A fundamental decomposition of type-2 fuzzy sets

Type-2 fuzzy sets let us model and minimize the effects of uncertainties in rule-base fuzzy logic systems; however, they are difficult to understand for a variety of reasons which we enunciate. In this paper we strive to overcome the difficulties by: (1) establishing a small set of terms that let us easily communicate about type-2 fuzzy sets and also let us define such sets very precisely, and (2) presenting a new representation for type-2 fuzzy sets. This new representation can be used to derive formulas for union, intersection and complement of type-2 fuzzy sets without having to use the Extension Principle.