Hans Roubos

GA-fuzzy modeling and classification: complexity and performance

The use of genetic algorithms (GAs) and other evolutionary optimization methods to design fuzzy rules for systems modeling and data classification have received much attention in recent literature. Authors have focused on various aspects of these randomized techniques, and a whole scale of algorithms have been proposed. We comment on some recent work and describe a new and efficient two-step approach that leads to good results for function approximation, dynamic systems modeling and data classification problems. First, fuzzy clustering is applied to obtain a compact initial rule-based model. Then this model is optimized by a real-coded GA subjected to constraints that maintain the semantic properties of the rules. We consider four examples from the literature: a synthetic nonlinear dynamic systems model, the iris data classification problem, the wine data classification problem, and the dynamic modeling of a diesel engine turbocharger. The obtained results are compared to other recently proposed methods.

Compact and transparent fuzzy models and classifiers through iterative complexity reduction

In our previous work (2000) we showed that genetic algorithms (GAs) provide a powerful tool to increase the accuracy of fuzzy models for both systems modeling and classification. In addition to these results, we explore the GA to find redundancy in the fuzzy model for the purpose of model reduction. An aggregated similarity measure is applied to search for redundancy in the rule base description. As a result, we propose an iterative fuzzy identification technique starting with data-based fuzzy clustering with an overestimated number of local models. The GA is then applied to find redundancy among the local models with a criterion based on maximal accuracy and maximal set similarity. After the reduction steps, the GA is applied with another criterion searching for minimal set similarity and maximal accuracy. This results in an automatic identification scheme with fuzzy clustering, rule base simplification and constrained genetic optimization with low-human intervention. The proposed modeling approach is then demonstrated for a system identification and a classification problem.

Learning Fuzzy Classification Rules from Data

Automatic design of fuzzy rule-based classification systems based on labeled data is considered. It is recognized that both classification performance and interpretability are of major importance and effort is made to keep the resulting rule bases small and comprehensible. An iterative approach for developing fuzzy classifiers is proposed. The initial model is derived from the data and subsequently, feature selection and rule base simplification are applied to reduce the model, and a GA is used for model tuning. An application to the Wine data classification problem is shown.

Accurate, Transparent, and Compact Fuzzy Models for Function Approximation and Dynamic Modeling through Multi-objective Evolutionary Optimization

Evolutionary algorithms to design fuzzy rules from data for systems modeling have received much attention in recent literature. Many approaches are able to find highly accurate fuzzy models. However, these models often contain many rules and are not transparent. Therefore, we propose several objectives dealing with transparency and compactness besides the standard accuracy objective. These objectives are used to find multiple Pareto-optimal solutions with a multi-objective evolutionary algorithm in a single run. Attractive models with respect to compactness, transparency and accuracy are the result.

Transparent fuzzy modeling using fuzzy clustering and GAs

A combined approach to data-driven fuzzy rule-based modeling is described. The rules of an initial model are derived from data by means of a supervised clustering method that to a certain degree ensures the transparency of the resulting rule base. This model is, however suboptimal and a real-coded genetic algorithm (GA) is proposed to optimize simultaneously both the antecedent and the consequent variables. The GA is subjected to constraints concerning the semantic properties of the rule base, inherited from the initial model. Two modeling problems illustrate the power of the combined approach.

Accurate, transparent and compact fuzzy models by multi-objective evolutionary algorithms

Interpretability aspects of fuzzy models have received quite some attention in recent years and may be obtained by using transparent rule-structures and well characterized fuzzy membership functions. Moreover, model compactness is important for the interpretability and is related to the number of rules and fuzzy sets. Besides these two criteria, the model accuracy should always be taken into account. In this way, several criteria appear in fuzzy modeling and then multiobjective evolutionary algorithms are a suitable, because these are able to capture several non-dominated solutions in a single run of the algorithm. For fuzzy modeling, we describe two multi-objective evolutionary algorithms that consider all three objectives. Differences between both algorithms arise in the fuzzy sets considered, trapezoidal and gaussian respectively. The algorithms apply an accuracy criterium and a transparency criterium, based on fuzzy set similarity, while compactness is achieved by a specific technique, incorporated ad hoc within the evolutionary algorithms. Finally, we propose a decision process to find the most satisfactory non-dominated solution. Results are shown for three approximation problems that were studied before by others authors.

Interpretable Semi-Mechanistic Fuzzy Models by Clustering, OLS and FIS Model Reduction

A semi-mechanistic fuzzy modeling technique is proposed to obtain compact and transparent process models based on small data-sets. Semi-mechanistic models are hybrid models that consist of a white box structure based on mechanistic relationships and black-box substructures to model less defined parts. First, it is shown that certain type of white-box models can be efficiently incorporated into a Takagi-Sugeno fuzzy rule structure. Next, the proposed models are identified from learning data and special attention is paid to transparency and accuracy aspects. The approach is based on a combination of (i) prior knowledge-based model structures, (ii) fuzzy clustering, (iii) orthogonal least-squares, and (iv) the modified Fisher’s interclass separability method. For the identification of the semimechanistic fuzzy model, a new fuzzy clustering method is proposed, i.e., clustering is achieved by the simultaneous identification of fuzzy sets defined on some of the scheduling variables and identification of the parameters of the local semimechanistic submodels. Subsequently, model reduction is applied to make the TS models as compact as possible, i.e., the most relevant consequent variables are selected by an orthogonal least squares method, and the modified Fisher’s interclass separability criteria is used for selection of relevant antecedent (scheduling) variables. The overall procedure is demonstrated by the development of a semimechanistic model for a biochemical process. Although the results do not carry over directly to other engineering fields, the main ideas and conclusions, will certainly hold for other application areas as well.