Knowledge-based parameter identification of TSK fuzzy models

Linear/1st order Takagi–Sugeno–Kang (TSK) fuzzy models are widely used to identify static nonlinear systems from a set of input–output pairs. The synergetic integration of TSK fuzzy models with artificial neural networks (ANN) has led to the emergence of hybrid neuro-fuzzy models that can have excellent adaptability and interpretability at the same time. One drawback of these hybrid models is that they tend to have more black-box characteristics of ANN than the transparency of fuzzy systems. If the quality of training data is questionable then it may lead to a fuzzy model with poor interpretability. In an attempt to remediate this problem, we propose a parameter identification technique for TSK models that relies on a-priori available qualitative domain knowledge. The technique is devised for rule-centered TSK models in which the consequent polynomial can be interpreted as the 1st order Taylor series approximation of the underlying nonlinear function that is being modeled. The resulting neuro-fuzzy model is named as a-priori knowledge-based fuzzy model (APKFM). We have shown that besides being reasonably accurate, APKFM has excellent interpretability and extrapolation capability. The effectiveness of APKFM is shown using two examples of static systems. In the first example, a toy nonlinear function is chosen for approximation by an APKFM. In the second example, a real world problem pertaining to the maintenance cost estimation of electricity distribution networks is addressed.