By Michał Baczyński (auth.), Humberto Bustince, Javier Fernandez, Radko Mesiar, Tomasas Calvo (eds.)
This quantity collects the prolonged abstracts of forty five contributions of contributors to the 7th foreign summer time institution on Aggregation Operators (AGOP 2013), held at Pamplona in July, 16-20, 2013. those contributions hide a truly extensive variety, from the merely 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 a very good review of modern tendencies in examine in aggregation services that 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.
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Extra 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
Proposition 1. Let N : [0, 1] → [0, 1] be a strong negation such that it is 1–Lipschitz on the interval [e, 1]. Then the function CN : [0, 1]2 → [0, 1] given by CN (x, y) = max (0, x ∧ y − N(x ∨ y)) (1) is a copula. Inspired by the form of the Farlie–Gumbel–Morgenstern copulas (FGM–copulas) CλFGM (x, y) = x · y + λ x · y · (1 − x) · (1 − y), (2) where λ ∈ [−1, 1], Kim et al. have studied in  the constraints for λ so that the function C : [0, 1]2 → [0, 1] given by C(x, y) = C∗ (x, y) + λ f (x) · g(y) (3) is a copula, where C∗ is an a priori given copula, f , g : [0, 1] → [0, 1] are Lipschitz continuous functions satisfying f (0) = g(0) = f (1) = g(1) = 0.
Multivariate hierarchical copulas with shocks. Methodol. Comput. Appl. Probab. : Spatial contagion between financial markets: a copula-based approach. 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.
Thus Cr is not a copula. 42 R. Mesiar, J. Komorník, and M. Komorníková Fig. 1 Formulae for the copula Cq We open a problem of characterizing all diagonal sections δ of bivariate semicopulas such that the formula (7) yields a copula. Note also that if a function Cp given by (7) is a copula, then Cq with q = (M, M, λ , f , f ) is a copula for any λ ∈ [−1, 0]. , consider a function Cp : [0, 1]2 → [0, 1] given by Cp (x, y) = max (0,C(x, y) − C(N(x), N(y))) . , Cp is a semicopula [2, 4]. For arbitrary Frank copula  and the standard negation Ns : [0, 1] → [0, 1] given by Ns (x) = 1 − x, we see that Cp = W is a copula.