) | a ∈ A}. • For any permutation σ ∈ S[n] , we set Inσ := {x ∈ In | xσ(1) ··· xσ(n) }. • Given an n-tuple x and a permutation σ ∈ S[n] , we set [x]σ := (xσ(1) , . . , xσ(n) ). • The identity function x → x is denoted by id. • For any number r ∈ R, we set r + := Max(r, 0) = r ∨ 0, and r − := Max(−r, 0) = (−r) ∨ 0. We then have r = r + − r − and |r| = r + + r − , where |r| denotes the absolute value of r.

Decomposability Introduced first in Bemporad [33, p. 87] in a characterization of the arithmetic mean, associativity of means has been used by Kolmogoroff [236] and Nagumo [330] to characterize the so-called mean values. More recently, Marichal and Roubens [289] proposed to call this property “decomposability" in order not to confuse it with classical associativity. Alternative names, such as associativity with repetitions or weighted associativity, could be naturally considered as well. When symmetry is not assumed, it is necessary to rewrite this property in such a way that the first variables are not privileged.

Download PDF sample

Rated 4.64 of 5 – based on 35 votes