Read e-book online Aggregation Functions in Theory and in Practise: Proceedings PDF
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 time tuition on Aggregation Operators (AGOP 2013), held at Pamplona in July, 16-20, 2013. those contributions disguise a truly huge diversity, from the merely 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 an exceptional review of contemporary 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 resources 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
For p = (M, M, −1, f , f ), it holds (7) Cp (x, y) = max (0, M(x, y) − M(x − δ (x), y − δ (y))). Applying formula (5) considering N = f , one gets C f (x, y) = max (0, x ∧ y − f (x ∨ y)) = max (0, δ (x ∨ y) − |x − y|) = CδMT (x, y), where CδMT is a Mayor–Torrens copula  derived from the diagonal section δ . On the other hand, Cp given by formula (7) for diagonal sections of 3 basic copulas W, Π , M yields copulas W,Cq , M, where q = (M, M, −1, fΠ , fΠ ), fΠ (x) = x · (1 − x). Observe that the copula Cq : [0, 1]2 → [0, 1] is described in Fig.
Starting with these, we present some new clustering procedures for extreme scenario. Such a methodology is grounded on the conditional (Spearman’s) correlation coefficient between time series. It aims at creating cluster of time series that are homogeneous, in the sense that they tend to be comonotone in their extreme low values (where the degree of extremeness is specified by a given threshold). The results have been discussed in details in  and are expected to be useful for portfolio management in crisis periods.
For all x ∈ [0, 1], it holds that C(x, 0) = C(0, x) = 0, C(x, 1) = C(1, x) = x ; 2. be H. Bustince et al. 1007/978-3-642-39165-1_8, c Springer-Verlag Berlin Heidelberg 2013 47 48 T. Jwaid, B. De Baets, and H. De Meyer VC ([x, x ] × [y, y ]) := C(x, y) + C(x , y ) − C(x, y ) − C(x , y) ≥ 0 . VC ([x, x ] × [y, y ]) is called the C-volume of the rectangle [x, x ] × [y, y ]. The copulas M and W , defined by M(x, y) = min(x, y) and W (x, y) = max(x + y − 1, 0), are called the Fréchet–Hoeffding upper and lower bounds: for any copula C it holds that W ≤ C ≤ M.
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.)