Computing Derivatives in Interval Type-2 Fuzzy Logic Systems

Abstract

This paper makes type-2 fuzzy logic systems much more accessible to fuzzy logic system designers, because it provides mathematical formulas and computational flowcharts for computing the derivatives that are needed to implement steepest-descent parameter tuning algorithms for such systems. It explains why computing such derivatives is much more challenging than it is for a type-1 fuzzy logic system. It provides derivative calculations that are applicable to any kind of type-2 membership functions, since the calculations are performed without prespecifying the nature of those membership functions. Some calculations are then illustrated for specific type-2 membership functions.