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—To date, because of the computational complexity of using a general type-2 fuzzy set (T2 FS) in a T2 fuzzy logic system (FLS), most people only use an interval T2 FS, the result being an interval T2 FLS (IT2 FLS). Unfortunately, there is a heavy educational burden even to using an IT2 FLS. This burden has to do with first having to learn general T2 FS… (More)

—This paper presents a very practical type-2-fuzzistics methodology for obtaining interval type-2 fuzzy set (IT2 FS) models for words, one that is called an interval approach (IA). The basic idea of the IA is to collect interval endpoint data for a word from a group of subjects, map each subject's data interval into a prespec-ified type-1 (T1) person… (More)

—By connecting work from two different problems— the fuzzy weighted average (FWA) and the generalized centroid of an interval type-2 fuzzy set—a new-cut algorithm for solving the FWA problem has been obtained, one that is monotonically and superexponentially convergent. This new algorithm uses the Karnik–Mendel (KM) algorithms to compute the FWA-cut… (More)

—Computing the centroid of an interval T2 FS is an important operation in a type-2 fuzzy logic system (where it is called type-reduction), but it is also a potentially time-consuming operation. The Karnik–Mendel (KM) iterative algorithms are widely used for doing this. In this paper, we prove that these algorithms converge monotonically and… (More)