This paper presents the architecture and learning procedure underlying ANFIS (AdaptiveNetwork -based Fuzzy Inference System), a fuzzy inference system implemented in the framework of adaptive networks. By using a hybrid learning procedure, the proposed ANFIS can construct an input-output mapping based on both human knowledge (in the form of fuzzy if-then rules) and stipulated input-output data pairs. In our simulation, we employ the ANFIS architecture to model nonlinear functions, identify nonlinear components on-linely in a control system, and predict a chaotic time series, all yielding remarkable results. Comparisons with artificail neural networks and earlier work on fuzzy modeling are listed and discussed. Other extensions of the proposed ANFIS and promising applications to automatic control and signal processing are also suggested. 1 Introduction System modeling based on conventional mathematical tools (e.g., differential equations) is not well suited for dealing with ill-define...

Fundamental and advanced developments in neuro-fuzzy synergisms for modeling and control are reviewed. The essential part of neuro-fuzzy synergisms comes from a common framework called adaptive networks, which unifies both neural networks and fuzzy models. The fuzzy models under the framework of adaptive networks is called ANFIS (Adaptive-Network-based Fuzzy Inference System), which possess certain advantages over neural networks. We introduce the design methods for ANFIS in both modeling and control applications. Current problems and future directions for neuro-fuzzy approaches are also addressed.

Abstract — This paper proposes an automaticfuzzy system design method that uses a Genetic Algorithm and integrates three design stages; our method determines membership functions, the number of fuzzy rules, and the ruleconsequent parameters at the same time. Because these design stages may not be independent, it is important to consider them simultaneously to obtain optimal fuzzy systems. The method includes a genetic algorithm and a penalty strategy that favors systems with fewer rules. The proposed method is applied to the classic inverted pendulum control problem and has been shown to be practical through a comparison with another method. 1 1

Many complex control problems require sophisticated solutions that are not amenable to traditional controller design. Not only is it difficult to model real world systems, but often it is unclear what kind of behavior is required to solve the task. Reinforcement learning (RL) approaches have made progress by using direct interaction with the task environment, but have so far not scaled well to large state spaces and environments that are not fully observable. In recent years, neuroevolution, the artificial evolution of neural networks, has had remarkable success in tasks that exhibit these two properties. In this paper, we compare a neuroevolution method called Cooperative Synapse Neuroevolution (CoSyNE), that uses cooperative coevolution at the level of individual synaptic weights, to a broad range of reinforcement learning algorithms on very difficult versions of the pole balancing problem that involve large (continuous) state spaces and hidden state. CoSyNE is shown to be significantly more efficient and powerful than the other methods on these tasks.

This paper presents an innovative approach to the structure determination problem in fuzzy modeling. By using the well-known CART (classification and regression tree) algorithm as a quick preprocess, the proposed method can roughly estimate the structure (numbers of membership functions and number of fuzzy rules, etc.) of a fuzzy inference system; then the parameter identification is carried out by the hybrid learning scheme developed in our previous work [3, 2, 5]. Morevoer, the identified fuzzy inference system has the property that the total of firing strengths is always equal to one; this speeds up learning processes and reduces round-off errors. 1 Introduction Fuzzy modeling [11, 10] is a new branch of system identification which concerns with the construction of a fuzzy inference system (or fuzzy model) that can predict and hopefully explain the behavior of an unknown system described by a set of sample data. Two primary tasks of fuzzy modeling are structure determination...

As control system tasks become more demanding, more robust controller design methodologies are needed. A Genetic Algorithm (GA) optimizer, which utilizes natural evolution strategies, offers a promising technology that supports optimization of the parameters of fuzzy logic and other parameterized non-linear controllers. This paper shows how GAs can effectively and efficiently optimize the performance of fuzzy net controllers employing high performance simulation to reduce the design cycle time from hours to minutes. Our results demonstrate the robustness of a GA-based Computer-Aided System Design methodology for rapid prototyping of control systems. Keywords: Genetic Algorithms; Fuzzy Logic Control; Oxygen Production System; Inverted Pendulum. Introduction Computer-Aided System Design (CASD) should support designing various functions of high autonomy systems[10], such as normal operation control, fault-tolerance, communication, planning and scheduling. Since conventional control schem...

Due to their powerful optimization property, genetic algorithms (GAs) are currently being investigated for the development of adaptive or self-tuning fuzzy logic control systems. This paper presents a neuro-fuzzy logic controller (NFLC) where all of its parameters can be tuned simultaneously by GA. The structure of the controller is based on the Radial Basis Function neural network (RBF) with Gaussian membership functions. The NFLC tuned by GA can somewhat eliminate laborious design steps such as manual tuning of the membership functions and selection of the fuzzy rules. The GA implementation incorporates dynamic crossover and mutation probabilistic rates for faster convergence. A flexible position coding strategy of the NFLC parameters is also implemented to obtain near optimal solutions. The performance of the proposed controller is compared with a conventional fuzzy controller and a PID controller tuned by GA. Simulation results show that the proposed controller offers encouraging advantages and has better performance.

Learning a large number of simple local concepts is both faster and easier than learning a single global concept. Inspired by this principle of divide and conquer, a number of modular learning approaches have been proposed by the computational intelligence community. In modular learning, the classification/regression/clustering problem is first decomposed into a number of simpler subproblems, a module is learned for each of these subproblems, and finally their results are integrated by a suitable combining method. Mixtures of experts and clustering are two of the techniques that are describable in this paradigm. In this paper we present a broad framework for Generalized Associative Modular Learning Systems (GAMLS). Modularity is introduced through soft association of each training pattern with every module. The coupled problems of learning the module parameters and learning associations are solved iteratively using deterministic annealing. Starting at a high temperature with only one modu...

During the last twenty years, fuzzy logic has been successfully applied to many modeling and control problems. One of the reasons of success is that fuzzy logic provides human-friendly and understandable knowledge representation that can be utilized in expert knowledge extraction and implementation. It is observed, however, that transparency, which is vital for undistorted information transfer, is not a default property of fuzzy systems, moreover, application of algorithms that identify fuzzy systems from data will most likely destroy any semantics a fuzzy system ever had after initialization. This thesis thoroughly investigates the issues related to transparency. Fuzzy systems are generally divided into two classes. It is shown here that for these classes different definitions of transparency apply. For standard fuzzy systems that use fuzzy propositions in IF-THEN rules, explicit transparency constraints have been derived. Based on these constraints, exploitation/modification schemes of existing identification algorithms are suggested, moreover, a new algorithm for training standard fuzzy systems has been proposed, with a considerable potential to reduce the gap between accuracy and transparency in fuzzy modeling. For 1st order Takagi-Sugeno systems that are interpreted in terms of local linear models, such conditions cannot be derived due to system architecture and its undesirable interpolation properties of 1st order TS systems. It is, however, possible to solve the transparency preservation problem in the context of modeling with another proposed method that benefits from rule activation degree exponents. 1st order TS systems that admit valid interpretation of local models as linearizations of the modeled system are useful, for example, in gain-scheduled control. Transparent standard fuzzy systems, on the other hand, are vital to this branch of intelligent control that seeks solutions by emulating the mechanisms of reasoning and decision processes of human beings not limited to knowledge-based fuzzy control. Performing the local inversion of the modeled system it is possible to extract relevant control information, which is demonstrated with the application of fed-batch fermentation. The more a fuzzy controller resembles the expert’s role in a control task, the higher will be the implementation benefit of the fuzzy engine. For example, a hierarchy of fuzzy (and non-fuzzy) controllers simulates an existing hierarchy in the human decision process and leads to improved control performance. Another benefit from hierarchy is that it assumes problem decomposition. This is especially important with fuzzy logic where large number of system variables leads to exponential explosion of rules (curse of dimensionality) that makes controller design extremely difficult or even impossible. The advantages of hierarchical control are illustrated with truck backer-upper applications.

The knowledge base in expert systems usually contains different types of information which can be classified as explicit and implicit with respect to its representation. The explicit representation is based on a symbolic expression of human expert knowledge while the numerical data which require additional processing to be really understood represent the implicit knowledge. The rule-based systems and neural networks are typical examples of these different representation approaches. The main problem of rule-based systems is the knowledge acquisition which can be overcoming by learning and adaptation in neural networks. On the other hand, the neural implicit knowledge representation loses the capability to explain and justify the inference. Thus, the advantages and disadvantages of explicit and implicit knowledge representation in expert systems are complementary and we will first give a general comparison of both. Then we will discuss how to process the neural knowledge to embed it into...