The study is concerned with data and feature reduction in fuzzy modeling. As these reduction activities are advantageous to fuzzy models in terms of both the effectiveness of their construction and the interpretation of the resulting models, their realization deserves particular attention. The formation of a subset of meaningful features and a subset of essential instances is discussed in the context of fuzzy-rule-based models. In contrast to the existing studies, which are focused predominantly on feature selection (namely, a reduction of the input space), a position advocated here is that a reduction has to involve both data and features to become efficient to the design of fuzzy model. The reduction problem is combinatorial in its nature and, as such, calls for the use of advanced optimization techniques. In this study, we use a technique of particle swarm optimization (PSO) as an optimization vehicle of forming a subset of features and data (instances) to design a fuzzy model. Given the dimensionality of the problem (as the search space involves both features and instances), we discuss a cooperative version of the PSO along with a clustering mechanism of forming a partition of the overall search space. Finally, a series of numeric experiments using several machine learning data sets is presented.
Training High-Order Takagi-Sugeno Fuzzy Systems Using Batch Least Squares and Particle Swarm Optimization
