By Michał Baczyński (auth.), Humberto Bustince, Javier Fernandez, Radko Mesiar, Tomasas Calvo (eds.)

ISBN-10: 3642391648

ISBN-13: 9783642391644

ISBN-10: 3642391656

ISBN-13: 9783642391651

This quantity collects the prolonged abstracts of forty five contributions of individuals to the 7th foreign summer season tuition on Aggregation Operators (AGOP 2013), held at Pamplona in July, 16-20, 2013. those contributions disguise a really huge variety, from the simply theoretical ones to these with a extra utilized concentration. furthermore, the summaries of the plenary talks and tutorials given on the related workshop are included.

Together they supply a superb evaluation of modern tendencies in examine in aggregation capabilities that are of curiosity to either researchers in Physics or arithmetic engaged on the theoretical foundation of aggregation capabilities, and to engineers who require them for applications.

**Read or Download Aggregation Functions in Theory and in Practise: Proceedings of the 7th International Summer School on Aggregation Operators at the Public University of Navarra, Pamplona, Spain, July 16-20, 2013 PDF**

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**Additional info for Aggregation Functions in Theory and in Practise: Proceedings of the 7th International Summer School on Aggregation Operators at the Public University of Navarra, Pamplona, Spain, July 16-20, 2013**

**Example text**

10) It can be proved that they are copulas and the following theorem holds. 26 A. Kolesárová Theorem 2. Let (c, d) be in Ω , c = 0. Then the only copula invariant with respect to the quadratic construction with coefficients (c, d) is the copula Cθ with θ = dc , given by (9) if θ ≤ 0, or by (10) if θ ≥ 1. On the other hand, each copula Cθ , θ ∈] − ∞, 0] ∪ [1, ∞[, is invariant with respect to the quadratic construction with an arbitrary pair of coefficients (c, d) ∈ Ω satisfying dc = θ . Note that solving the problem of invariantness of copulas wrt.

Durante of occurrence to the scenario in which many things go wrong at the same time – the perfect storm scenario [31]. For such problems, it is necessary to consider models with increasing dependencies in the tails, since a dramatic underestimation of the risk can be obtained when one tries to use copulas that do not exhibit any peculiar behaviour in the tails. This was exactly one of the main pitfalls of the criticized Li’s model (see [29]) for credit risk (see, for example, [26, 36]). In fact, as clarified, for instance, in [4], using Gaussian copulas (as Li did) “will always underestimate joint extremal events”.

Recall, for example, conic copulas [10], univariate conditioning method proposed in [15], UCS (univariate conditioning stable) copulas [8], a method proposed by Rodríguez–Lallena and Úbeda–Flores [17] and its generalization in [11], another method introduced by Aguilló et al. in [1], quadratic construction introduced in [13], several construction methods based on diagonal or horizontal (vertical) sections discussed in [5, 3, 7], etc. O. sk H. Bustince et al. 1007/978-3-642-39165-1_7, c Springer-Verlag Berlin Heidelberg 2013 39 40 R.

### Aggregation Functions in Theory and in Practise: Proceedings of the 7th International Summer School on Aggregation Operators at the Public University of Navarra, Pamplona, Spain, July 16-20, 2013 by Michał Baczyński (auth.), Humberto Bustince, Javier Fernandez, Radko Mesiar, Tomasas Calvo (eds.)

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