From Interval Methods of Representing Uncertainty to a General Description of Uncertainty

Abstract

Measurements do not result in an exact value of the measured quantity; even after the most accurate measurement, there is still some uncertainty about the actual value of the measured quantity. Traditionally, in science and engineering, this uncertainty is characterized by a probability distribution; however, often, we do not know this probability distribution exactly. So, to get a more adequate description of this uncertainty, we must consider classes of possible probability distributions. A natural question is: Are all possible classes needed for this description? In this paper, we show that even for simple situations, we indeed need arbitrary closed convex classes of probability distributions. Traditional Description of Uncertainty in Science and Engineering and its Drawbacks Uncertainty is typical in science and engineering. A large portion of knowledge in science and engineering comes from measurements. Some of this knowledge comes not from measurements but from the expertise o...

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