A Design for Genetically Oriented Rules-Based Incremental Granular Models and Its Application

In this paper, we develop a genetically oriented rule-based Incremental Granular Model (IGM). The IGM is designed using a combination of a simple Linear Regression (LR) model and a local Linguistic Model (LM) to predict the modeling error obtained by the LR. The IGM has been successfully applied to various examples. However, the disadvantage of IGM is that the number of clusters in each context is determined, with the same number, by trial and error. Moreover, a weighting exponent is set to the typical value. In order to solve these problems, the goal of this paper is to design an optimized rule-based IGM with the use of a Genetic Algorithm (GA) to simultaneously optimize the number of cluster centers in each context, the number of contexts, and the weighting exponent. The experimental results regarding a coagulant dosing process in a water purification plant, an automobile mpg (miles per gallon) prediction, and a Boston housing data set revealed that the proposed GA-based IGM showed good performance, when compared with the Radial Basis Function Neural Network (RBFNN), LM, Takagi–Sugeno–Kang (TSK)-Linguistic Fuzzy Model (LFM), GA-based LM, and IGM itself.