Showing papers on "Fuzzy associative matrix published in 1993"
TL;DR: A general approach to quali- tative modeling based on fuzzy logic is discussed, which proposes to use a fuzzy clustering method (fuzzy c-means method) to identify the structure of a fuzzy model.
Abstract: This paper discusses a general approach to quali- tative modeling based on fuzzy logic. The method of qualitative modeling is divided into two parts: fuzzy modeling and linguistic approximation. It proposes to use a fuzzy clustering method (fuzzy c-means method) to identify the structure of a fuzzy model. To clarify the advantages of the proposed method, it also shows some examples of modeling, among them a model of a dynamical process and a model of a human operator's control action.
2,447 citations
TL;DR: Graduality, measurability, and distance in the fuzzy sense are introduced, which enable the introduction of the concept of similarity between two fuzzy terms, by their closeness derived from their distance.
424 citations
TL;DR: An architecture for neural networks that can handle fuzzy input vectors is proposed, and learning algorithms that utilize fuzzy if-then rules as well as numerical data in neural network learning for classification problems and for fuzzy control problems are derived.
Abstract: An architecture for neural networks that can handle fuzzy input vectors is proposed, and learning algorithms that utilize fuzzy if-then rules as well as numerical data in neural network learning for classification problems and for fuzzy control problems are derived. The learning algorithms can be viewed as an extension of the backpropagation algorithm to the case of fuzzy input vectors and fuzzy target outputs. Using the proposed methods, linguistic knowledge from human experts represented by fuzzy if-then rules and numerical data from measuring instruments can be integrated into a single information processing system (classification system or fuzzy control system). It is shown that the scheme works well for simple examples. >
295 citations
TL;DR: This work describes six important defuzzification methods and their respective merits and shortcomings, dependent on the rules, domains, etc, and gives an alternative approach for the case in which the output fuzzy sets have different shapes or are asymmetrical.
Abstract: An important subject in fuzzy control theory is tuning of a fuzzy controller. If one wants to tune a fuzzy controller, one can focus on the choice of rules, membership functions, number of input and output fuzzy sets and their degree of overlapping, implication, and connection operations, and defuzzification method. All these choices are closely related and in no way independent of each other. We describe six important defuzzification methods and their respective merits and shortcomings, dependent on the rules, domains, etc. Further, we give an alternative approach for the case in which the output fuzzy sets have different shapes or are asymmetrical. We illustrate this by several examples.
284 citations
Proceedings Article•
11 Jul 1993TL;DR: This work hopes to resolve paradoxes in fuzzy logic by identifying which aspects of fuzzy logic render it useful in practice, and which aspects are inessential.
Abstract: This paper investigates the question of which aspects of fuzzy logic are essential to its practical usefulness. We show that as a formal system, a standard version of fuzzy logic collapses mathematically to two-valued logic, while empirically, fuzzy logic is not adequate for reasoning about uncertain evidence in expert systems. Nevertheless, applications of fuzzy logic in heuristic control have been highly successful. We argue that the inconsistencies of fuzzy logic have not been harmful in practice because current fuzzy controllers are far simpler than other knowledge-based systems. In the future, the technical limitations of fuzzy logic can be expected to become important in practice, and work on fuzzy controllers will also encounter several problems of scale already known for other knowledge-based systems.
274 citations
01 Jul 1993
TL;DR: A methodology for designing adaptive hierarchical fuzzy controllers is presented and a supervisory fuzzy rule set was constructed and used to change the parameters of a hierarchical fuzzy controller to accommodate the variations of system parameters.
Abstract: A methodology for designing adaptive hierarchical fuzzy controllers is presented. In order to evaluate this concept, several suitable performance indices were developed and converted to linguistic fuzzy variables. Based on those variables, a supervisory fuzzy rule set was constructed and used to change the parameters of a hierarchical fuzzy controller to accommodate the variations of system parameters. The proposed algorithm was used in feedwater flow control to a steam generator. Simulation studies are presented that illustrate the effectiveness of the approach. >
241 citations
TL;DR: A sufficient condition to guarantee the stability of the proposed fuzzy control system is proposed in terms of Lyapunov's method and can be applied to the design of a Fuzzy-PID control system.
223 citations
TL;DR: The direct fuzzification of a standard layered, feedforward, neural network where the signals and weights are fuzzy sets is discussed and a fuzzified delta rule is presented for learning.
Abstract: We discuss the direct fuzzification of a standard layered, feedforward, neural network where the signals and weights are fuzzy sets. A fuzzified delta rule is presented for learning. Three applications are given including fuzzy expert systems, fuzzy hierarchical analysis, and fuzzy systems modeling. © 1993 John Wiley & Sons, Inc.
211 citations
TL;DR: This work provides a unifying approach to this selection process of selecting a crisp element based on information provided by a fuzzy set, and puts the defuzzification methods of mean of maxima and center of gravity in the same framework.
182 citations
TL;DR: Conventional fuzzy control systems using PID (proportional-integral-derivative) control and their limitations are discussed and ways to incorporate adaptivity are examined.
Abstract: Conventional fuzzy control systems using PID (proportional-integral-derivative) control and their limitations are discussed. Ways to incorporate adaptivity are examined. The functioning of adaptive fuzzy logic and adaptive fuzzy control systems is described. The use of rule weights is explained. >
179 citations
TL;DR: Two fuzzy adaptive filters are developed: one uses a recursive-least-squares (RLS) adaptation algorithm, and the other uses a least-mean-square (LMS) adaptation algorithms, which are applied to nonlinear communication channel equalization problems.
Abstract: Two fuzzy adaptive filters are developed: one uses a recursive-least-squares (RLS) adaptation algorithm, and the other uses a least-mean-square (LMS) adaptation algorithm. The RLS fuzzy adaptive filter is constructed through the following four steps: (1) define fuzzy sets in the filter input space Rn whose membership functions cover U; (2) construct a set of fuzzy IF-THEN rules which either come from human experts or are determined during the adaptation procedure by matching input-output data pairs; (3) construct a filter based on the set of rules; and (4) update the free parameters of the filter using the RLS algorithm. The design procedure for the LMS fuzzy adaptive filter is similar. The most important advantage of the fuzzy adaptive filters is that linguistic information (in the form of fuzzy IF-THEN rules) and numerical information (in the form of input-output pairs) can be combined in the filters in a uniform fashion. The filters are applied to nonlinear communication channel equalization problems. >
TL;DR: In this paper, a fuzzy control model with well-founded semantics is introduced to explain the concepts applied in fuzzy control, assuming that the domains of the input and output variables for the process are endowed with equality relations, that reflect the indistinguishability of values lying closely together.
TL;DR: A mathematical formulation of the optimal reactive power control problem using fuzzy set theory is presented, to minimize real power losses and improve the voltage profile of a given system.
Abstract: A mathematical formulation of the optimal reactive power control problem using fuzzy set theory is presented. The objectives are to minimize real power losses and improve the voltage profile of a given system. Transmission losses are expressed in terms of voltage increments by relating the control variables to the voltage increments in a modified Jacobian matrix. This formulation does not require Jacobian matrix inversion, and hence it will save computation time and memory space. The objective function and the constraints are modeled by fuzzy sets. Linear membership functions of the fuzzy sets are defined and the fuzzy linear optimization problem is formulated. The solution space is defined as the intersection of the fuzzy sets describing the constraints and the objective functions. Each solution is characterized by a parameter that determines the degree of satisfaction with the solution. The optimal solution is the one with the maximum value for the satisfaction parameter. Results for test systems reveal the advantages of the approach. >
28 Mar 1993
TL;DR: The authors develop a mathematically motivated set of 13 constraints characterizing rational defuzzification procedures, which can be used for direct operator derivation, for comparative examinations or as quality criteria for parameter optimization.
Abstract: Fuzzy systems internally process fuzzy values, which have to be mapped to crisp output in most applications. This conversion is called defuzzification. In many cases the standard algorithms like center of gravity and mean of maxima lead to irrational results. Better defuzzification procedures are required. For the development of rational defuzzification algorithms a definition of essential properties is necessary. The authors develop a mathematically motivated set of 13 constraints characterizing rational defuzzification procedures. The constraints proposed will aid defuzzification operator designers. They can be used for direct operator derivation, for comparative examinations or as quality criteria for parameter optimization. >
TL;DR: Some criteria for selecting a fuzzy subspace to be subdivided are proposed and compared with each other by computer simulations and the proposed method is also compared with other fuzzy classification methods.
28 Mar 1993
TL;DR: An architecture of multi-layer feedforward neural networks whose weights and biases are given as fuzzy numbers is proposed, and a learning algorithm of the fuzzy neural networks is derived for real input vectors and fuzzy target outputs.
Abstract: An architecture of multi-layer feedforward neural networks whose weights and biases are given as fuzzy numbers is proposed The fuzzy neural network with the proposed architecture maps an input vector of real numbers to a fuzzy output The input-output relation of each unit is defined by the extension principle A learning algorithm of the fuzzy neural networks is derived for real input vectors and fuzzy target outputs The derived learning algorithm is extended to the case of fuzzy input vectors and fuzzy target outputs >
TL;DR: In this paper, the fuzzy closure operator, fuzzy compactness and fuzzy connectedness are given in a redefined fuzzy topological space and then some characteristic properties of fuzzy closure operation, product theorems of fuzzy compactess and fuzzy connectivity are studied.
22 Dec 1993
TL;DR: In this paper, the authors proposed a new approach to the learning of fuzzy rules by clustering via the mountain function to identify the most important rules, those are the rules that are associated with higher values of the peaks of the mountain functions.
Abstract: The paper deals with a new approach to the learning of fuzzy rules. It suggests a solution to one of the problems of crucial importance for the learning of fuzzy rules by back propagation- -the issue of estimation of the initial values of the unknown parameters. We introduce the method of clustering via the mountain function to identify the most important rules. Those are the rules that are associated with higher values of the peaks of the mountain function. From the centers of the clusters that are obtained by the mountain function method are determined the initial estimates of the parameters of the reference antecedent and consequent fuzzy sets of the rules. In the next step the method of back propagation is used for more precise identification of those parameters.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
01 Jan 1993
TL;DR: The authors show how to model the Mackey-Glass chaotic time series with 16 fuzzy if-then rules, which outperforms various standard statistical approaches and artificial neural network modeling methods reported in the literature.
Abstract: The authors continue work on a previously proposed ANFIS (adaptive-network-based fuzzy inference system) architecture, with emphasis on the applications to time series prediction. They show how to model the Mackey-Glass chaotic time series with 16 fuzzy if-then rules. The performance obtained outperforms various standard statistical approaches and artificial neural network modeling methods reported in the literature. Other potential applications of ANFIS are also suggested. >
28 Mar 1993
TL;DR: The authors analyze the stability of a fuzzy logic controller, designed using the phase portrait assignment algorithm from a topological point of view, designed for a simplified automobile engine which is a two-state dynamic model.
Abstract: The authors analyze the stability of a fuzzy logic controller, designed using the phase portrait assignment algorithm from a topological point of view. The fuzzy logic controller was designed for a simplified automobile engine which is a two-state dynamic model. The controller was designed using the automatic rule generation technique reported by G.J. Vachtsevanos et al. (1992). The general form of the rule is given. >
28 Mar 1993
TL;DR: The authors propose a reinforcement neural-network-based fuzzy logic control system (RNN-FLCS) for solving various reinforcement learning problems and finds it best applied to learning environments where obtaining exact training data is expensive.
Abstract: The authors propose a reinforcement neural-network-based fuzzy logic control system (RNN-FLCS) for solving various reinforcement learning problems. RNN-FLCS is best applied to learning environments where obtaining exact training data is expensive. It is constructed by integrating two neural-network-based fuzzy logic controllers (NN-FLCs), each of which is a connectionist model with a feedforward multilayered network developed for the realization of a fuzzy logic controller. One NN-FLC functions as a fuzzy predictor and the other as a fuzzy controller. Using the temporal difference prediction method, the fuzzy predictor can predict the external reinforcement signal and provide a more informative internal reinforcement signal to the fuzzy controller. The fuzzy controller implements a stochastic exploratory algorithm to adapt itself according to the internal reinforcement signal. During the learning process, the RNN-FLCs can construct a fuzzy logic control system automatically and dynamically through a reward-penalty signal or through very simple fuzzy information feedback. Structure learning and parameter learning are performed simultaneously in the two NN-FLCs. Simulation results are presented. >
TL;DR: Two types of analog fuzzy processors are described, one is a rule chip FP-9000 and the other a defuzzifier chipFP-9001, and both can achieve high-speed fuzzy inference, which is characterized by a fuzzy if-then rule, in analog mode.
Abstract: This article describes two types of analog fuzzy processors. One is a rule chip FP-9000 and the other a defuzzifier chip FP-9001, and both can achieve high-speed fuzzy inference. The inference speed is more than 1 Mega fuzzy logical inferences per second, excluding defuzzification. The rule chip includes four fuzzy inference engines. Each engine achieves one fuzzy inference, which is characterized by a fuzzy if-then rule, in analog mode. These rules can be directly read out and written in through an external digital computer. The rule chip is fabricated in 2 μm BiCMOS technology. The defuzzifier chip converts a fuzzy value to a crisp one, necessary for a fuzzy control system. The defuzzifier chip is implemented by 3 μm bipolar technology. A high-speed fuzzy controller hardware system can be efficiently constructed with these chips. The chips accelerate to develop fuzzy logic systems, especially high-speed applications.
25 Aug 1993
TL;DR: All normal fuzzy sets may be realized as the interpolation of paradigmatic examples by a similarity relation and the class of fuzzy if-then rules that may be obtained by interpolation is a proper subset of the rules definable by disjunctive combination.
Abstract: A method for the construction of fuzzy concepts and fuzzy if-then rules based on similarity and paradigmatic examples is presented. It is shown that all normal fuzzy sets may be realized as the interpolation of paradigmatic examples by a similarity relation. The class of fuzzy if-then rules that may be obtained by interpolation, however, is a proper subset of the rules definable by disjunctive combination.
01 Aug 1993-International Journal of Human-computer Studies \/ International Journal of Man-machine Studies
TL;DR: This work shows how a number of the classic aggregation methods fall out as special cases of this very general formulation based upon the use of fuzzy subsets to model the criteria and a form of the fuzzy integral to connect these two to obtain the overall decision function.
Abstract: The central focus of this work is to provide a general formulation for the aggregation of multi-criteria. This formulation is based upon the use of fuzzy subsets to model the criteria and the use of fuzzy measures to capture the interrelationship between criteria. A form of the fuzzy integral is used to connect these two to obtain the overall decision function. We are particularly interested here in the formulations obtained under different assumptions about the nature of the underlying fuzzy measure. We show how a number of the classic aggregation methods fall out as special cases of this very general formulation.
TL;DR: Fuzzy inference, a data processing method based on the fuzzy theory that has found wide use in the control field, is reviewed and a fuzzy inference date processor that operates at 200000 fuzzy logic inferences per second is described.
Abstract: Fuzzy inference, a data processing method based on the fuzzy theory that has found wide use in the control field, is reviewed. Consumer electronics, which accounts for most current applications of this concept, does not require very high speeds. Although software running on a conventional microprocessor can perform these inferences, high-speed control applications require much greater speeds. A fuzzy inference date processor that operates at 200000 fuzzy logic inferences per second and features 12-b input and 16-b output resolution is described. >
28 Mar 1993
TL;DR: The aim of the proposed method is to find a minimum set of fuzzy if-then rules that can correctly classify all training patterns and its fitness is determined by the two objectives in the combinatorial optimization problem.
Abstract: The authors propose a genetic algorithm method for choosing an appropriate set of fuzzy if-then rules for classification problems The aim of the proposed method is to find a minimum set of fuzzy if-then rules that can correctly classify all training patterns This is achieved by formulating and solving a combinatorial optimization problem that has two objectives, which are to maximize the number of correctly classified patterns and to minimize the number of fuzzy if-then rules A genetic algorithm was applied to this problem and simulation results are shown An individual (ie, a solution) in the genetic algorithm is the set of fuzzy if-then rules, and its fitness is determined by the two objectives in the combinatorial optimization problem >
28 Mar 1993
TL;DR: The main point argued and illustrated here is the ease with which methods and ideas emerging in the connectionist community can be imported for control applications as soon as the fuzzy controller is supplied with a gradient-based automatic tuning of its parameters.
Abstract: The main point argued and illustrated here is the ease with which methods and ideas emerging in the connectionist community can be imported for control applications as soon as the fuzzy controller is supplied with a gradient-based automatic tuning of its parameters. Such a gradient method is applied for the simplest member of Sugeno's fuzzy systems. An example of a direct adaptive fuzzy controller derived from its neural equivalent is presented, and shown to compare favorably with its neural equivalent. >
28 Jun 1993
TL;DR: This paper discusses approaches which combine fuzzy controllers and neural networks, and presents their own hybrid architecture where principles from fuzzy control theory and from neural networks are integrated into one system.
Abstract: Fuzzy controllers are designed to work with knowledge in the form of linguistic control rules. But the translation of these linguistic rules into the framework of fuzzy set theory depends on the choice of certain parameters, for which no formal method is known. The optimization of these parameters can be carried out by neural networks, which are designed to learn from training data, but which are in general not able to profit from structural knowledge. In this paper we discuss approaches which combine fuzzy controllers and neural networks, and present our own hybrid architecture where principles from fuzzy control theory and from neural networks are integrated into one system.
Book•
31 Aug 1993
TL;DR: This work focuses on the development of Choice Rules with Binary Relations for Fuzzy Relational Systems and their applications to Decision Support Systems and to Multipurpose Decision-Making.
Abstract: Foreword by D. Dubois, H. Prade. Preface. 1. Introduction. 2. Common Notations. 3. Systematization of Choice Rules with Binary Relations. 4. Fuzzy Decision Procedures. 5. Contensiveness Criteria. 6. Fuzzy Inclusions. 7. Contensiveness of Fuzzy Dichotomous Decision Procedures in Universal Environment. 8. Choice with Fuzzy Relations. 9. Ranking and C-Spectral Properties of Fuzzy Relations (Fuzzy Von Neumann--Morgenstern--Zadeh Solutions). 10. Invariant, Antiinvariant and Eigen Fuzzy Subsets. Mainsprings of Cut Technique in Fuzzy Relational Systems. 11. Contensiveness of Fuzzy Decision Procedures in Restricted Environment. 12. Efficiency of Fuzzy Decision Procedures. 13. Decision-Making with Special Classes of Fuzzy Binary Relations. 14. Applications to Crisp Choice Rules. 15. Applications to Decision Support Systems and to Multipurpose Decision-Making. Literature. Index.
28 Mar 1993
TL;DR: A novel fuzzy logic design, called Neufuz, using neural net learning is proposed, which significantly improves performance, accuracy, and reliability and reduces design time.
Abstract: A novel fuzzy logic design, called Neufuz, using neural net learning is proposed. Artificial neural net algorithms are used to generate fuzzy rules and membership functions. The combination of learned fuzzy rules, membership functions, and a fuzzy design technique based on new fuzzy inferencing and defuzzification methods significantly improves performance, accuracy, and reliability and reduces design time. Neufuz also minimizes system cost by optimizing the number of rules and membership functions. Simulation results are very encouraging. >