Improved uncertainty capture for non-singleton fuzzy systems - Pourabdollah, Amir; Wagner, Christian; Aladi, Jabran Hussain; Garibaldi, Jonathan M. (IEEE, 2016)
In non-singleton fuzzy logic systems (NSFLSs), input uncertainties are modelled with input fuzzy sets in order to capture input uncertainty (e.g., sensor noise). The performance of NSFLSs in handling such uncertainties depends on both: the appropriate modelling in the input fuzzy sets of the uncertainties present in the system’s inputs, and on how the input fuzzy sets (and their inherent model of uncertainty) interact with the antecedent and thus affect the inference within the remainder of the NSFLS. This paper proposes a novel development on the latter. Specifically, an alteration to the standard composition method of type-1 fuzzy relations is proposed, and applied to build a new type of NSFLS. The proposed approach is based on employing the centroid of the intersection of input and antecedent sets as origin of the firing degree, rather than the traditional maximum of their intersection, thus making the NSFLS more sensitive to changes in the input’s uncertainty characteristics. The traditional and novel approach to NSFLSs are experimentally compared for two well-known problems of Mackey-Glass and Lorenz chaotic time series predictions, where the NSFLSs’ inputs have been perturbed with different levels of Gaussian noise. Experiments are repeated for system training under noisy and noise-free conditions. Analyses of the results show that the new method outperforms the traditional approach. Moreover, it is shown that while formally more complex, in practice, the new method has no significant computational overhead compared to the standard approach.