Study On Fuzzy Modeling Based On Interpretability And Precision

This dissertation focuses on how to construct interpretable and accurate fuzzy systems.The main parts are concluded as follows:First of all, the fundamental interpretability issues in fuzzy modeling are analyzedqualitatively. The well-recognized aspects of interpretability, including characteristics ofthe membership functions, characteristics of the fuzzy rules, the number of input variablesand fuzzy rules, etc., are detailed.Secondly, an approach to construct fuzzy systems based on genetic algorithm isdeveloped. The CART algorithm and the fuzzy GK clustering algorithm are used toidentify initial fuzzy systems respectively. Then a Pittsburgh-style real-coded geneticalgorithm is adopted to optimize the obtained fuzzy systems. During the optimizationprocess, the similarity-driven rule base simplification technique is embedded to reduce thefuzzy system. The proposed approach is applied to several benchmark problems, and theresults show its validity.Thirdly, the Multi-Objective Cooperative Co-evolutionary Algorithm (MOCCA) isintroduced in fuzzy modeling. Different components of fuzzy system, such as the numberof fuzzy rules, the antecedents of fuzzy rules and the parameters of the antecedents, aredecomposed to corresponding sub-species. The multiple objectives are aggregated to asingle objective using the weighted sum method. The MOCCA is carried out to evolve theinitial fuzzy system obtained by fuzzy clustering algorithm to optimize multiple objectivessimultaneously. For high-dimensional problems, the preprocessed feature selection method,called Simba, is used to select feasible features/input variables. The proposed approach isapplied to TS fuzzy systems and fuzzy classification systems, and the results show itsvalidity. To help guide the designing of fuzzy systems, how to determine the structureparameters of the fuzzy system and parameters of the MOCCA that effect the performancein fuzzy modeling is analyzed qualitatively.Fourthly, in order to obtain Pareto-optimal fuzzy systems, the Pareto Multi-ObjectiveCooperative Co-evolutionary Algorithm (PMOCCA) is proposed. The NSGA-â…¡algorithmis generalized from one species to multi-species, and a new non-dominated sortingtechnique and collaboration mechanism are developed. Different from classical weightedsum method in which multiple objectives are aggregated to a single objective and only afinal solution can be obtained in a single run, the PMOCCA can yield a set of fuzzysystems with different precision and interpretability. Finally, a novel hybrid co-evolutionary algorithm is proposed to design fuzzyclassification system. The Michigan-style genetic algorithm is a local optimizationalgorithm, while the Pittsburgh-style genetic algorithm is a global optimization algorithm.The proposed hybrid algorithm integrates the two advantages: first, a set of optimal fuzzyrules are generated by the Michigan-style genetic algorithm, then the Pittsburgh-stylePareto co-evolutionary algorithm is used to optimize the structure and parameters of thefuzzy classification system. The proposed approach is applied to several benchmarkproblems, and the results show its validity.