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Fuzzy logic provides a method for representing analog processes in a digital framework. Processes that are implemented through fuzzy logic are often not easily separated into discrete segments and may be difficult to model with conventional mathematical or rule-based paradigms that require hard boundaries or decisions, i.e., binary logic where elements are either a member of a given set or they are not. Consequently, fuzzy logic is valuable where the boundaries between sets of values are not sharply defined or there is partial occurrence of an event. In fuzzy set theory, an element's membership in a set is a matter of degree. This chapter describes the concepts inherent in fuzzy set theory and applies them to the solution of the inverted-pendulum problem and a Kalman-filter problem. Fuzzy and artificial neural network concepts may be combined to form adaptive fuzzy neural systems where either the weights and/or the input signals are fuzzy sets. Fuzzy set theory may be extended to fuse information from multiple sensors as discussed in the concluding section.

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