A collection operator for type-2 fuzzy logic systems

Since the rise in popularity of type-2 fuzzy logic systems a reoccurring problem has been the transition from existing type-1 fuzzy sets to type-2 fuzzy sets. As part of this paper, we are providing an overview of the said transition and discuss the requirement for an operation which allows to generate a single type-2 fuzzy set from multiple type-1 fuzzy sets. In this context, we discuss the limitations of the often cited union operation and establish an operation which we tentatively refer to as the Collection operation. We will provide details on the interpretation of this new operation as well as examples and mathematical implementation details.