Advocates of the theory of fuzzy sets as a system for representing uncertainty have based their case on five basic arguments. These are 1) the reality hypothesis, which holds that imprecision is an inherent property of the world external to an observer, 2) the subjectivity hypothesis, which holds that probability is an exclusively objective measure of uncertainty, and that therefore subjective uncertainty can only be represented with fuzzy sets, 3) the behaviorist hypothesis, which claims that uncertainty systems should emulate rather than prescribe human behavior in the face of uncertainty, 4) the "probability as fiction" hypothesis, which claims that probability does not comprise a field of study in its own right, and 5) the superset hypothesis, which holds that fuzzy set theory includes probability as a special case and thus provides a richer uncertainty modeling environment. We discuss and criticize all five. We then criticize the argument that fuzziness represents a type of uncertainty distinct from probability, and also the inordinate complexity of fuzzy methods. We present a method for assessing the efficacy of fuzzy representations of uncertainty and apply this method in three examples: 1) a fuzzy ordering scheme is found to be insensitive to radical shifts in an underlying probabilistic model, 2) a fuzzy method of quality control of multiple attributes is found in certain cases to be less sensitive to shifts in quality proportions than methods based on probability, and 3) a method of linear regression based on fuzzy sets fails to show any conceptual advantages over classical regression methods and can be much less efficient.
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