From uncertainty to approximate reasoning: part 1: conceptual models and engineering interpretations

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Abstract
Different models of uncertainties from the simplest interval representation to fuzzy sets and random numbers are reviewed. Mathematical theories spawned by these conceptual models are described, including interval analysis, possibility and fuzzy set theories, probability theory and the theory of evidence. The relationship among these theories is delineated from the perspective of understanding human reasoning. The discussion emphasizes conceptual understanding and physical intuition rather than mathematical theorems and axioms. It is intended to remove some of the mysteries surrounding existing viewpoints on uncertainties, which may have hindered wider understanding and acceptance of these viewpoints by practicing civil engineers. Subsequent parts of this paper will discuss the process of uncertainty propagation in a rules framework with reference to the various kinds of uncertainty representations.