learning theory, noise, non-linear filters An Occam approximation is an algorithm that takes as input a set of samples of a function and a tolerance e, and produces as output a compact representation of a function that is within e of the given samples. We show that the existence of an Occam approximation is sufficient to guarantee the probably approximate learnability of classes of functions on...

Modeling case-base competence is a crucial issue in the field of CBR. In fact it has led to a number of important developments in CBR recently, the most well known being in case deletion and case-base visualization and authoring support. This is highlighted by Smyth and Keane’s competence model (called the S-K model in this paper), which was shown to be efficient. In this paper, we argue that t...

fuzzy relation inequalities based on max-f composition are discussed, where f is a binary aggregation on [0,1]. for a fixed fuzzy relation inequalities system $ a circ^{f}textbf{x}leqtextbf{b}$, we characterize all matrices $ a^{'} $ for which the solution set of the system $ a^{' } circ^{f}textbf{x}leqtextbf{b}$ is the same as the original solution set. similarly, for a fixed matrix ...

A problem which is appealing to the intuition in view of the relative frequency interpretation of probability is to define a measure on a countable space which assigns to each point the measure 0. Such a measure of course becomes trivial if it is countably additive. Finitely additive measures of this type have been discussed by R. C. Buck [l] and by E. F. Buck and R. C. Buck [2]. In a discussio...