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“Operations on Type-2 Fuzzy Sets”
by Nilesh N. Karnik and Jerry M. Mendel
June 1998
A type-2 fuzzy set is characterized by a fuzzy membership function, i.e., the membership grade of each element of this set is itself a fuzzy set in [0,1]. Such sets can be used in situations where there is uncertainty about the membership grades of a fuzzy set. Operations on type-2 fuzzy sets are defined by using Zadeh's Extension Principle. In this report, we give some examples of type-2 fuzzy sets; discuss set theoretic and algebraic operations on type-2 sets in great detail; and, introduce the concept of the centroid of a type-2 fuzzy set. We provide easily implementable algorithms for performing these set theoretic and algebraic operations on type-2 sets; and, also provide practical approximations for the cases where actual results are difficult to generalize or implement.