The incorporation of qualitative information into T-S fuzzy model

The Takagi-Sugeno (T-S) type of fuzzy model combines linguistic information and quantitative training procedures, and is therefore a most suitable candidate for accommodating additional a-priori knowledge in input-output modeling. The idea is to regard the a-priori knowledge as constraints that penalize a performance criterion used for identifying the unknown parameters in the T-S fuzzy model. The relative importance of various sources of a-priori knowledge, as expressed in the penalty weighting parameters, can be assessed by optimizing a generalized cross-validation criterion. A synthetic example is presented, showing that significant effects can be achieved by adding penalties to the optimization performance criterion. The identified T-S fuzzy model has comparative performance in the interpolation (training) range and a convincing improvement in the extrapolation (validation) range as compared to the T-S fuzzy model without adding any a-priori knowledge.