In this paper we study a generalization of a submeasure notion which is related to a probabilistic concept, especially to Menger spaces where triangular norms play a crucial role. The resulting notion of a τT -submeasure is suitable for modeling those situations in which we have only probabilistic information about the measure of the set. We characterize a class of universal τT -submeasures (i....

This paper discusses the property of local finiteness for t-norm monoids and extensions of them. The focus is (i) on t-norm bimonoids, which are of interest in the context of weighted automata, (ii) on those extensions of t-norm monoids which are reducts of t-algebras, i.e. of the basic semantic entities for the (fuzzy) logics of left-continuous and of continuous t-norms, and (iii) on extension...

In the paper we define the convergence of compact fuzzy sets as a convergence of α-cuts in the topology of compact subsets of a metric space. Furthermore we define typical convergences of fuzzy variables and show relations with convergence of their fuzzy distributions. In this context we prove a general formulation of the Strong Law of Large Numbers for fuzzy sets and fuzzy variables with Archi...

In imbalanced multi-class classification problems, the misclassification rate as an error measure may not be a relevant choice. Several methods have been developed where the performance measure retained richer information than the mere misclassification rate: misclassification costs, ROC-based information, etc. Following this idea of dealing with alternate measures of performance, we propose to...

In imbalanced multi-class classification problems, the misclassification rate as an error measure may not be a relevant choice. Several methods have been developed where the performance measure retained richer information than the mere misclassification rate: misclassification costs, ROC-based information, etc. Following this idea of dealing with alternate measures of performance, we propose to...

The paper deals with fuzzy Horn logic (FHL) which is a fragment of predicate fuzzy logic with evaluated syntax. Formulas of FHL are of the form of simple implications between identities. We show that one can have Pavelka-style completeness of FHL w. r. t. semantics over the unit interval [0, 1] with (residuated lattices given by) left-continuous t-norm and a residuated implication, provided tha...

We consider the problem of choosing an alternative in a set A = {A1, A2, ..., Am} of alternatives, given a set D = {d1, d2, ..., dh} of decision makers and a set Ω = {O1, O2, ..., On} of objectives. We assume that any decision maker dk assigns to any pair (alternative Ai, objective Oj) a number aijk that measures to what extent Ai satisfies Oj . We assume that Ω is a subset of a universal set U...

1.1 Notations and Hypotheses In the sequel, Ω is a bounded domain in R (N ≥ 2), with a Lipschitz continuous boundary. n is the unit normal to ∂Ω outward to Ω. We denote by x · y the usual Euclidean product of two vectors (x, y) ∈ R × R ; the associated Euclidean norm is written |.|. The Lebesgue measure of a measurable subset E of R is denoted by |E|; σ is the Lebesgue measure on ∂Ω (i.e. the (...

In this paper a general theory will be introduced that allows the description of a melodic surface i.e. a score-like representation of a melody in terms of local grouping, accentuation and metrical structures. Firstly, a formal model will be proposed that detects points of maximum local change that allow a listener to identify local perceptual boundaries in a melodic surface. The Local Botmdary...