Unnormalized Interval Type-2 TSK Fuzzy Logic System Design Based on Convexity and Sample Data

Prior knowledge of convexity is encoded into a Single-Input Single-Output (SISO) unnormalized interval type-2 Takagi-Sugeno-Kang (TSK) Fuzzy Logic System (FLS) such that the system converges to a given convex target function. After giving sufficient conditions to guarantee convexity with respect to inputs, we show how to combine convexity with Unnormalized Interval Type-2 TSK FLSs (UIT2FLSs) to design convex fuzzy systems enabling derived systems to approach the target function. A simulation example demonstrates the usefulness of convexity and the advantages of UIT2FLSs in the presence of noise.