Displaying similar documents to “Determination of reliability bounds for structural systems using linear programming.”

Non additive ordinal relations representable by lower or upper probabilities

Andrea Capotorti, Giulianella Coletti, Barbara Vantaggi (1998)

Kybernetika

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We characterize (in terms of necessary and sufficient conditions) binary relations representable by a lower probability. Such relations can be non- additive (as the relations representable by a probability) and also not “partially monotone” (as the relations representable by a belief function). Moreover we characterize relations representable by upper probabilities and those representable by plausibility. In fact the conditions characterizing these relations are not immediately deducible...

Limit state analysis on the un-repeated multiple selection bounded confidence model

Jiangbo Zhang, Yiyi Zhao (2023)

Kybernetika

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In this paper, we study the opinion evolution over social networks with a bounded confidence rule. Node initial opinions are independently and identically distributed. At each time step, each node reviews the average opinions of several different randomly selected agents and updates its opinion only when the difference between its opinion and the average is below a threshold. First of all, we provide probability bounds of the opinion convergence and the opinion consensus, are both nontrivial...

An extended problem to Bertrand's paradox

Mostafa K. Ardakani, Shaun S. Wulff (2014)

Discussiones Mathematicae Probability and Statistics

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Bertrand's paradox is a longstanding problem within the classical interpretation of probability theory. The solutions 1/2, 1/3, and 1/4 were proposed using three different approaches to model the problem. In this article, an extended problem, of which Bertrand's paradox is a special case, is proposed and solved. For the special case, it is shown that the corresponding solution is 1/3. Moreover, the reasons of inconsistency are discussed and a proper modeling approach is determined by...

Probabilities of discrepancy between minima of cross-validation, Vapnik bounds and true risks

Przemysław Klęsk (2010)

International Journal of Applied Mathematics and Computer Science

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Two known approaches to complexity selection are taken under consideration: n-fold cross-validation and structural risk minimization. Obviously, in either approach, a discrepancy between the indicated optimal complexity (indicated as the minimum of a generalization error estimate or a bound) and the genuine minimum of unknown true risks is possible. In the paper, this problem is posed in a novel quantitative way. We state and prove theorems demonstrating how one can calculate pessimistic...