Hybridization of fuzzy GBML approaches for pattern classification problems

We propose a hybrid algorithm of two fuzzy genetics-based machine learning approaches (i.e., Michigan and Pittsburgh) for designing fuzzy rule-based classification systems. First, we examine the search ability of each approach to efficiently find fuzzy rule-based systems with high classification accuracy. It is clearly demonstrated that each approach has its own advantages and disadvantages. Next, we combine these two approaches into a single hybrid algorithm. Our hybrid algorithm is based on the Pittsburgh approach where a set of fuzzy rules is handled as an individual. Genetic operations for generating new fuzzy rules in the Michigan approach are utilized as a kind of heuristic mutation for partially modifying each rule set. Then, we compare our hybrid algorithm with the Michigan and Pittsburgh approaches. Experimental results show that our hybrid algorithm has higher search ability. The necessity of a heuristic specification method of antecedent fuzzy sets is also demonstrated by computational experiments on high-dimensional problems. Finally, we examine the generalization ability of fuzzy rule-based classification systems designed by our hybrid algorithm.     

一种进化模糊逻辑控制器的新方法

结合进化学习分类器的密歇根和匹兹堡方法的优点,首次将对单条控制规则的评价引入了模糊逻辑控制器（ＦＬＣ）的进化过程中,解决了匹兹堡类型的学习分类器系统“强化信息的带宽窄”的问题,实现了ＦＬＣ在控制器级和规则级的同时进化,控制器的控制规则数目也可以自由变化,实验结果表明新方法有较高的效率,优化的模糊控制器的结构简单,性能良好。     

A hybrid fuzzy cognitive model based on weighted OWA operators and single‐antecedent rules

Conventional fuzzy cognitive maps (FCMs) can only represent monotonic or symmetric causal relationships and cannot simulate the AND/OR combinations of the antecedent nodes. The rule‐based fuzzy cognitive maps (RBFCMs) usually suffer from the well‐known combinatorial rule explosion problem. A hybrid fuzzy cognitive model based on weighted OWA operators and single‐antecedent rules is proposed to eliminate the drawbacks of the existing FCM models. Hybrid fuzzy cognitive maps (HFCMs) represent the causal relationships with single‐antecedent fuzzy rules and handle the various AND/OR relationships among the antecedent nodes with weighted OWA aggregation operators. Compared with conventional FCMs, HFCMs have more powerful cognitive capability. Compared with RBFCMs, HFCMs reduce the scale and complexity of the rule bases significantly and have better representation and inference performance. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 1189–1196, 2007.     

Online tuning of fuzzy PID controllers via rule weighing based on normalized acceleration

In this study, an on-line tuning method is proposed for fuzzy PID controllers via rule weighing. The rule weighing mechanism is a fuzzy rule base with two inputs namely; “error” and “normalized acceleration”. Here, the normalized acceleration provides relative information on the fastness or slowness of the system response. In deriving the fuzzy rules of the weighing mechanism, the transient phase of the unit step response of the closed loop system is to be analyzed. For this purpose, this response is assumed to be divided into certain regions, depending on the number of membership functions defined for the error input of the fuzzy logic controller. Then, the relative importance or influence of the fired fuzzy rules is determined for each region of the transient phase of the unit step response of the closed loop system. The output of the fuzzy rule weighing mechanism is charged as the tuning variable of the rule weights; and, in this manner, an on-line self-tuning rule weight assignment is accomplished. The effectiveness of the proposed on-line weight adjustment method is demonstrated on linear and non-linear systems by simulations. Moreover, a real time application of this new method is accomplished on a pH neutralization process.     

Emergence of self‐learning fuzzy systems by a new virus DNA–based evolutionary algorithm

In this article, we propose a new approach to the virus DNA–based evolutionary algorithm (VDNA‐EA) to implement self‐learning of a class of Takagi‐Sugeno (T‐S) fuzzy controllers. The fuzzy controllers use T‐S fuzzy rules with linear consequent, the generalized input fuzzy sets, Zadeh fuzzy logic and operators, and the generalized defuzzifier. The fuzzy controllers are proved to be nonlinear proportional‐integral (PI) controllers with variable gains. The fuzzy rules are discovered automatically and the design parameters in the input fuzzy sets and the linear rule consequent are optimized simultaneously by the VDNA‐EA. The VDNA‐EA uses the VDNA encoding method that stemmed from the structure of the VDNA to encode the design parameters of the fuzzy controllers. We use the frameshift decoding method of the VDNA to decode the DNA chromosome into the design parameters of the fuzzy controllers. In addition, the gene transfer operation and bacterial mutation operation inspired by a microbial evolution phenomenon are introduced into the VDNA‐EA. Moreover, frameshift mutation operations based on the DNA genetic operations are used in the VDNA‐EA to add and delete adaptively fuzzy rules. Our encoding method can significantly shorten the code length of the DNA chromosomes and improve the encoding efficiency. The length of the chromosome is variable and it is easy to insert and delete parts of the chromosome. It is suitable for complex knowledge representation and is easy for the genetic operations at gene level to be introduced into the VDNA‐EA. We show how to implement the new method to self‐learn a T‐S fuzzy controller in the control of a nonlinear system. The fuzzy controller can be constructed automatically by the VDNA‐EA. Computer simulation results indicate that the new method is effective and the designed fuzzy controller is satisfactory. © 2003 Wiley Periodicals, Inc.     

Hybrid compensation control for affine TSK fuzzy control systems

The paper proposes a way of designing state feedback controllers for affine Takagi-Sugeno-Kang (TSK) fuzzy models. In the approach, by combining two different control design methodologies, the proposed controller is designed to compensate all rules so that the desired control performance can appear in the overall system. Our approach treats all fuzzy rules as variations of a nominal rule and such variations are individually dealt with in a Lyapunov sense. Previous approaches have proposed a similar idea but the variations are dealt with as a whole in a robust control sense. As a consequence, when fuzzy rules are distributed in a wide range, the stability conditions may not be satisfied. In addition, the control performance of the closed-loop system cannot be anticipated in those approaches. Various examples were conducted in our study to demonstrate the effectiveness of the proposed control design approach. All results illustrate good control performances as desired.     

Boosting fuzzy rules in classification problems under single‐winner inference

In previous studies, we have shown that an Adaboost‐based fitness can be successfully combined with a Genetic Algorithm to iteratively learn fuzzy rules from examples in classification problems. Unfortunately, some restrictive constraints in the implementation of the logical connectives and the inference method were assumed. Alas, the knowledge bases Adaboost produces are only compatible with an inference based on the maximum sum of votes scheme, and they can only use the t‐norm product to model the “and” operator. This design is not optimal in terms of linguistic interpretability. Using the sum to aggregate votes allows many rules to be combined, when the class of an example is being decided. Because it can be difficult to isolate the contribution of individual rules to the knowledge base, fuzzy rules produced by Adaboost may be difficult to understand linguistically. In this point of view, single‐winner inference would be a better choice, but it implies dropping some nontrivial hypotheses. In this work we introduce our first results in the search for a boosting‐based genetic method able to learn weighted fuzzy rules that are compatible with this last inference method. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 1021–1034, 2007.     

Robust adaptive fuzzy controller for non‐affine nonlinear systems with dynamic rule activation

This paper describes the design of a robust adaptive fuzzy controller for an uncertain single‐input single‐output nonlinear dynamical systems. While most recent results on fuzzy controllers considers affine systems with fixed rule‐base fuzzy systems, we propose a control scheme for non‐affine nonlinear systems and a dynamic fuzzy rule activation scheme in which an appropriate number of the fuzzy rules are chosen on‐line. By using the proposed scheme, we can reduce the computation time, storage space, and dynamic order of the adaptive fuzzy system without significant performance degradation. The Lyapunov synthesis approach is used to guarantee a uniform ultimate boundedness property for the tracking error, as well as for all other signals in the closed loop. No a priori knowledge of an upper bounds on the uncertainties is required. The theoretical results are illustrated through a simulation example. Copyright © 2002 John Wiley & Sons, Ltd.     

Mining the fuzzy control rules of aeration in a Submerged Biofilm Wastewater Treatment Process

This paper presents a special rule base extraction analysis for optimal design of an integrated neural-fuzzy process controller using an “impact assessment approach.” It sheds light on how to avoid some unreasonable fuzzy control rules by screening inappropriate fuzzy operators and reducing over fitting issues simultaneously when tuning parameter values for these prescribed fuzzy control rules. To mitigate the design efforts, the self-learning ability embedded in the neural networks model was emphasized for improving the rule extraction performance. An aeration unit in an Aerated Submerged Biofilm Wastewater Treatment Process (ASBWTP) was picked up to support the derivation of a solid fuzzy control rule base. Four different fuzzy operators were compared against one other in terms of their actual performance of automated knowledge acquisition in the system based on a partial or full rule base prescribed. Research findings suggest that using bounded difference fuzzy operator (O_b) in connection with back propagation neural networks (BPN) algorithm would be the best choice to build up this feedforward fuzzy controller design.     

A NEW DESIGN APPROACH FOR FUZZY‐LEARNING FUZZY CONTROLLERS

In this paper, a new approach to designing fuzzy‐learning fuzzy controllers for a system plant without an exact mathematical model is presented. The cost function is defined as the square of the sliding function to alleviate the difficulty of overshoot when on‐line learning is conducted. The learning mechanism of a fuzzy controller is constructed so as to minimize the cost function with a set of linguistic rules. Moreover, to reduce the complexity of the fuzzy‐learning fuzzy controller, the fuzzy mechanism used for learning and the fuzzy mechanism contained in the fuzzy controller are designed so as to have the identical structures. Finally, simulations are included to show the effectiveness of the fuzzy‐learning fuzzy controllers.     

Simultaneous design of membership functions and rule sets for fuzzycontrollers using genetic algorithms

This paper examines the applicability of genetic algorithms (GA's) in the simultaneous design of membership functions and rule sets for fuzzy logic controllers. Previous work using genetic algorithms has focused on the development of rule sets or high performance membership functions; however, the interdependence between these two components suggests a simultaneous design procedure would be a more appropriate methodology. When GA's have been used to develop both, it has been done serially, e.g., design the membership functions and then use them in the design of the rule set. This, however, means that the membership functions were optimized for the initial rule set and not the rule set designed subsequently. GA's are fully capable of creating complete fuzzy controllers given the equations of motion of the system, eliminating the need for human input in the design loop. This new method has been applied to two problems, a cart controller and a truck controller. Beyond the development of these controllers, we also examine the design of a robust controller for the cart problem and its ability to overcome faulty rules     

Increasing fuzzy rules cooperation based on evolutionary adaptive inference systems

This article presents a study on the use of parametrized operators in the Inference System of linguistic fuzzy systems adapted by evolutionary algorithms, for achieving better cooperation among fuzzy rules. This approach produces a kind of rule cooperation by means of the inference system, increasing the accuracy of the fuzzy system without losing its interpretability. We study the different alternatives for introducing parameters in the Inference System and analyze their interpretation and how they affect the rest of the components of the fuzzy system. We take into account three applications in order to analyze their accuracy in practice. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 1035–1064, 2007.     

Development of genetic fuzzy logic controllers for complex production systems

Complex production systems can produce more than one part type. For these systems, production rate and priority of production for each part type is determined by production controllers. In this paper, genetic fuzzy logic control (GFLC) methodology is used to develop two production control architectures namely “genetic distributed fuzzy” (GDF), and “genetic supervisory fuzzy” (GSF) controllers. Previously these controllers have been applied to single-part-type production systems. In the new approach the GDF and GSF controllers are developed to control complex production systems. The methodology is illustrated and evaluated using two test cases; two-part-type production line and re-entrant production systems. Genetic algorithm is used to tune the membership functions of input variables of GSF or GDF controllers. The objective function of the GSF controller minimizes the production cost based on work-in-process (WIP) and backlog costs, while surplus minimization is considered by GDF controller. The results show that GDF and GSF controllers can improve the performance of production systems. GSF controllers decrease the WIP level and its variations. GDF controllers show their abilities in reducing the backlog level but generally, production cost for GDF controller is greater than GSF controller.     

An evolutionary‐based adaptive neuro‐fuzzy inference system for intelligent short‐term load forecasting

The continuing growth in size and complexity of electric power systems requires the development of applicable load forecasting models to estimate the future electrical energy demands accurately. This paper presents a novel load forecasting approach called genetic‐based adaptive neuro‐fuzzy inference system (GBANFIS) to construct short‐term load forecasting expert systems and controllers. At the first stage, all records of data are searched by a novel genetic algorithm (GA) to find the most suitable feature of inputs to construct the model. Then, determined inputs are fed into the adaptive neuro‐fuzzy inference system to evolve the initial knowledge‐base of the expert system. Finally, the initial knowledge‐base is searched by another robust GA to induce a better cooperation among the rules by rule weight derivation and rule selection mechanisms. We show the superiority and applicability of our approach by applying it to the Iranian monthly electrical energy demand problem and comparing it with the most frequently adopted approaches in this field. Results indicate that GBANFIS outperforms its rival approaches and is a promising tool for dealing with short‐term load forecasting problems.     

Local identification of prototypes for genetic learning of accurate TSK fuzzy rule‐based systems

This work presents the use of local fuzzy prototypes as a new idea to obtain accurate local semantics‐based Takagi–Sugeno–Kang (TSK) rules. This allow us to start from prototypes considering the interaction between input and output variables and taking into account the fuzzy nature of the TSK rules. To do so, a two‐stage evolutionary algorithm based on MOGUL (a methodology to obtain Genetic Fuzzy Rule‐Based Systems under the Iterative Rule Learning approach) has been developed to consider the interaction between input and output variables. The first stage performs a local identification of prototypes to obtain a set of initial local semantics‐based TSK rules, following the Iterative Rule Learning approach and based on an evolutionary generation process within MOGUL (taking as a base some initial linguistic fuzzy partitions). Because this generation method induces competition among the fuzzy rules, a postprocessing stage to improve the global system performance is needed. Two different processes are considered at this stage, a genetic niching‐based selection process to remove redundant rules and a genetic tuning process to refine the fuzzy model parameters. The proposal has been tested with two real‐world problems, achieving good results. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 909–941, 2007.     

基于矢量“隶属度”的模糊控制器结构优化

针对传统模糊控制器在控制过程中容易发生规则爆炸的缺点,提出一种基于矢量“隶属度”的模糊控制器结构优化方法。这种优化方法通过对传统模糊控制器的隶属度和模糊等级进行改进,把当前输入量的相对方向和大小等级分别反映在矢量“隶属度”和标量模糊等级上,从而能够大大减少模糊规则数目,降低结构复杂度,提高控制效率。直流电动机的仿真控制效果表明,矢量“隶属度”法优化后的控制器比传统控制器结构简单和误差小,从而验证了这种方法的有效性和可行性。     

Design and analysis of fuzzy schedulers using fuzzy Lyapunov synthesis

Recently, a new approach to the design of fuzzy control rules was suggested. The method, referred to as fuzzy Lyapunov synthesis, extends classical Lyapunov synthesis to the domain of “computing with words”, and allows the systematic, instead of heuristic, design and analysis of fuzzy controllers given linguistic information about the plant. In this paper, we use fuzzy Lyapunov synthesis to design and analyze the rule-base of a fuzzy scheduler. Here, too, rather than use heuristics, we can derive the fuzzy rule-base systematically. This suggests that the process of deriving the rules can be automated. Our approach may lead to a novel computing with words algorithm: the input is linguistic information concerning the “plant” and the “control” objective, and the output is a suitable fuzzy rule-base.     

Learning cooperative linguistic fuzzy rules using the best–worst ant system algorithm

Within the field of linguistic fuzzy modeling with fuzzy rule‐based systems, the automatic derivation of the linguistic fuzzy rules from numerical data is an important task. In the last few years, a large number of contributions based on techniques such as neural networks and genetic algorithms have been proposed to face this problem. In this article, we introduce a novel approach to the fuzzy rule learning problem with ant colony optimization (ACO) algorithms. To do so, this learning task is formulated as a combinatorial optimization problem. Our learning process is based on the COR methodology proposed in previous works, which provides a search space that allows us to obtain fuzzy models with a good interpretability–accuracy trade‐off. A specific ACO‐based algorithm, the Best–Worst Ant System, is used for this purpose due to the good performance shown when solving other optimization problems. We analyze the behavior of the proposed method and compare it to other learning methods and search techniques when solving two real‐world applications. The obtained results lead us to remark the good performance of our proposal in terms of interpretability, accuracy, and efficiency. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 433–452, 2005.     

Clustering-based initialization of Learning Classifier Systems

The present paper investigates whether an “informed” initialization process can help supervised LCS algorithms evolve rulesets with better characteristics, including greater predictive accuracy, shorter training times, and/or more compact knowledge representations. Inspired by previous research suggesting that the initialization phase of evolutionary algorithms may have a considerable impact on their convergence speed and the quality of the achieved solutions, we present an initialization method for the class of supervised Learning Classifier Systems (LCS) that extracts information about the structure of studied problems through a pre-training clustering phase and exploits this information by transforming it into rules suitable for the initialization of the learning process. The effectiveness of our approach is evaluated through an extensive experimental phase, involving a variety of real-world classification tasks. Obtained results suggest that clustering-based initialization can indeed improve the predictive accuracy, as well as the interpretability of the induced knowledge representations, and paves the way for further investigations of the potential of better-than-random initialization methods for LCS algorithms.     

A fuzzy logic approach to experience‐based reasoning

Experience‐based reasoning (EBR) is a reasoning paradigm that has been used in almost every human activity such as business, military missions, and teaching activities since early human history. However, EBR has not been seriously studied from either a logical or mathematical viewpoint, although case‐based reasoning (CBR) researchers have paid attention to EBR to some extent. This article will attempt to fill this gap by providing a unified fuzzy logic‐based treatment of EBR. More specifically, this article first reviews the logical approach to EBR, in which eight different rules of inference for EBR are discussed. Then the article proposes fuzzy logic‐based models to these eight different rules of inference that constitute the fundamentals for all EBR paradigms from a fuzzy logic viewpoint, and therefore will form a theoretical foundation for EBR. The proposed approach will facilitate research and development of EBR, fuzzy systems, intelligent systems, knowledge management, and experience management. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 867–889, 2007.