Number Of Fuzzy If-then Rules Research Articles

ILMI Approach to Static Output Feedback Fuzzy Control for Synchronization of Hyperchaotic Systems via T-S Models

A static output feedback fuzzy (SOFF) control approach is proposed in order to deal with the problem of syn- chronization of two identical hyperchaotic systems. The T-S fuzzy model with its small number of fuzzy IF-THEN rules is employed to represent many typical nonlinear hyperchaotic systems. Based on the T-S fuzzy hyperchaotic models and Lyapunov stability theory, a necessary condition for the existence of robust SOFF controllers is presented in terms of a set of matrix inequalities, which guarantees the stable synchronization of two different hyperchaotic systems. An iterative lin- ear matrix inequality (ILMI) algorithm is proposed to compute the feedback gains of the suboptimal SOFF controller. Fi- nally, numerical examples are given to demonstrate the validity and effectiveness of the proposed fuzzy modeling and synchronization scheme of the hyper chaotic systems.

Fuzzy Modeling and H¥ Synchronization of Different Hyperchaotic Systems via T–S Models

In this paper, a unified fuzzy H¥ control approach is proposed to deal with the problem of synchronization of two different hyperchaotic systems. The T-S fuzzy models with a small number of fuzzy IF-THEN rules are employed to represent many typical hyperchaotic systems exactly. Based on the T-S fuzzy hyperchaotic models, a fuzzy H¥ synchronization controller is designed via parallel distributed compensation (PDC) techniques. The sufficient condition for the H¥ synchronization of two different hyperchaotic systems is derived by applying Lyapunov stability theory. The results are expressed in terms of LMIs, and therefore it is very convenient to check in practice. This method is a universal one for synchronization of two different hyperchaotic systems. Numerical examples are given to demonstrate the validity of the proposed fuzzy modeling and hyperchaotic synchronization scheme.

Data Mining of Gene Expression Data by Fuzzy and Hybrid Fuzzy Methods

Microarray studies and gene expression analysis have received tremendous attention over the last few years and provide many promising avenues toward the understanding of fundamental questions in biology and medicine. Data mining of these vasts amount of data is crucial in gaining this understanding. In this paper, we present a fuzzy rule-based classification system that allows for effective analysis of gene expression data. The applied classifier consists of a set of fuzzy if-then rules that enable accurate nonlinear classification of input patterns. We further present a hybrid fuzzy classification scheme in which a small number of fuzzy if-then rules are selected through means of a genetic algorithm, leading to a compact classifier for gene expression analysis. Extensive experimental results on various well-known gene expression datasets confirm the efficacy of our approaches.

통계적 정보기반 계층적 퍼지-러프 분류기법

본 논문에서는 학습기법을 사용하지 않고 패턴분류의 성능을 최대화하면서 규칙의 수를 줄일 수 있는 통계적 정보기반 계층적 퍼지-러프 분류방법을 제안한다. 제안된 방법에서 통계적 정보는 계층적 퍼지-러프 분류 시스템에서 각 계층의 입력부 퍼지집합의 분할 구간을 추출하기 위해서 사용되었고, 러프집합은 통계적 정보로부터 추출된 분할 구간들과 연관된 퍼지 if-then 규칙의 수를 최소화하기 위해서 사용되었다. 제안된 방법의 효과성을 보이기 위해 Fisher의 IRIS 데이터를 사용한 기존 패턴분류 방법의 분류 정확도와 규칙들의 수를 비교하였다. 그 결과, 제안된 방법은 기존 방법들의 분류 성능과 유사함을 확인할 수 있었다. In this paper, we propose a hierarchical fuzzy-rough classification method based on statistical information for maximizing the performance of pattern classification and reducing the number of rules without learning approaches such as neural network, genetic algorithm. In the proposed method, statistical information is used for extracting the partition intervals of antecedent fuzzy sets at each layer on hierarchical fuzzy-rough classification systems and rough sets are used for minimizing the number of fuzzy if-then rules which are associated with the partition intervals extracted by statistical information. To show the effectiveness of the proposed method, we compared the classification results(e.g. the classification accuracy and the number of rules) of the proposed with those of the conventional methods on the Fisher's IRIS data. From the experimental results, we can confirm the fact that the proposed method considers only statistical information of the given data is similar to the classification performance of the conventional methods.

An approach to fuzzy default reasoning for function approximation

This paper discusses fuzzy reasoning for approximately realizing nonlinear functions by a small number of fuzzy if-then rules with different specificity levels. Our fuzzy rule base is a mixture of general and specific rules, which overlap with each other in the input space. General rules work as default rules in our fuzzy rule base. First, we briefly describe existing approaches to the handling of default rules in the framework of possibility theory. Next, we show that standard interpolation-based fuzzy reasoning leads to counterintuitive results when general rules include specific rules with different consequents. Then, we demonstrate that intuitively acceptable results are obtained from a non-standard inclusion-based fuzzy reasoning method. Our approach is based on the preference for more specific rules, which is a commonly used idea in the field of default reasoning. When a general rule includes a specific rule and they are both compatible with an input vector, the weight of the general rule is discounted in fuzzy reasoning. We also discuss the case where general rules do not perfectly but partially include specific rules. Then we propose a genetics-based machine learning (GBML) algorithm for extracting a small number of fuzzy if-then rules with different specificity levels from numerical data using our inclusion-based fuzzy reasoning method. Finally, we describe how our approach can be applied to the approximate realization of fuzzy number-valued nonlinear functions

Fuzzy rule selection by multi-objective genetic local search algorithms and rule evaluation measures in data mining

This paper shows how a small number of simple fuzzy if-then rules can be selected for pattern classification problems with many continuous attributes. Our approach consists of two phases: candidate rule generation by rule evaluation measures in data mining and rule selection by multi-objective evolutionary algorithms. In our approach, first candidate fuzzy if-then rules are generated from numerical data and prescreened using two rule evaluation measures (i.e., confidence and support) in data mining. Then a small number of fuzzy if-then rules are selected from the prescreened candidate rules using multi-objective evolutionary algorithms. In rule selection, we use three objectives: maximization of the classification accuracy, minimization of the number of selected rules, and minimization of the total rule length. Thus the task of multi-objective evolutionary algorithms is to find a number of non-dominated rule sets with respect to these three objectives. The main contribution of this paper is to propose an idea of utilizing the two rule evaluation measures as prescreening criteria of candidate rules for fuzzy rule selection. An arbitrarily specified number of candidate rules can be generated from numerical data for high-dimensional pattern classification problems. Through computer simulations, we demonstrate that such a prescreening procedure improves the efficiency of our approach to fuzzy rule selection. We also extend a multi-objective genetic algorithm (MOGA) in our former studies to a multi-objective genetic local search (MOGLS) algorithm where a local search procedure adjusts the selection (i.e., inclusion or exclusion) of each candidate rule. Furthermore, a learning algorithm of rule weights (i.e., certainty factors) is combined with our MOGLS algorithm. Such extensions to our MOGA for fuzzy rule selection are another contribution of this paper.

Robust tracking designs for both holonomic and nonholonomic constrained mechanical systems: adaptive fuzzy approach

Adaptive fuzzy-based tracking control designs are proposed in the paper for both holonomic mechanical systems as well as a large class of nonholonomic mechanical systems with plant uncertainties and external disturbances. A unified and systematic procedure is employed to derive the controllers for both holonomic and nonholonomic mechanical control systems, respectively. First, a fuzzy logic system is introduced to learn the behavior of unknown (or uncertain) mechanical dynamics by using an adaptive algorithm. Next, the effect of approximation error on the tracking error must be efficiently eliminated by employing an additional robustifying algorithm. Consequently, hybrid adaptive-robust controllers can be constructed such that the resulting closed-loop mechanical systems guarantee a satisfactorily transient and asymptotic performance. Furthermore, a partitioned procedure with respect to the above developed adaptive fuzzy logic approximators is introduced such that the number of fuzzy IF-THEN rules is significantly reduced and the developed control schemes can be easily implemented from the viewpoint of practical applications. Finally, simulation examples are presented to illustrate the tracking performance of a two-link constrained robot manipulator and a vertical wheel rolling on a plane surface by the proposed adaptive fuzzy-based control algorithms.

An advanced fuzzy controller

A methodology for the reduction of complexity of the fuzzy if-then rules for a robust controller system is presented. An analysis of the fuzzy if-then rules is performed by viewing the fuzzy sets in the rules as crisp sets. The knowledge of the analysis is used to reduce the number of variables and the number of fuzzy if-then rules. By applying fuzzy logic to the reduced linguistic if-then rules, a robust controller system based on fuzzy if-then rules is reconstructed. The simulation results show that the reconstructed controller is more efficient and performs as well as the original controller.

Improving the performance of fuzzy classifier systems for pattern classification problems with continuous attributes

In this paper, various methods are introduced for improving the ability of fuzzy classifier systems to automatically generate fuzzy if-then rules for pattern classification problems with continuous attributes. First, we describe a simple fuzzy classifier system where a randomly generated initial population of fuzzy if-then rules is evolved by typical genetic operations, such as selection, crossover, and mutation. By computer simulations on a real-world pattern classification problem with many continuous attributes, we show that the search ability of such a simple fuzzy classifier system is not high. Next, we examine the search ability of a hybrid algorithm where a learning procedure of fuzzy if-then rules is combined with the fuzzy classifier system. Then, we introduce two heuristic procedures for improving the performance of the fuzzy classifier system. One is a heuristic rule generation procedure for an initial population where initial fuzzy if-then rules are directly generated from training patterns. The other is a heuristic population update procedure where new fuzzy if-then rules are generated from misclassified and rejected training patterns, as well as from existing fuzzy if-then rules by genetic operations. By computer simulations, we demonstrate that these two heuristic procedures drastically improve the search ability of the fuzzy classifier system. We also examine a variant of the fuzzy classifier system where the population size (i.e., the number of fuzzy if-then rules) varies depending on the classification performance of fuzzy if-then rules in the current population.

Comparison of the Michigan and Pittsburgh approaches to the design of fuzzy classification systems

Fuzzy systems based on fuzzy if-then rules have been applied to various problems. The main application area has been fuzzy control problems. In many cases, such fuzzy systems can handle only a few input variables. This is because the number of fuzzy if-then rules exponentially increases as the number of input variables increases. In this paper, we try to design fuzzy classification systems based on fuzzy if-then rules for multidimensional pattern classification problems with many attributes. For designing such fuzzy classification systems, we compare two frameworks in the area of genetics-based machine learning: the Michigan approach and the Pittsburgh approach. The performance of fuzzy rule-based classification systems is also compared with that of various pattern classification methods. In computer simulations, we use a wine classification problem with 13 attributes, a cancer diagnosis problem with 9 attributes, and a credit approval problem with 14 attributes. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(12): 10–19, 1997

Comparison of the Michigan and Pittsburgh approaches to the design of fuzzy classification systems

Fuzzy systems based on fuzzy if-then rules have been applied to various problems. The main application area has been fuzzy control problems. In many cases, such fuzzy systems can handle only a few input variables. This is because the number of fuzzy if-then rules exponentially increases as the number of input variables increases. In this paper, we try to design fuzzy classification systems based on fuzzy if-then rules for multidimensional pattern classification problems with many attributes. For designing such fuzzy classification systems, we compare two frameworks in the area of genetics-based machine learning: the Michigan approach and the Pittsburgh approach. The performance of fuzzy rule-based classification systems is also compared with that of various pattern classification methods. In computer simulations, we use a wine classification problem with 13 attributes, a cancer diagnosis problem with 9 attributes, and a credit approval problem with 14 attributes. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(12): 10–19, 1997

Pointer adaptation and pruning of min-max fuzzy inference and estimation

A new technique for adaptation of fuzzy membership functions in a fuzzy inference system is proposed. The pointer technique relies upon the isolation of the specific membership functions that contributed to the final decision, followed by the updating of these functions' parameters using steepest descent. The error measure used is thus backpropagated from output to input, through the min and max operators used during the inference stage. This occurs because the operations of min and max are continuous differentiable functions and, therefore, can be placed in a chain of partial derivatives for steepest descent backpropagation adaptation. Interestingly, the partials of min and max act as pointers with the result that only the function that gave rise to the min or max is adapted; the others are not. To illustrate, let /spl alpha/=max [/spl beta//sub 1/, /spl beta//sub 2/, /spl middot//spl middot//spl middot/, /spl beta//sub N/]. Then /spl part//spl alpha///spl part//spl beta//sub n/=1 when /spl beta//sub n/ is the maximum and is otherwise zero. We apply this property to the fine tuning of membership functions of fuzzy min-max decision processes and illustrate with an estimation example. The adaptation process can reveal the need for reducing the number of membership functions. Under the assumption that the inference surface is in some sense smooth, the process of adaptation can reveal overdetermination of the fuzzy system in two ways. First, if two membership functions come sufficiently close to each other, they can be fused into a single membership function. Second, if a membership function becomes too narrow, it can be deleted. In both cases, the number of fuzzy IF-THEN rules is reduced. In certain cases, the overall performance of the fuzzy system can be improved by this adaptive pruning.

Selecting fuzzy if-then rules for classification problems using genetic algorithms

This paper proposes a genetic-algorithm-based method for selecting a small number of significant fuzzy if-then rules to construct a compact fuzzy classification system with high classification power. The rule selection problem is formulated as a combinatorial optimization problem with two objectives: to maximize the number of correctly classified patterns and to minimize the number of fuzzy if-then rules. Genetic algorithms are applied to this problem. A set of fuzzy if-then rules is coded into a string and treated as an individual in genetic algorithms. The fitness of each individual is specified by the two objectives in the combinatorial optimization problem. The performance of the proposed method for training data and test data is examined by computer simulations on the iris data of Fisher.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>