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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)
This paper provides an answer to the question that the type-2 fuzzy logic community is now asking: ldquoWhat comes after interval type-2 fuzzy logic systems (TT2 FLSs)?rdquo It demonstrates, through a geometrical understanding of the type-reduced set, that logical next steps in the progression from type-1 to interval type-2 to type-2 FLSs are(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)
—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)
In this paper, we demonstrate that it is unnecessary to take the route from general type-2 fuzzy set to interval type-2 fuzzy set, and that all of the results that are needed to implement an interval type-2 fuzzy logic system can be obtained using type-1 fuzzy set mathematics. As such, this paper makes an interval type-2 fuzzy logic system much more(More)