The Paradoxical Success of Fuzzy Logic

Charles Elkan

This paper investigates the question of which aspects of fuzzy logic are essential to its practical usefulness. We show that as a formal system, a standard version of fuzzy logic collapses mathematically to two-valued logic, while empirically, fuzzy logic is not adequate for reasoning about uncertain evidence in expert systems. Nevertheless, applications of fuzzy logic in heuristic control have been highly successful. We argue that the inconsistencies of fuzzy logic have not been harmful in practice because current fuzzy controllers are far simpler than other knowledge-based systems. In the future, the technical limitations of fuzzy logic can be expected to become important in practice, and work on fuzzy controllers will also encounter several problems of scale already known for other knowledge-based systems.

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