Imprecise choices can be described using either a probabilistic or a fuzzy formalism. No relation between them has been studied so far. In this contribution we present a connection between the two formalisms that strongly makes use of fuzzy implication operators and t-norms. In this framework, Luce’s Choice Axiom turns out to be a special case when the product t-norm is considered and other sim...

In this paper, we prove that every F ∗ space (i.e., Hausdorff topological vector space satisfying the first countable axiom) can be characterized by means of its “standard generating family of pseudo-norms”. By using the standard generating family of pseudo-norms P, the concepts of P-bounded set and γ-maxpseudo-norm-subadditive operator in F ∗ space are introduced. The uniform boundedness princ...

Conclusions To improve network reliability & management in today’s high-speed communication networks, we propose an intelligent system using adaptive statistical approaches. The system learns the normal behavior (norm) of the network. Deviations from the norm are detected and the information is combined in the probabilistic framework of a Bayes network. The proposed system thereby can detect un...

Given a quadruple of finite index subfactors we explicitly compute the Pimsner-Popa probabilistic constant for pair intermediate and relate it with corresponding Connes-Størmer relative entropy between them. This generalizes an old result Pimsner Popa [Ann. Sci. École Norm. Sup. (4) 19 (1986), pp. 57–106].

We estimate the rate of convergence and sample complexity of a recent robust estimator for a generalized version of the inverse covariance matrix. This estimator is used in a convex algorithm for robust subspace recovery (i.e., robust PCA). Our model assumes a sub-Gaussian underlying distribution and an i.i.d. sample from it. Our main result shows with high probability that the norm of the diff...

The probability that a fish matures at a certain age and length (the so-called probabilistic maturation reaction norm, PMRN) was analysed for a European whitefish Coregonus lavaretus species complex population living in the Austrian pre-alpine Lake Irrsee. Fish length was found to be the only relevant determinant of maturation probability, and females matured at slightly smaller sizes than males.

We obtain explicit upper estimates in direct inequalities with respect to the usual sup-norm distance for Bernstein-type operators. Our approach combines analytical and probabilistic techniques based on representations of the operators in terms of stochastic processes. We illustrate our results by considering some classical families of operators, such as Weierstrass, Sza sz, and Bernstein opera...

Kahneman and Tversky (1972) affirmed: “In his evaluation of evidence, man is not Bayesian at all.“ In their book Judgment under uncertainty (1982), they attempted to prove that human judgment is riddled with systematic deviations from the logical and probabilistic norm. In chapter 18 of the same book David M. Eddy stressed that medical doctors do not follow Bayes’formula when solving the follow...

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....