35,724 research outputs found
Empirical interpretation of imprecise probabilities
This paper investigates the possibility of a frequentist interpretation of imprecise probabilities, by generalizing the approach of Bernoulli’s Ars Conjectandi. That is, by studying, in the case of games of chance, under which assumptions imprecise probabilities can be satisfactorily estimated from data. In fact, estimability on the basis of finite amounts of data is a necessary condition for imprecise probabilities in order to have a clear empirical meaning. Unfortunately, imprecise probabilities can be estimated arbitrarily well from data only in very limited settings
Representation of uncertain multichannel digital signal spaces and study of pattern recognition based on metrics and difference values on fuzzy n-cell number spaces
In this paper, we discuss the problem of characterization for uncertain multichannel digital signal spaces, propose using fuzzy n-cell number space to represent uncertain n-channel digital signal space, and put forward a method of constructing such fuzzy n-cell numbers. We introduce two new metrics and concepts of certain types of difference values on fuzzy n -cell number space and study their properties. Further, based on the metrics or difference values appropriately defined, we put forward an algorithmic version of pattern recognition in an imprecise or uncertain environment, and we also give practical examples to show the application and rationality of the proposed technique
Using imprecise continuous time Markov chains for assessing the reliability of power networks with common cause failure and non-immediate repair.
We explore how imprecise continuous time Markov
chains can improve traditional reliability models based
on precise continuous time Markov chains. Specifically,
we analyse the reliability of power networks under very
weak statistical assumptions, explicitly accounting for
non-stationary failure and repair rates and the limited
accuracy by which common cause failure rates can be
estimated. Bounds on typical quantities of interest
are derived, namely the expected time spent in system
failure state, as well as the expected number of
transitions to that state. A worked numerical example
demonstrates the theoretical techniques described.
Interestingly, the number of iterations required for
convergence is observed to be much lower than current
theoretical bounds
Final solution to the problem of relating a true copula to an imprecise copula
In this paper we solve in the negative the problem proposed in this journal
(I. Montes et al., Sklar's theorem in an imprecise setting, Fuzzy Sets and
Systems, 278 (2015), 48-66) whether an order interval defined by an imprecise
copula contains a copula. Namely, if is a nonempty set of
copulas, then and are quasi-copulas and the pair
is an imprecise copula according to the
definition introduced in the cited paper, following the ideas of -boxes. We
show that there is an imprecise copula in this sense such that there is
no copula whatsoever satisfying . So, it is
questionable whether the proposed definition of the imprecise copula is in
accordance with the intentions of the initiators. Our methods may be of
independent interest: We upgrade the ideas of Dibala et al. (Defects and
transformations of quasi-copulas, Kybernetika, 52 (2016), 848-865) where
possibly negative volumes of quasi-copulas as defects from being copulas were
studied.Comment: 20 pages; added Conclusion, added some clarifications in proofs,
added some explanations at the beginning of each section, corrected typos,
results remain the sam
The Combination of Paradoxical, Uncertain, and Imprecise Sources of Information based on DSmT and Neutro-Fuzzy Inference
The management and combination of uncertain, imprecise, fuzzy and even
paradoxical or high conflicting sources of information has always been, and
still remains today, of primal importance for the development of reliable
modern information systems involving artificial reasoning. In this chapter, we
present a survey of our recent theory of plausible and paradoxical reasoning,
known as Dezert-Smarandache Theory (DSmT) in the literature, developed for
dealing with imprecise, uncertain and paradoxical sources of information. We
focus our presentation here rather on the foundations of DSmT, and on the two
important new rules of combination, than on browsing specific applications of
DSmT available in literature. Several simple examples are given throughout the
presentation to show the efficiency and the generality of this new approach.
The last part of this chapter concerns the presentation of the neutrosophic
logic, the neutro-fuzzy inference and its connection with DSmT. Fuzzy logic and
neutrosophic logic are useful tools in decision making after fusioning the
information using the DSm hybrid rule of combination of masses.Comment: 20 page
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