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In this paper a technique is proposed to tolerate missing values based on a system of fuzzy rules for classiication. The presented method is mathematically solid but nevertheless easy and eecient to implement. Three possible applications of this methodology are outlined: the classiication of patterns with an incomplete feature vector, the completion of the(More)
1 Introduction In a highly original, but not yet sufficiently appreciated contribution entitled " Six theorems about metric spaces " [32], John Isbell presented and discussed the following intriguing observations: from X into X with α • α = Id X and with d(α (x), α (y)) ≤ d (x , y) for all x , y ∈ X. (ii) Every metric space (X, d) can be embedded(More)
In 1970, Farris introduced a procedure that can be used to transform a tree metric into an ultra metric. Since its discovery, Farris' procedure has been used extensively within phylogenetics where it has become commonly known as the Farris transform. Remarkably, the Farris transform has not only been rediscovered several times within phylogenetics, but also(More)
In this note, we continue our work devoted to investigating the concept of embedding complexity (cf. Cieslik et al. [3]) and present a new Divide and Conquer algorithm for solving the Steiner-tree problem for graphs that relies on dynamic-programming schemes. In this way, we show how the rather general conceptual framework developed in our previous paper(More)
In this note, we describe a new and quite natural way of analyzing instances of discrete optimization problems in terms of what we call the embedding complexity of an associated (more or less) canonical embedding of the (in general, vast) solution space of a given problem into a product of (in general, small) sets. This concept arises naturally within the(More)
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