| Data-driven fuzzy modeling has been applied to many fields, such as patternrecognition, data mining, classification, prediction, and process control, and etc.Generally speaking, the so called "data-driven fuzzy modeling" is just a optimizationprocess in determining the structure and the parameter of a fuzzy system via sample data,and in the fuzzy system, partial or total parameters having been grouped into the searchspace. However, in such studies people often miss the observation that interpretabilityand accuracy are conflicting concepts. Actually, interpretability is a highly desirablefeature of a fuzzy system, and it is the most prominent feature that distinguishes fuzzysystems from many other modeling techniques. The research toward the interpretabilityof fuzzy system can help people to extract knowledge from large amount data, and thento know better the nature of the fuzzy system. But improve the interpretability of thefuzzy system and to improve the accuracy of fuzzy system are two conflicting criteria forfuzzy system modeling. It is difficult to just improve the interpretability of the systemwhile not loss its accuracy. Therefore, trade-off between accuracy and interpretability isthe most active research direction in data-driven fuzzy modeling.Based on understanding and analyzing the actual research state, research focuses anddevelopment trend in the domain of data-driven fuzzy modeling, this dissertation focuson modeling methods for trade-off between accuracy and interpretability. The methodsand models proposed by this dissertation syncretize multidisciplinary studies, includingfuzzy inference, artificial neural network, evolutionary computing, and swarmintelligence and so on. Many effective algorithms are proposed for the difficult problemsin above study fields, such as the fuzzy input space partitioning problem, the extraction offuzzy rules and parameters learning problem. Theory analysis and experimental resultsshow that the models are feasible and effective. In conclusion, the main achievements ofthis dissertation include:(1) In this dissertation, relevant fuzzy system theory, including fuzzy sets operators,fuzzy rules and fuzzy inference model, are summed up. As the focal point, it makes asurvey about the research on fuzzy system modeling, including the appearing background,the actual research state, challenging problems and development trend, etc.(2) In this dissertation the interpretability issues are discussed in detail. Thisdissertation proposes an evaluation criterion related to the interpretability of fuzzysystems, including the evaluation criterion to the fuzzy input space partitioning, and tothe fuzzy rules.(3) This dissertation proposes a fuzzy system modeling method based on geneticalgorithm.The antecedents of fuzzy system and input variables are coded into a binary stringand treated as an individual in genetic algorithm. Moreover, by the extraction of fuzzyIF-THEN rules the initial fuzzy system is constructed based on improving fuzzy weightedreasoning method. In the initial fuzzy system model Grid Partitioning is used to partitionfuzzy input space ,and the Gradient Descent optimization algorithm is used forparameters learning, so that the initial fuzzy system model has a trade-off betweenaccuracy and interpretability in a certain degree.(4) This dissertation proposes a fuzzy system modeling method based onhierarchical genetic algorithm.Because that grid partitioning method was adopted in constructing the initial fuzzysystem, the fuzzy rules had existed large redundancy feature, and the feature of fuzzyreasoning was inadequate. Besides, in the initial fuzzy system, after fuzzy subsets wasdecided, all available grid positions had been already determined, and it could have beenapparently lowering down the accuracy of the system. For the purpose of compensatingthe above-mentioned inadequacy, an optimized algorithm is proposed based onhierarchical genetic algorithm. It can evolve both the structure and weighting parametersof the fuzzy system, and a system parameter is used to adjust a trade-off between theinterpretability and the accuracy. Numerical simulations show the fuzzy system can beobtained with better interpretability and a higher or comparative accuracy compared withother methods known in the literature.(5) This dissertation proposes a fuzzy system modeling method based on ParticleSwarm Optimization.Particle Swarm Optimization (PSO) is an optimization algorithm proposed byKennedy and Eberhart in 1995. It has been applied in many optimization problems.Based on the analysis of PSO a fuzzy system modeling method is proposed. Thealgorithm can be automatically removing redundant fuzzy rules concerning theoptimization process of membership function parameters and connection parameters ofthe fuzzy system. Numerical simulations show the fuzzy system can be obtained withgood accuracy and interpretability. In the fuzzy system modeling methods a ParticleSwarm Optimization with Division of Work (PSOwDOW) is proposed. The strategy ofwork-dividing is adopted to overcome the disadvantages of the standard PSO inPSOwDOW. The whole swarm is divided into two subgroups: P_Near, and P_Far.Because the particle converges in P_Near, the particle's searching areas are considered asthe most hopeful to find new individual best and swarm best. Moreover, adopts the ideasof EP and seeks new swarm best near the optimum, and it is ensured to perform sufficientsearching near the optimum by this way;the movement track of the particles diverges inP_Far and they act as a role for exploring new searching areas during the operation of thealgorithm. These particles can keep the diversity of the population and avoid the"premature" phenomenon to taking place.(6) This dissertation proposes a fuzzy system modeling method based onmulti-objective PSO.Traditional multi objective optimization is settled by turning the multi objectiveproblem into single objective problem through weighted sum. However, this methodrequires a priori knowledge of the problem itself, so it cannot solve real multi objectiveproblems. Evolutionary Algorithm is a computer technique based on population, whichcan search for several solutions in the solution space and can improve the efficiency ofworking out solutions through the similarity of different solutions. Therefore,Evolutionary Algorithms are very suitable for solving multi objective optimizationproblems. This dissertation has conducted introduction and analysis to some of thecommonly utilized multi-objective evolutionary algorithm. And a multi-objective PSOalgorithm applied for fuzzy system optimization has been proposed.Designing a set of fuzzy systems can be considered as solving a multi-objectiveoptimization problem. An algorithm for solving the multi objective optimization problemis presented based on particle swarm optimization through the improvement of theselection manner for global and individual extremum. The search for the Pareto OptimalSet of fuzzy systems optimization problems is performed, and a tradeoff betweenaccuracy and interpretability of fuzzy systems is clearly shown by obtainednon-dominated solutions. Numerical simulations for taste identification of tea show theeffectiveness of the proposed algorithm.In conclusion, in the background of fuzzy logic, evolutionary algorithm and swamintelligence, this dissertation studies fuzzy system modeling and deals with trade-offbetween accuracy and interpretability. The achievements of this dissertation make appliedresearch on fuzzy system modeling theory progress, and provide effective methods andmeans for practical research of data-driven fuzzy system modeling.
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