We consider the bit-probe complexity of the set membership problem, where a set S of size at most n from a universe of size m is to be represented as a short bit vector in order to answer membership queries of the form “Is x in S?” by adaptively probing the bit vector at t places. Let s(m,n, t) be the minimum number of bits of storage needed for such a scheme. Several recent works investigate s...

Interval methods have been shown to be efficient, robust and reliable to solve difficult set-membership localization problems. However they are unsuitable in a probabilistic context, where the approximation of an unbounded probability density function by a set cannot be accepted. This paper proposes a new probabilistic approach which makes possible to use classical set-membership localization m...

In this paper we propose a method, based on a Set Membership approach, for the estimation of nonlinear regressions models. At the contrary of most of the existing identi...cation approaches, the method presented in this paper does not need any assumption about the functional form of the model to be identi...ed, but uses only some prior information on its regularity and on the size of noise corr...

This paper addresses the problem of robust filtering in color images. We propose to improve the bilateral filter by using Ordered Weighted Averaging (OWA) filters. Bilateral filter decreases amount of noise preserving edges when filtering. But the results could be strongly affected by the presence of outliers. In this paper, we define the filtering in the framework of fuzzy logic. If the filter...

Assertions of set membership, such as Amy is an artist, should not be confused with those of set inclusion, such as All artists are bohemians. Membership is not a transitive relation, whereas inclusion is. Cognitive scientists have neglected the topic, and so we developed a theory of inferences yielding conclusions about membership, e.g., Amy is a bohemian, and about non-membership, Abbie is no...

This paper concerns the concept of set-membership identifiability introduced in [4]. Given a model, a set-membership identifiable set is a connected set in the parameter domain of the model such that its corresponding trajectories are distinct to trajectories arising from its complementary. For obtaining the so-called set-membership identifiable sets, we propose an algorithm based on interval a...

In the present paper, a Nonlinear Set Membership prediction method previously proposed by the authors is applied to a river flow prediction problem. The method does not require the choice of the functional form of the model used for prediction, but assumes a bound on the gradient norm of the regression function defining the model. The method is used for the univariate prediction of the time ser...