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

This quantity collects the prolonged abstracts of forty five contributions of members to the 7th overseas summer season tuition on Aggregation Operators (AGOP 2013), held at Pamplona in July, 16-20, 2013. those contributions hide a really huge diversity, from the only theoretical ones to these with a extra utilized concentration. additionally, the summaries of the plenary talks and tutorials given on the similar workshop are included.

Together they supply an exceptional review of modern developments in learn in aggregation features which are of curiosity to either researchers in Physics or arithmetic engaged on the theoretical foundation of aggregation services, 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**

**Sample text**

The function Cu,f ,gδ : [0, 1]2 → [0, 1] defined by f ,g ˆ gˆ f, (1 − x, 1 − y) , l,δˆ Cu,δ (x, y) = x + y − 1 + C (3) Semiquadratic Copulas 51 is a copula with diagonal section δ if and only if (i) f (0) = g(0) = 0 , (ii) max ( f (t) + (1 − t) | f (t)| , g(t) + (1 − t) |g (t)|) ≤ (iii) f (t) + g(t) ≥ (1 − t) 2t−1−δ (t) (1−t)2 t−δ (t) 1−t , , for all t ∈ [0, 1[ where the derivatives exist. The function Cu,f ,gδ defined by (3) is called an upper semiquadratic function with diagonal section δ . 2 Horizontal and Vertical Semiquadratic Copulas with a Given Diagonal Section Horizontal (resp.

For example, the copula Kδ , defined by Kδ (x, y) = min(x, y, (δ (x) + δ (y))/2), is the greatest symmetric copula with a given diagonal section δ [11] (see also [5, 7]). Moreover, the Bertino copula Bδ defined by Bδ (x, y) = min(x, y) − min{t − δ (t) | t ∈ [min(x, y), max(x, y)]} , is the smallest copula with a given diagonal section δ . Note that Bδ is symmetric. Similarly, the opposite diagonal section of a copula C is the function ωC : [0, 1] → [0, 1] defined by ωC (x) = C(x, 1 − x). e. for all x, x ∈ [0, 1], it holds that ω (x ) − ω (x) ≤ x − x .

Appl. Stoch. Models Bus. Ind. : Semilinear copulas. : New constructions of diagonal patchwork copulas. Inform. Sci. : On the construction of multivariate extreme value models via copulas. : Autocorrelation-based fuzzy clustering of time series. : No contagion, only interdependence: measuring stock market comovements. J. Financ. : The Bertino family of copulas. , Rodríguez-Lallena, J. ) Distributions with given Marginals and Statistical Modelling, pp. 81–91. , Härdle, W. ): Copulae in Mathematical and Quantitative Finance.