A triangular type-2 fuzzy logic system

So far, computational complexity of non-interval type-2 fuzzy logic sytems (FLS) has not allowed to make an engineering use of them. This paper provides a new method for complexity reduction of operations on triangular type-2 fuzzy sets. The method for the algebraic product case is validated with the use of an original theorem for calculating extended continuous t-norms for arguments characterized by normal and upper semicontinuous membership functions (MF). A new approximate type-reduction method similar to the Karnik-Mendel iterative procedure is proposed. Finally, a triangular type-2 FLS and its neuro-fuzzy structure is developed. The use of triangular uncertainties in FLS is justified by the example.