The construction of general type-2 fuzzy sets

Focus on constructing of general type-2 fuzzy set, the essence of type-n fuzzy sets are discovered. We first proved the consistency between interval estimation and nested sets representation theorem of type-1 fuzzy sets, which guarantees the rationality of our methods in this paper. Then, based on the fact that a type-1 fuzzy set can be constructed by a collection of intervals, an algorithm for constructing general type-2 fuzzy sets based on the collections of interval type-2 fuzzy sets was proposed. Furthermore, a new concept, interval type-2 fuzzy sets with uncertain bounds, was defined. And the ways for constructing general type-2 fuzzy sets by give interval type-2 fuzzy sets with uncertain bounds and constructing interval type-2 fuzzy sets with uncertain bounds by given general type-2 fuzzy sets were proposed. Finally, from the viewpoint of uncertain bounds, the essence of type-n fuzzy sets was discussed.