Abstract
Type-2 fuzzy sets that is, fuzzy sets with fuzzy sets as truth values seem destined to play an increasingly important role in applications. They were introduced by Zadeh [13], extending the notion of ordinary fuzzy sets. The Mendel's book [5] on Uncertain Rule-based Fuzzy Logic Systems and other researches [6, 7, 8, 11] are discussions of both theoretical and practical aspects of type-2 fuzzy sets. In [1] Atanassov K. introduced the concept of intuitionistic fuzzy set characterized by a membership function and a non-membership function, which is a generalization of fuzzy set. In [1] Atanassov K. also defined some operators of IFSs. Recently, intuitionistic fuzzy set (IFS) theory have been applied to many different fields, such as decision making, medical diagnosis, pattern recognition. In this paper, we introduce concept of type-2 intuitionistic fuzzy sets. We define some basic operations and derive some their properties. The paper is organized as follow: Section 2 gives a briefly review some basic definitions of fuzzy sets, type-2 fuzzy sets and intuitionistic fuzzy sets. Section 3 is devoted to the new main definitions and some their properties. Section 4 is a first discussion of a subclass of the type-2 IFS.
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