Constraint-Based Fuzzy Models for an Environment with Heterogeneous Information-Granules

A novel framework for fuzzy modeling and model-based control design isdescribed. Based on the theory of fuzzy constraint processing, the fuzzymodel can be viewed as a generalized Takagi-Sugeno (TS) fuzzy model withfuzzy functional consequences. It uses multivariate antecedentmembership functions obtained by granular-prototype fuzzy clusteringmethods and consequent fuzzy equations obtained by fuzzy regressiontechniques. Constrained optimization is used to estimate the consequentparameters, where the constraints are based on control-relevant apriori knowledge about the modeled process. The fuzzy-constraint-basedapproach provides the following features. 1) The knowledge base of aconstraint-based fuzzy model can incorporate information with varioustypes of fuzzy predicates. Consequently, it is easy to provide a fusionof different types of knowledge. The knowledge can be from data-drivenapproaches and/or from control-relevant physical models. 2) Acorresponding inference mechanism for the proposed model can deal withheterogeneous information granules. 3) Both numerical and linguisticinputs can be accepted for predicting new outputs.The proposed techniques are demonstrated by means of two examples: anonlinear function-fitting problem and the well-known Box-Jenkins gasfurnace process. The first example shows that the proposed model usesfewer fuzzy predicates achieving similar results with the traditionalrule-based approach, while the second shows the performance canbe significantly improved when the control-relevant constraints areconsidered.