Closed-Form Mathematical Representations of Interval Type-2 Fuzzy Logic Systems

Interval type-2 fuzzy logic systems have a wide range of applications due to their abilities to handle uncertainties compared to their type-1 counterparts. This paper presents an approach for developing closed-form mathematical representations for interval type-2 fuzzy logic systems. Having such a representation can be useful in real-time implementation of the system and in its mathematical analysis. We start by deriving an approximate form of the Geometric Centroid defuzzifaciation method. Next, we extend the results to give another closed form expression based on the Nie-Tan operator. We discuss the use of both derived expressions when the antecedent interval type-2 fuzzy sets are Gaussian with either uncertain means or uncertain standard deviations.