Uncertainties may arise in complex human thinking processes, which can become particularly challenging in the decision-making context for hard engineering problems with vague, imprecise and incomplete knowledge and information. As an important branch of computational intelligence, the logical approach can be employed to deal with such uncertainties. This chapter presents three mathematical theories, i.e. the Dempster–Shafer theory, the probability theory and the fuzzy logic (FL) theory, to handle different kinds of uncertainties. The FL theory can deal with the imprecision (or vagueness) of defined knowledge, whilst the Dempster–Shafer theory provides two measures (support and plausibility) for formulating a mechanism to represent “ignorance”. As a probabilistic technique, Bayesian networks (BNs) are introduced as graphical representations of uncertain knowledge. In later chapters, the three methodologies are employed to tackle uncertainties arising from complicated condition assessment procedures for detecting transformer faults.
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