The main problem with fuzzy logic is that there is no link from the claimed fuzzy degree-of-membership back to the real world. This means that there is no clea

The main problem with fuzzy logic is that there is no link from the claimed fuzzy degree-of-membership back to the real world. This means that there is no clear-cut way to build hierarchies of fuzzy logic systems, i.e., to combine fuzzy values. In contrast, mathematical probability has a link to the real world in terms of long-run averages. The constraint that "the average or relative frequency must work out correctly" yields a calculus for combining probabilities, that we call independence, conditional probability, and Bayes' rule. In some ways, fuzzy logic is a less powerful solution to a less-well-characterized problem.