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Stratification in the type-reduced set and the generalised Karnik-Mendel iterative procedure

Type-2 defuzzification is a two-stage process. Type-reduction, the first stage, gives rise to a type-1 fuzzy set known as the type-reduced set (TRS), which for the second stage is defuzzified to give a crisp number. This paper focusses on the TRS itself, which reveals a fascinating internal structure. We provide a description of and explanation for this structure, then go on to suggest how it may be exploited to enable the application of the Karnik-Mendel Iterative Procedure to generalised type-2 fuzzy sets.