The efficacy of fuzzy representations of uncertainty

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