Efficient triangular type-2 fuzzy logic systems

In this study, an efficient fuzzy logic system (FLS) based on triangular type-2 fuzzy sets is designed. In detail, this paper provides a new method for computational complexity reduction in t-norm operations extended on triangular type-2 fuzzy sets. It is demonstrated that our approximate extended t-norms for arguments with triangular membership functions (MFs) satisfy axiomatics of the type-2 t-norm. A new efficient approximate iterative procedure based on the K–M type-reduction is proposed in order to develop triangular type-2 FLSs. The utility of triangular type-2 FLSs in approximate reasoning is illustrated by numerical examples.