Evolutionary Reduction of Fuzzy Rule-Based Models

Abstract

In the design of fuzzy rule-based models we strive to develop models that are both accurate and interpretable (transparent). The approach proposed here is aimed at the enhancement of transparency of the fuzzy model already constructed with the accuracy criterion in mind by proposing two modifications to the rules. First, we introduce a mechanism of reduction of the input space by eliminating some less essential input variables. This results in rules with the reduced subspaces of input variables making the rules more transparent. The second approach is concerned with an isolation of input variables: fuzzy sets defined in the n-dimensional input space and forming the condition part of the rules are subject to a decomposition process in which some variables are isolated and interpreted separately. The reduced dimensionality of the input subspaces in the first approach and the number of isolated input variables in the second one are the essential parameters controlling impact of enhanced transparency on the accuracy of the obtained fuzzy model. The two problems identified above are of combinatorial character and the optimization tasks emerging there are handled with the use of Genetic Algorithms (GAs). A series of numeric experiments is reported where we demonstrate the effectiveness of the two approaches and quantify the relationships between the criterion of accuracy and interpretability.