Design of interval type-2 fuzzy logic systems using prior knowledge via optimization algorithms

The paper presents the methods of integrating prior knowledge with a first-order Single-Input Single-Output (SISO) Interval Type-2 Takagi-Sugeno-Kang (TSK) Fuzzy Logic System (IT2FLS) for function approximation under noisy circumstances. Firstly, sufficient conditions on the antecedent and the consequent parameters of the IT2FLS are given to ensure that three kinds of prior knowledge monotonicity, symmetry and special points, can be embedded into the IT2FLS. And then, we use three optimization algorithms constrained least squares algorithm, active-set algorithm and hybrid learning algorithm to design the IT2FLS, respectively. The effectiveness of the three algorithms and the comparisons of their performance are demonstrated by simulation examples.