As an auxiliary result, we also show that a similar explanation can be given in terms of fuzzy logic.

]]>In this paper, we show that this "dark matter confinement" can explain the discrepancy between different estimates of the Universe's expansion speed. It also explains the observed ratio of dark matter to regular matter.

]]>In practice, many dependencies are *random*, in the sense that for each combination of the values x_{1}, ..., x_{n}, we may get different values y with different probabilities. It has been proven that fuzzy systems are universal approximators for such random dependencies as well. However, the existing proofs are very complicated and not intuitive. In this paper, we provide a simplified proof of this universal approximation property.

In practice, often, we do not know the distributions, we only know the bound D on the measurement accuracy -- hence, after the get the measurement result X, the only information that we have about the actual (unknown) value x of the measured quantity is that $x$ belongs to the interval [X − D, X + D]. Techniques for data processing under such interval uncertainty are called interval computations; these techniques have been developed since 1950s.

In many practical problems, we have a combination of different types of uncertainty, where we know the probability distribution for some quantities, intervals for other quantities, and expert information for yet other quantities. The purpose of this paper is to describe the theoretical background for interval and combined techniques and to briefly describe the existing practical applications.

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