Z-Adaptive Fuzzy Inference Systems

Z-numbers consist of two components, restriction and restriction reliability, to cover both possibilistic and probabilistic uncertainties. So far, the components of Z-numbers are merely determined by expert knowledge and lack automated learning/training. To overcome this limitation, we propose a Z-Adaptive Fuzzy Inference System (ZAFIS) that systematically learns the parameters of Z-numbers from input-output data pairs. We first convert the second component of Z-numbers to a crisp number. We then use this number as a weight for the first fuzzy membership part of Z-numbers. Finally, the resultant membership is placed in a fuzzy inference system, and the parameters of the system are learned based on the input-output data pairs using a gradient descent algorithm. The proposed method is evaluated on several functions (sine, increasing sine, Hermite, Gabor, and a nonlinear function) with/without added noise scenarios. The results show that the ZAFIS is more robust against the noisy inputs and is superior to the Fuzzy Inference Systems (FISs) in terms of MSE.