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In 1987 Dubois and Prade defined an interval-valued expectation of fuzzy numbers, viewing them as consonant random sets. In 2001 Carlsson and Fullér defined an interval-valued mean value of fuzzy numbers, viewing them as possibility distributions, and they introduced the notation of crisp possibilistic mean value and crisp possibilistic variance of continuous possibility distributions, which ar...

The expectation of a random variable is its average value, where each value is weighted according to the probability that it comes up. The expectation is also called the expected value or the mean of the random variable. For example, suppose we select a student uniformly at random from the class, and let R be the student’s quiz score. Then E [R] is just the class average —the first thing everyo...

To avoid both the inconsistency of the Kalman filter and the performance conservation of the covariance intersection (CI) in the case of unknown correlations, an internal ellipsoidal approximation (IEA) method is proposed to fuse the local estimations. A numerical example of three-state radar tracking system is presented to illustrate the implementation and effectiveness of the proposed algorit...

Treating mRNA transcript abundances as quantitative traits and examining their relationships with clinical traits have been pursued by using an analytical approach of quantitative genetics. Recently, Kraft et al. presented a family expression association test (FEXAT) for correlation between gene expressions and trait values with a family-based (sibships) design. This statistic did not account f...

In this note we consider several versions of the bootstrap and argue that it can be helpful in explaining and thinking about such procedures to use an explicit representation of the random resampling process. To illustrate the point we give such explicit representations and use them to produce some results about bootstrapping linear models that are, apparently, not widely known, at least in the...

Given the collapse hypothesis (CH) of quantummeasurement, EPRtype correlations along with the hypothesis of the impossibility of superluminal communication (ISC) have the effect of globalizing gross features of the quantum formalism making them universally true. In particular, these hypotheses imply that state transformations of density matrices must be linear and that evolution which preserves...