Mathematical logic and Boolean logic deal with crisp certainty. A value is either true or it is false. There is nothing between those values. This makes logic easy, or at least relatively easy. The real world is imprecise. Experimental errors or uncertainties and less than rigorous categories lead to uncertainties in the data. Fitting these uncertainties as if they were crisp leads to overtraining, overly complex models, and fragile results. Fuzzy methods directly address this problem by assigning a likelihood or belief to data and classifications. Beliefs are a somewhat relaxed version of probabilities where normalization and other nice proper mathematical formalisms are ignored. They keep just enough rigor to be useful. In essence, fuzzy methods trade nominal (overestimated) precision for the ability to give the support of the conclusion from the data and model.