Measures of uncertainty for type-2 fuzzy sets

The Extension Principle based on alpha-cuts plays a pivotal role in many applications of type-1 fuzzy sets. We recently defined an alpha-based extension principle for type-2 fuzzy sets. In this paper we investigate the use of the alpha-extension principle to define uncertainty measures for type-2 fuzzy sets. We investigate cardinality, similarity, and subsethood for type-2 fuzzy sets and demonstrate when the alpha-plane representation can be used.