Multi-source knowledge based Unnormalized Interval Type-2 Fuzzy Logic Systems design

In this paper we propose an effective method to design a Single-Input Single-Output (SISO) Unnormalized Interval Type-2 Takagi-Sugeno-Kang (TSK) Fuzzy Logic System (UIT2FLS) for noisy regression problems based on multi-source knowledge which includes here the information from sample data and the prior knowledge of bounded range, symmetry and monotonicity. The sufficient conditions are given which ensure that the prior knowledge can be embedded into the UIT2FLS, and then the UIT2FLS is designed so that the target function can be approached as accurately as possible via constrained least squares algorithm. The performance of the UIT2FLS is verified through comparisons with unnormalized type-1 Fuzzy Logic Systems (FLSs) and normalized interval type-2 FLSs under three different noisy circumstances. Simulation results verify the correctness of the sufficient conditions, and demonstrate that the UIT2FLS has the best overall performance.