Showing papers on "Fuzzy associative matrix published in 1998"

Fuzzy Modeling for Control

Abstract: From the Publisher: Fuzzy Modeling for Control addresses fuzzy modeling from the systems and control engineering point of view. It focuses on the selection of appropriate model structures, on the acquisition of dynamic fuzzy models from process measurements (fuzzy identification), and on the design of nonlinear controllers based on fuzzy models. The main features of the presented techniques are illustrated by means of simple examples. In addition, three real-world applications are described. Finally, software tools for building fuzzy models from measurements are available from the author.

Mining fuzzy association rules in databases

Abstract: Data mining is the discovery of previously unknown, potentially useful and hidden knowledge in databases. In this paper, we concentrate on the discovery of association rules. Many algorithms have been proposed to find association rules in databases with binary attributes. We introduce the fuzzy association rules of the form, 'If X is A then Y is B', to deal with quantitative attributes. X, Y are set of attributes and A, B are fuzzy sets which describe X and Y respectively. Using the fuzzy set concept, the discovered rules are more understandable to human. Moreover, fuzzy sets handle numerical values better than existing methods because fuzzy sets soften the effect of sharp boundaries.

Rule-based modeling: precision and transparency

Abstract: This article is a reaction to recent publications on rule-based modeling using fuzzy set theory and fuzzy logic. The interest in fuzzy systems has recently shifted from the seminal ideas about complexity reduction toward data-driven construction of fuzzy systems. Many algorithms have been introduced that aim at numerical approximation of functions by rules, but pay little attention to the interpretability of the resulting rule base. We show that fuzzy rule-based models acquired from measurements can be both accurate and transparent by using a low number of rules. The rules are generated by product-space clustering and describe the system in terms of the characteristic local behavior of the system in regions identified by the clustering algorithm. The fuzzy transition between rules makes it possible to achieve precision along with a good qualitative description in linguistic terms. The latter is useful for expert evaluation, rule-base maintenance, operator training, control systems design, user interfacing, etc. We demonstrate the approach on a modeling problem from a recently published article.

Decoupled fuzzy sliding-mode control

Abstract: A decoupled fuzzy sliding-mode controller design is proposed. The decoupled method provides a simple way to achieve asymptotic stability for a class of fourth-order nonlinear systems with only five fuzzy control rules. The ideas behind the controller are as follows. First, decouple the whole system into two second-order systems such that each subsystem has a separate control target expressed in terms of a sliding surface. Then, information from the secondary target conditions the main target, which, in turn, generates a control action to make both subsystems move toward their sliding surface, respectively. A closely related fuzzy controller to the sliding-mode controller is also presented to show the theoretical aspect of the fuzzy approach in which the characteristics of fuzzy sets are determined analytically to ensure the stability and robustness of the fuzzy controller. Finally, the decoupled sliding-mode control (SMC) is used to control three highly nonlinear systems and confirms the validity of the proposed approach.

On fuzzy logic applications for automatic control, supervision, and fault diagnosis

Abstract: The degree of vagueness of variables, process description, and automation functions is considered and is shown. Where quantitative and qualitative knowledge is available for design and information processing within automation systems. Fuzzy-rule-based systems with several levels of rules form the basis for different automation functions. Fuzzy control can be used in many ways, for normal and for special operating conditions. Experience with the design of fuzzy controllers in the basic level is summarized, as well as criteria for efficient applications. Different fuzzy control schemes are considered, including cascade, feedforward, variable structure, self-tuning, adaptive and quality control leading to hybrid classical/fuzzy control systems. It is then shown how fuzzy logic approaches can be applied to process supervision and to fault diagnosis with approximate reasoning on observed symptoms. Based on the properties of fuzzy logic approaches the contribution gives a review and classification of the potentials of fuzzy logic in process automation.

General SISO Takagi-Sugeno fuzzy systems with linear rule consequent are universal approximators

Abstract: Takagi-Sugeno (TS) fuzzy systems have been employed as fuzzy controllers and fuzzy models in successfully solving difficult control and modeling problems in practice. Virtually all the TS fuzzy systems use linear rule consequent. At present, there exist no results (qualitative or quantitative) to answer the fundamentally important question that is especially critical to TS fuzzy systems as fuzzy controllers and models, "Are TS fuzzy systems with linear rule consequent universal approximators?" If the answer is yes, then how can they be constructed to achieve prespecified approximation accuracy and what are the sufficient renditions on systems configuration? In this paper, we provide answers to these questions for a general class of single-input single-output (SISO) fuzzy systems that use any type of continuous input fuzzy sets, TS fuzzy rules with linear consequent and a generalized defuzzifier containing the widely used centroid defuzzifier as a special case. We first constructively prove that this general class of SISO TS fuzzy systems can uniformly approximate any polynomial arbitrarily well and then prove, by utilizing the Weierstrass approximation theorem, that the general TS fuzzy systems can uniformly approximate any continuous function with arbitrarily high precision. Furthermore, we have derived a formula as part of sufficient conditions for the fuzzy approximation that can compute the minimal upper bound on the number of input fuzzy sets and rules needed for any given continuous function and prespecified approximation error bound, An illustrative numerical example is provided.

Type-2 fuzzy logic systems: type-reduction

Abstract: Type-reduction in a type-2 fuzzy logic system (FLS) is an "extended" version of the defuzzification operation in a type-1 FLS. In this paper, we briefly review the structure of a type-2 FLS and describe type-reduction in detail. We focus on a center-of-sets type-reducer, and provide some examples to illustrate it. We also provide some practical approximations to type-reduction computations for certain type-2 membership functions.

FuGeNeSys-a fuzzy genetic neural system for fuzzy modeling

Abstract: The author has developed a novel approach to fuzzy modeling from input-output data. Using the basic techniques of soft computing, the method allows supervised approximation of multi-input multi-output (MIMO) systems. Typically, a small number of rules are produced. The learning capacity of FuGeNeSys is considerable, as is shown by the numerous applications developed. The paper gives a significant example of how the fuzzy models developed are generally better than those to be found in literature as concerns simplicity and both approximation and classification capabilities.

Sufficient conditions on uniform approximation of multivariate functions by general Takagi-Sugeno fuzzy systems with linear rule consequent

Abstract: We have constructively proved a general class of multi-input single-output Takagi-Sugeno (TS) fuzzy systems to be universal approximators. The systems use any types of continuous fuzzy sets, fuzzy logic AND, fuzzy rules with linear rule consequent and the generalized defuzzifier. We first prove that the TS fuzzy systems can uniformly approximate any multivariate polynomial arbitrarily well, and then prove they can also uniformly approximate any multivariate continuous function arbitrarily well. We have derived a formula for computing the minimal upper bounds on the number of fuzzy sets and fuzzy rules necessary to achieve the prespecified approximation accuracy for any given bivariate function. A numerical example is furnished. Our results provide a solid-theoretical basis for fuzzy system applications, particularly as fuzzy controllers and models.

A transformed input-domain approach to fuzzy modeling

Abstract: This paper presents an explanation of a fuzzy model considering the correlation among components of input data. Generally, fuzzy models have a capability of dividing an input space into several subspaces compared to a linear model. But hitherto suggested fuzzy modeling algorithms have not taken into consideration the correlation among components of sample data and have addressed them independently, which results in an ineffective partition of the input space. In order to solve this problem, this paper proposes a new fuzzy modeling algorithm, which partitions the input space more effectively than conventional fuzzy modeling algorithms by taking into consideration the correlation among components of sample data. As a way to use the correlation and divide the input space, the method of principal component is used. Finally, the results of the computer simulation are given to demonstrate the validity of this algorithm.

Minimal fuzzy memberships and rules using hierarchical genetic algorithms

Abstract: A new scheme to obtain optimal fuzzy subsets and rules is proposed. The method is derived from the use of genetic algorithms, where the genes of the chromosome are classified into two different types. These genes can be arranged in a hierarchical form, where one type of gene controls the other. The effectiveness of this genetic formulation enables the fuzzy subsets and rules to be optimally reduced and, yet, the system performance is well maintained. In this paper, the details of formulation of the genetic structure are given. The required procedures for coding the fuzzy membership function and rules into the chromosome are also described. To justify this approach to fuzzy logic design, the proposed scheme is applied to control a constant water pressure pumping system. The obtained results, as well as the associated final fuzzy subsets, are included in this paper. Because of its simplicity, the method could lead to a potentially low-cost fuzzy logic implementation.

A multilevel weighted fuzzy reasoning algorithm for expert systems

Abstract: The applications of fuzzy production rules (FPR) are rather limited if the relative degree of importance of each proposition in the antecedent contributing to the consequent (i.e., the weight) is ignored or assumed to be equal. Unfortunately, this is the case for many existing FPR and most existing fuzzy expert system development shells or environments offer no such functionality for users to incorporate different weights in the antecedent of FPR. This paper proposes to assign a weight parameter to each proposition in the antecedent of a FPR and a new fuzzy production rule evaluation method (FPREM) which generalizes the traditional method by taking the weight factors into consideration is devised. Furthermore, a multilevel weighted fuzzy reasoning algorithm (MLWFRA) incorporating this new FPREM, which is based on the reachability and adjacent place characteristics of a fuzzy Petri net, is developed. The MLWFRA has the advantages that i) it offers multilevel reasoning capability; ii) it allows multiple conclusions to be drawn if they exist; iii) it offers a new fuzzy production rule evaluation method; and iv) it is capable of detecting cycle rules.

Fuzzy model-based control of complex plants

Abstract: In the field of fuzzy modeling, the Takagi-Sugeno fuzzy model has been used to approximate accurately the dynamics of complex plants. The paper addresses two control design problems associated with state-space realizations of such fuzzy models. First, we treat the stability robustness of fuzzy model-based controllers against modeling uncertainty. Second, we develop observer-based control schemes and further investigate the behavior of estimated-state feedback. In both cases, we provide sufficient conditions that guarantee stability of the closed loop. The results are demonstrated on the fuzzy model of a gas furnace process.

An effective algorithm for discovering fuzzy rules in relational databases

Abstract: We present a novel technique, called F-APACS, for discovering fuzzy association rules in relational databases. F-APACS employs linguistic terms to represent the revealed regularities and exceptions. The definitions of these linguistic terms are based on fuzzy set theory and the association rules expressed in them are called fuzzy association rules. To discover these rules, F-APACS utilizes an objective interestingness measure when determining if two attribute values are related. This measure is defined in terms of an "adjusted difference" between observed and expected frequency counts. The use of such a measure has the advantage that no user-supplied thresholds are required. In addition to this interestingness measure, F-APACS has another unique feature that it provides a mechanism to allow quantitative values be inferred from the rules. Such feature, as shown here, make F-APACS very effective at various data mining tasks.

Extracting rules from fuzzy neural network by particle swarm optimisation

Abstract: A four layer fuzzy neural network is presented to realise knowledge acquisition from input-output samples. The network parameters including the necessary membership functions of the input variables and the consequent parameters are tuned and identified using a modified particle swarm algorithm which uses each particle's best current performance of its neighbours to replace the best previous one and uses a non accumulative rate of change to replace the accumulative one for accelerating search procedure. The trained network is then pruned so that the general rules can be extracted and explained. The experimental results have shown that the similar classification rules can be obtained in comparison to that of other fuzzy neural approaches.

Fuzzy switched hybrid systems-modeling and identification

Abstract: The combination of hybrid systems and fuzzy multiple model systems is described. Further, a hierarchical identification of the resulting fuzzy switched hybrid system is outlined. The behavior of the discrete component is identified by black box fuzzy clustering and subsequent parameter identification taking into account some prior-knowledge about the discrete states. The identification of the continuous models for each discrete state is done based on local linear fuzzy models.

A neuro-fuzzy approach to obtain interpretable fuzzy systems for function approximation

Abstract: Fuzzy systems can be used for function approximation based on a set of linguistic rules. We present a method to obtain the necessary parameters for such a fuzzy system by a neuro-fuzzy training method. The learning algorithm is able to determine the structure and the parameters of a fuzzy system from sample data. The approach is an extension to our already published NEFCON and NEFCLASS models which are used for control or classification purposes. The NEFPROX model, which is discussed in this paper is more general, and it can be used for any problem based on function approximation. We especially consider the problem to obtain interpretable fuzzy systems by learning.

Neural Networks and Fuzzy Logic

Abstract: In Chapter 9 (this volume), Pedrycz, Kandel and Zhang present an extensive survey of Neurofuzzy systems. The authors give a clear exposition of the complementary technologies offered by fuzzy logic and neural networks. The basic functions of a “fuzzy neuron” are developed and learning algorithms for neurofuzzy systems are presented. In this chapter, we briefly discuss the Synergistic issues in the integration of these technologies. The development and results of an integrated system are presented.

Robustness of fuzzy logic control for an uncertain dynamic system

Abstract: Based on the similarity between prevalent fuzzy logic controllers (FLC) and the conventional robust controller, i.e., the variable structure controller, control theoretic analysis of a fuzzy control system is presented in the sense of Lyapunov. As well as the robustness of the fuzzy control system against uncertainties of a controlled process, this analysis gives an account of the relationship between control performance and the design parameters of the FLC, which has been obscure in the theory of fuzzy control.

Fuzzy Systems, Modeling and Identification

Abstract: This text provides an introduction to the use of fuzzy sets and fuzzy logic for the approximation of functions and modeling of static and dynamic systems. The concept of a fuzzy system is first explained. Afterwards, the motivation and practical relevance of fuzzy modeling are highlighted. Two types of rule-based fuzzy models are described: the linguistic (Mamdani) model and the Takagi–Sugeno model. For each model, the structure of the rules, the inference and defuzzification methods are presented. Fuzzy modeling of dynamic systems is addressed, as well as the methods to construct fuzzy models from knowledge and data (measurements). Illustrative examples are given throughout the text. At the end, homework problems are included. MATLAB programs implementing some of the examples are available from the author. The reader is encouraged to study and possibly modify these examples in order to get a better insight in the methods presented. Preface Prerequisites: This text provides an introduction to the use of fuzzy sets and fuzzy logic for the approximation of functions and modeling of static and dynamic systems. It is assumed that the reader has basic knowledge of set and fuzzy set theory (membership functions, operations on fuzzy sets – union, intersection and complement, fuzzy relations, max-min composition, extension principle), mathematical analysis (univariate and multivariate functions, composition of functions), and linear algebra (system of linear equations, least-square solution). Organization. The material is organized in five sections: In the Introduction, different modeling paradigms are first presented. Then, the concept of a fuzzy system is first explained and the motivation and practical relevance of fuzzy modeling are highlighted. Section 2 describes two types of rule-based fuzzy models: the linguistic (Mamdani) model and the Takagi–Sugeno model. For each model, the structure of the rules, the inference and defuzzification methods are presented. At the end of this section, fuzzy modeling of dynamic systems is addressed. In Section 3, methods to construct fuzzy models from knowledge and numerical data are presented. Section 4 reviews some engineering applications of fuzzy modeling, and the concluding Section 5 gives a short summary. Illustrative examples are provided throughout the text, and at the end, homework problems are included. Some of the numerical examples given have been implemented in MATLAB. The code is available from the author on request. The reader is encouraged to study and possibly modify these examples in order to get a better insight in the methods presented. A subject index …

Mixed analog-digital fuzzy logic controller with continuous-amplitude fuzzy inferences and defuzzification

Abstract: A fuzzy logic controller has been realized using mixed analog-digital CMOS very large scale integration (VLSI) circuits for application in cases where the input and output variables are in analog form. It employs a new architecture where time sweeping of variables allows continuous-amplitude evaluation of fuzzy inferences and defuzzification during each evaluation cycle without having to discretize input and output variables. Direct processing of the analog input signal is used to obtain the corresponding crisp value; the digital portion is used only for programmability. No A/D and D/A converters are needed. The controller can handle three inputs, one output, and 25 programmable fuzzy rules. The test IC chips were fabricated using 0.7-/spl mu/m CMOS technology. A control problem of stabilizing a ping-pong ball in a tube with a controllable air flow has been successfully demonstrated.

Fuzzy Logic for Biological and Agricultural Systems

Abstract: Fuzzy logic is a powerful concept for handling non-linear, time-varying, adaptive systems. It permits the use of linguistic values of variables and imprecise relationships for modeling system behavior. The paper presents an overview of fuzzy logic modeling techniques, its applications to biological and agricultural systems and an example showing the steps of constructing a fuzzy logic model.

FuzzyShell: a large-scale expert system shell using fuzzy logic for uncertainty reasoning

Abstract: There exist in the literature today many contributions dealing with the incorporation of fuzzy logic in expert systems. However, unfortunately, much of what has been proposed can only be applied to small-scale expert systems; that is, when the number of rules is in the dozens as opposed to in the hundreds. The more traditional (nonfuzzy) expert systems are able to cope with large numbers of rules by using Rete networks for maintaining matches of all the rules and all the facts. (A Rete network obviates the need to match the rules with the facts on every cycle of the inference engine.) In this paper, we present a more general Rete network that is particularly suitable for reasoning with fuzzy logic. The generalized Rete network consists of a cascade of three networks: the pattern network, the join network, and the evidence aggregation network. The first two layers are modified versions of similar layers for the traditional Rete networks and the last, the aggregation layer, is a new concept that allows fuzzy evidence to be aggregated when fuzzy inferences are made about the same fuzzy variable by different rules.