A Granular Approach to Interval Output Estimation for Rule-Based Fuzzy Models

Optimization by Context Refinement for Development of Incremental Granular Models

Optimization by refinement of linguistic contexts produced from an output variable in the construction of an incremental granular model (IGM) is presented herein. In contrast to the conventional learning method using the backpropagation algorithm, we use a novel method to learn both the cluster centers of Gaussian fuzzy sets representing the symmetry in the premise part and the contexts of the consequent part in the if–then fuzzy rules. Hence, we use the fundamental concept of context-based fuzzy clustering and design with an integration of linear regression (LR) and granular fuzzy models (GFMs). This GFM is constructed based on the association between the triangular membership function produced both in the input–output variables. The context can be established by the system user or using an optimization method. Hence, we can obtain superior performances based on the combination of simple linear regression and local GFMs optimized by context refinement. Experimental results pertaining to coagulant dosing in a water purification plant and automobile miles per gallon prediction revealed that the presented method performed better than linear regression, multilinear perceptron, radial basis function networks, linguistic model, and the IGM.