Notes on Sugeno and Yasukawa's fuzzy modelling approach

2003

AI knowledge based systems have proven a very valuable tool to understand and model complex real-world problems. Unfortunately, human experts are often required to provide the knowledge or rules. Due to limited availability and sometimes experts' reluctance, or even inability, to give such expertise, knowledge acquisition has become the bottleneck in the development of knowledge based systems. However, there may well be a sensible amount of data that represents typical description of the domain problems. Therefore, data-driven techniques for automated generation of rules have been developed over the years to assist knowledge acquisition. While there have been efforts to make the automatically generated models transparent and readable, in most cases complexity ends up taking over. Fuzzy sets offers a way to deal with vague, imprecise or inaccurate information while reducing the complexity of knowledge representation. However, most of fuzzy rule generation methods, while fast, accurate and easily scalable to high dimensional problems, follow the so-called approximative approach, which works by creating and tuning the fuzzy rule bases and the fuzzy sets to best fit the data. Opposing this stands the descriptive approach, where semantics are as important as accuracy and the definition of the fuzzy sets is human given, thereby representing human interpretable concepts. Unfortunately, the methods to obtain descriptive models are generally rather slow, inaccurate and poorly scalable. It would be desirable to create a method to use the benefits of fast and efficient generation of the approximative approaches with the clarity and comprehensibility of descriptive approaches. The purpose of this thesis is the development of such a method. The thesis presents an effective and efficient approach for translating fuzzy rules that use approximative sets (accurate but unreadable) to rules that use descriptive sets and linguistic hedges of predefined meaning. It works by first generating rules that use approximative sets from training data, using a fast and accurate approximative algorithm that already exists. Then the resulting approximative rules are translated into descriptive ones. First, a heuristic conversion is performed to obtain a crude descriptive translation. Such a heuristically generated descriptive fuzzy model is then used to initialize a multi-objective GA. The GA, guided by the novel functional equivalence objectives, will fine-tune the heuristic translation into the final descriptive fuzzy rule set. Hedges that are useful for supporting such translations are provided. This thesis presents an improved version of more effective hedges specifically devised for trapezoidal fuzzy sets, to be applied to dilate or concentrate a given set by expanding or shrinking its constituent parts. It also introduces three new hedges not existing in the literature. Considerable experimental studies have been carried out, on the issues of the accuracy and transparency of the descriptive rules generated by the proposed approach. These include comparative analysis between alternative modelling approaches, v vi Declaration I hereby declare that I composed this thesis entirely myself and that it describes my own research.

2015

Abstract. Recently, a number of extensions to classical fuzzy logic systems (type-1 fuzzy logic systems) have been attracting interest. One of the most widely used extensions is the interval type-2 fuzzy logic systems. An interval type-2 TSK fuzzy logic system can be obtained by considering the membership functions of its existed type-1 counterpart as primary membership functions and assigning uncertainty to cluster centers, standard deviation of Gaussian membership functions and consequence parameters. This paper presents a review and comparison of type-1 fuzzy logic system and type-2 fuzzy systems in fuzzy modeling and identification. TSK fuzzy model is considered for both type-1 and type-2 fuzzy systems and model parameters are updated using gradient descent method. The experimental study is done on two widely known data, namely chemical plant data and the stock market data.

IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2008

One of the main attractions of a fuzzy rule-based system is its interpretability which is hindered severely with an increase in the dimensionality of the data. For high-dimensional data, the identification of fuzzy rules also possesses a big challenge. Feature selection methods often ignore the subtle nonlinear interaction that the features and the learning system can have. To address this problem of structure identification, we propose an integrated method that can find the bad features simultaneously when finding the rules from data for Takagi-Sugeno-type fuzzy systems. It is an integrated learning mechanism that can take into account the nonlinear interactions that may be present between features and between features and fuzzy rule-based systems. Hence, it can pick up a small set of useful features and generate useful rules for the problem at hand. Such an approach is computationally very attractive because it is not iterative in nature like the forward or backward selection approaches. The effectiveness of the proposed approach is demonstrated on four function-approximation-type well-studied problems.

Winter Simulation Conference, 1980

F~zzy sets theory and fuzzy logic constitute the basis for the linguistic approach. Under this approach, variables can assume linguistic values. Each linguistic value is characterized by a label and a meaning. The label is a sentence of a language. The meaning is a fuzzy subset of a universe of discourse. Models, based on this approach, can be constructed to simulate approximate reasoning. The implementation of these models presents two major problems, namely how to associate a label to an unlabelled fuzzy set on the basis of semantic similarity (linguistic approximation) and how to perform arithmetic operations with fuzzy numbers. For each problem a solution is proposed. Two illustrative applications are discussed. I.

International Journal of Systems Science, 2000

This paper presents an algorithm for incorporating a priori knowledge into data-driven identification of dynamic fuzzy models of the Takagi-Sugeno type. Knowledge about the modelled process such as its stability, minimal or maximal static gain, or the settling time of its step response can be translated into inequality constraints on the consequent parameters. By using input-output data, optimal parameter values are then found by means of quadratic programming. The proposed approach has been applied to the identification of a laboratory liquid level process. The obtained fuzzy model has been used in model-based predictive control. Real-time control results show that when the proposed identification algorithm is applied, not only physically justified models are obtained, but also the performance of the model-based controller improves with regard to the case where no prior knowledge is involved.