Footprint of Uncertainty and Its Importance to Type-2 Fuzzy Sets

J.M. Mendel (USA) and R.I. John (UK)


type-2 fuzzy sets, footprint of uncertainty, type-2 fuzzy logic systems


Type-2 fuzzy sets let us directly model uncertainty. In this paper we introduce some new definitions associated with a type-2 fuzzy set that encapsulate the different forms of its primary and secondary memberships. We also provide three new axioms for such three-dimensional fuzzy sets and extend the general notion of a Footprint of Uncertainty (FOU) (a FOU lets us easily visualize a type 2 fuzzy set in two-dimensions) to an unconstrained and constrained FOU. We also show, by use of the FOU, that using type-2 fuzzy sets resolves the problem of determining membership functions in type-1 fuzzy systems.

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