On a Class of General Type-n Normal Fuzzy Sets Synthesized From Subject Matter Expert Inputs

The performance of fuzzy systems has been shown both theoretically and empirically to improve with increasing fuzziness, e.g., when fuzzy values are modeled using interval type 2 (IT2) or interval type 3 (IT3) fuzzy sets. This performance gain comes at a computational cost. We describe a new class of higher order fuzzy sets constructed from IT2 fuzzy sets that supports efficient type reduction. Our focus is on representations that use input from experts (SMEs) in the subject matter of interest. Differing interpretations of a concept by different subject matter experts (SMEs) leads to imprecision, which is captured in an IT2 fuzzy set defined on the relevant domain by approaches such as the Hao–Mendel approach. A second source of imprecision that has largely been ignored is SME confidence in their own judgments. This can also be captured as an IT2 fuzzy set, defined on the unit interval. We present a novel and intuitive construction to combine these representations into an IT3 fuzzy set. We show more generally how imprecision in hierarchical estimates of knowledge can be incorporated into a type-n fuzzy set representation.