Study on non-iterative algorithms for center-of-sets type-reduction of Takagi–Sugeno–Kang type general type-2 fuzzy logic systems

Abstract

Abstract The paper performs the center-of-sets (COS) type-reduction (TR) and de-fuzzification for Takagi–Sugeno–Kang (TSK) type general type-2 fuzzy logic systems (GT2 FLSs) on the basis of the $$\alpha$$ α -planes expression of general type-2 fuzzy sets. Actually, comparing the popular Karnik–Mendel (KM) algorithms with other non-iterative algorithms is an important question in T2 society. Here the modules of fuzzy inference, COS TR, and de-fuzzification for TSK type GT2 FLSs are discussed by means of non-iterative Nagar–Bardini (NB) algorithms, Nie–Tan (NT) algorithms, and Begian–Melek–Mendel (BMM) algorithms. Simulation instances are constructed to illustrate the performances of three types of non-iterative algorithms compared with the KM algorithms. It is proved that, the proposed non-iterative algorithms can enhance the computational efficiencies significantly, which afford the potential application value for designers of GT2 FLSs.

Keywords

• General type-2 fuzzy logic systems
• Computational efficiency
• Center-of-sets type-reduction
• Alpha-planes
• Non-iterative algorithms