Extraction of Fuzzy Rules with Completeness and Robustness

2006

Abstract “Fuzzy Functions” are proposed to be determined separately by two regression estimation models: the least squares estimation (LSE), and Support Vector Machines for Regression (SVR), techniques for the development of fuzzy system models. LSE model tries to estimate the fuzzy function parameters linearly in the original space, whereas SVR algorithm maps the data samples into higher dimensional feature space and estimates a linear fuzzy function in the feature space.

Fuzzy Sets and Systems, 2007

The relationship between support vector machines (SVMs) and Takagi-Sugeno-Kang (TSK) fuzzy systems is shown. An exact representation of SVMs as TSK fuzzy systems is given for every used kernel function. Restricted methods to extract rules from SVMs have been previously published. Their limitations are surpassed with the presented extraction method. The behavior of SVMs is explained by means of fuzzy logic and the interpretability of the system is improved by introducing the -fuzzy rule-based system ( -FRBS). The -FRBS exactly approximates the SVM's decision boundary and its rules and membership functions are very simple, aggregating the antecedents with uninorms as compensation operators. The rules of the -FRBS are limited to two and the number of fuzzy propositions in each rule only depends on the cardinality of the set of support vectors. For that reason, the -FRBS overcomes the course of dimensionality and problems with high-dimensional data sets are easily solved with the -FRBS.

Artificial Intelligence in Real-Time Control 1994, 1995

Fuzzy identi~cation means to find a set of fuzzy if-then rules with well defined attributes, that can describe the given I/O-behaviour of a system. In the identification algorithm proposed here the subject of learning are the rule conclusians, i.e. the membership functions of output attributes in form of singletons. For fixed input membership functions learning is shown to be a least squares optimization problem linear in the unknown parameters. Examples show appli~tio~s of the algorithm to the linguistic fo~ulation of a PI control strategy and to identification of a nonlinear time-discrete dynamic system.

2002

This paper discusses how training algorithms for determining membership functions in fuzzy rule based systems can be applied. There are several training algorithms, which have been developed initially for neural networks and can be adapted to fuzzy systems. In this paper the Levenberg-Marquardt algorithm is introduced, allowing the determination of an optimal rule base and converging faster than some more classic methods (e.g. the standard Back Propagation algorithm). The class of membership functions investigated is the trapezoidal one as it is general enough and widely used. The method can be easily extended to arbitrary piecewise linear function as well.

IEEE Transactions on Systems, Man, and Cybernetics, 1992

Abstract-A general method is developed to generate fuzzy rules from numerical data. This new method consists of five steps: Step 1 divides the input and output spaces of the given numerical data into fuzzy regions; Step 2 generates fuzzy rules from the given data; Step 3 assigns a ...

International Journal of Approximate Reasoning, 2004

In Mixed Fuzzy Rule Formation [Int. J. Approx. Reason. 32 (2003) 67] a method to extract mixed fuzzy rules from data was introduced. The underlying algorithm's performance is influenced by the choice of fuzzy t-norm and t-conorm, and a heuristic to avoid conflicts between patterns and rules of different classes throughout training. In the following addendum to [Int. J. Approx. Reason. 32 (2003) 67], we discuss in more depth how these parameters affect the generalization performance of the resulting fuzzy rule models.

IEEE Transactions on Systems, Man, and Cybernetics, 1996

The two most essential fuzzy rule-based models used in the literature and in the industrial applications are briefly described. The way of reasoning in these models is shown. Interpolative reasoning for the case of sparse rule bases is also discussed. Rule base compression by eliminating redundant rules whose information can be reconstructed within a set accuracy interval from the remaining rules by using the previous interpolation method is shown. A general fuzzy model is discussed that contains the previous fuzzy models (as well as the nonfuzzy one) as special cases. Ways of transforming the different approximative models into each other via the general model and interpolation are presented.

NAFIPS 2006 - 2006 Annual Meeting of the North American Fuzzy Information Processing Society, 2006

In this paper, a new fuzzy inference method which is suitable for systems with large number of rules, is proposed. As we know, there are two well-known fuzzy inference systems, Mamdani and TSK. Each one has its own drawbacks and advantages but both of them have been encountered with problem while tuning their parameters especially when there is large number of rules in the system. Mamdani type systems faced to a huge amount of calculation and TSK type faced to large number of parameters. In our proposed method a combination of these two systems, is used. So it has small number of parameters for tuning as Mamdani has and it is as fast as TSK. We called this system Extended TSK because it is based upon it.

Engineering Letters, 2007

IEEE Transactions on Fuzzy Systems, 2002

The identification of a model is one of the key issues in the field of fuzzy system modeling and function approximation theory. There are numerous approaches to the issue of parameter optimization within a fixed fuzzy system structure but no reliable method to obtain the optimal topology of the fuzzy system from a set of input-output data. This paper presents a reliable method to obtain the structure of a complete rule-based fuzzy system for a specific approximation accuracy of the training data, i.e., it can decide which input variables must be taken into account in the fuzzy system and how many membership functions (MFs) are needed in every selected input variable in order to reach the approximation target with the minimum number of parameters.