ET-Lipschitzian aggregation operators

Lipschitzian and kernel aggregation operators with respect to the natural Tindistinguishability operator ET and their powers are studied. A t-norm T is proved to be ET -lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an archimedean t-norm T with additive generator t, the quasi-arithmetic mean generated by t is proved to be the more stable aggregation operator with respect to T.Peer ReviewedPostprint (published version

Aggregation operators and lipschitzian conditions

Lipschitzian aggregation operators with respect to the natural T - indistin- guishability operator Et and their powers, and with respect to the residuation ! T with respect to a t-norm T and its powers are studied. A t-norm T is proved to be E T -Lipschitzian and -Lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an Archimedean t-norm T with additive generator t , the quasi- arithmetic mean generated by t is proved to be the most stable aggregation operator with respect to TPeer Reviewe

ET-lipschitzian and ET-kernel aggregation operators

AbstractLipschitzian and kernel aggregation operators with respect to natural T-indistinguishability operators ET and their powers are studied. A t-norm T is proved to be ET-lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an archimedean t-norm T with additive generator t, the quasi-arithmetic mean generated by t is proved to be the most stable aggregation operator with respect to T

Aggregation functions: Means

The two-parts state-of-art overview of aggregation theory summarizes the essential information concerning aggregation issues. Overview of aggregation properties is given, including the basic classification of aggregation functions. In this first part, the stress is put on means, i.e., averaging aggregation functions, both with fixed arity (n-ary means) and with open arity (extended means).

The full Keller--Segel model is well-posed on fairly general domains

In this paper we prove the well-posedness of the full Keller-Segel system, a quasilinear strongly coupled reaction-crossdiffusion system, in the spirit that it always admits a unique local-in-time solution in an adequate function space, provided that the initial values are suitably regular. Apparently, there exists no comparable existence result for the full Keller-Segel system up to now. The proof is carried out for general source terms and is based on recent nontrivial elliptic and parabolic regularity results which hold true even on fairly general spatial domains, combined with an abstract solution theorem for nonlocal quasilinear equations by Amann

The full Keller-Segel model is well-posed on fairly general domains

In this paper we prove the well-posedness of the full Keller-Segel system, a quasilinear strongly coupled reaction-crossdiffusion system, in the spirit that it always admits a unique local-in-time solution in an adequate function space, provided that the initial values are suitably regular. Apparently, there exists no comparable existence result for the full Keller-Segel system up to now. The proof is carried out for general source terms and is based on recent nontrivial elliptic and parabolic regularity results which hold true even on fairly general spatial domains, combined with an abstract solution theorem for nonlocal quasilinear equations by Amann. Nous considèrons le système de Keller et Segel dans son intégralité, un système quasilinéaire à réaction-diffusion fortement couplé. Le résultat principal montre que ce syst`eme est bien posé, cest-à-dire il admet une solution unique existant localement en temps à valeurs dans un espace fonctionnel approprié, pourvu que les valeurs initiales sont réguliers. Apparemment, il nexiste pas encore des résultats comparables. Pour la demonstration, nous utilisons des résultats récents de régularité elliptique et parabolique applicable à des domaines assez générals, combiné avec un théorème abstrait dAmann concernant les équations quasilinéaires non locales

Subcalculus for set functions and cores of TU games.

This paper introduces a subcalculus for general set functions and uses this framework to study the core of TU games. After stating a linearity theorem, we establish several theorems that characterize mea- sure games having finite-dimensional cores. This is a very tractable class of games relevant in many economic applications. Finally, we show that exact games with Þnite dimensional cores are generalized linear production games.TU games; non-additive set functions; subcalculus; cores