Set Systems and Dissimilarities

Inconsistency-Tolerance in Knowledge-Based Systems by Dissimilarities

Distance-based reasoning is a well-known approach for defining non-monotonic and paraconsistent formalisms, which so far has been mainly used in the context of standard two-valued semantics. In this paper, we extend this approach to arbitrary denotational semantics by considering dissimilarities, a generalization of distances. Dissimilarity-based reasoning is then applied for handling inconsist...

Recognizing Treelike k-Dissimilarities

A k-dissimilarity D on a finite set X, |X| ≥ k, is a map from the set of size k subsets of X to the real numbers. Such maps naturally arise from edge-weighted trees T with leaf-set X: Given a subset Y of X of size k, D(Y ) is defined to be the total length of the smallest subtree of T with leaf-set Y . In case k = 2, it is well-known that 2-dissimilarities arising in this way can be characteriz...

Stability results for set solution of fuzzy integro-differential systems

On Not Making Dissimilarities Euclidean

Non-metric dissimilarity measures may arise in practice e.g. when objects represented by sensory measurements or by structural descriptions are compared. It is an open issue whether such non-metric measures should be corrected in some way to be metric or even Euclidean. The reason for such corrections is the fact that pairwise metric distances are interpreted in metric spaces, while Euclidean d...

Learning Dissimilarities for Categorical Symbols

In this paper we learn a dissimilarity measure for categorical data, for effective classification of the data points. Each categorical feature (with values taken from a finite set of symbols) is mapped onto a continuous feature whose values are real numbers. Guided by the classification error based on a nearest neighbor based technique, we repeatedly update the assignment of categorical symbols...