An approximation method for Type reduction of an Interval Type-2 fuzzy set based on α-cuts

This paper shows a proposal for Type-reduction of an Interval Type-2 fuzzy set composed from α-cuts done over its primary membership functions. The definition of available Type-reduction methods for Interval Type-2 fuzzy sets are based on an homogeneous subdivision of the universe of discourse, so we propose an approximation algorithm for Type-reduction of an Interval type-2 fuzzy set through its primary α-cuts. Some definitions about the α-cut of a Type-2 fuzzy set are provided and used for computing the centroid of an Interval Type-2 fuzzy set through a mapping of its membership function, instead of its universe of discourse.