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allows propagation of uncertainties along extended chains of reasoning, and eases implementation of large knowledge bases. Several techniques for representing uncertainty in expert systems have been proposed in the AI literature including Bayesian analysis and certainty measures [4]. For the most part, these techniques are ad-hoc methods that emphasize simplifying coding of the uncertainty. This work begins from a fundamental model of uncertainty based on fuzzy mathematics and leads to a rule-based representation for expert system development. Techniques are developed which show the most effective method for extracting information from an observation and suggest actions to take which will lead to the most coherent conclusion. Fuzzy mathematics applications within power systems have been proposed in several areas, see [5]. In particular, there have been several applications to transformer diagnosis of fuzzy set methods. In [6,7], fuzzy logic is used to implement dissolved gas analysis methods. An acoustic technique for finding partial discharges applied fuzzy logic to representation of uncertainties [8]. The techniques developed in this chapter have also been applied to transformer diagnostics and condition monitoring [9-11] and thus, examples in this chapter will focus on this problem. This chapter is organized as follows. The diagnostic framework is discussed and requirements for a model of uncertainty are presented. An introduction to fuzzy mathematics with emphasis on the lesser known fuzzy information aspects is then given. Several detailed examples show the usefulness of the proposed technique. Implementation and representation issues are discussed. Learning methods and performance improvement of a diagnostic expert system are explored. A method for performance evaluation and improvement is proposed within the developed fuzzy set framework. Some directions for further research are discussed. 3