Our Reasoning is Clearly Fuzzy, So Why is Crisp Logic So often Adequate?
Hung Tan Nguyen, Berlin Wu, Владик Крейнович · scholarworks - UTEP (The University of Texas at El Paso) · 2015
Our reasoning is clearly fuzzy, so why is crisp logic so often adequate? We explain this phenomenon by showing that in the presence of noise, an arbitrary continuous (e.g., fuzzy) system can be well described by its discrete analog. However, as the description gets more accurate, the con-tinuous description becomes necessary. 1 Formulation of the Problem Fuzzy logic is needed. Our reasoning is clearly fuzzy. Whenever we use terms like “small”, “young”, etc., there is no crisp boundary: some people are clearly 1 young, some are clearly not young, but there is always an area in between in which a natural answer should be “young to a certain degree”. Fuzzy logic has been specifically designed to capture this “fuzziness”; see, e.g., [2, 3, 7]. While fuzzy logic is successful, crisp methods are, surprisingly, suc-