Showing papers on "Fuzzy set published in 1993"
TL;DR: In this paper, a new book about fuzzy set theory and its applications is presented, which can be used to explore the knowledge of the knowledge in a new way, even for only few minutes to read a book.
Abstract: Spend your time even for only few minutes to read a book. Reading a book will never reduce and waste your time to be useless. Reading, for some people become a need that is to do every day such as spending time for eating. Now, what about you? Do you like to read a book? Now, we will show you a new book enPDFd fuzzy set theory and its applications that can be a new way to explore the knowledge. When reading this book, you can get one thing to always remember in every reading time, even step by step.
4,041 citations
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: An appropriate objective function whose minimum will characterize a good possibilistic partition of the data is constructed, and the membership and prototype update equations are derived from necessary conditions for minimization of the criterion function.
Abstract: The clustering problem is cast in the framework of possibility theory. The approach differs from the existing clustering methods in that the resulting partition of the data can be interpreted as a possibilistic partition, and the membership values can be interpreted as degrees of possibility of the points belonging to the classes, i.e., the compatibilities of the points with the class prototypes. An appropriate objective function whose minimum will characterize a good possibilistic partition of the data is constructed, and the membership and prototype update equations are derived from necessary conditions for minimization of the criterion function. The advantages of the resulting family of possibilistic algorithms are illustrated by several examples. >
2,388 citations
TL;DR: The definition of fuzzy time series is given, some properties of fuzzyTime series are explored, and procedures to develop fuzzy timeseries models are discussed.
1,048 citations
01 Jan 1993
TL;DR: The concept of fuzzy sets (precisely speaking, fuzzy subsets of an ordinary set) is nothing but an extended concept of ordinary sets, and the concept of probabilities is absolutely different from that of sets.
Abstract: As is well-known in recent years, there are two kinds of uncertainities, randomness and fuzziness, which can be both dealt with from a mathematical point of view. We know the concept of probabilities with respect to randomness and also that of fuzzy sets with respect to fuzziness. This fact tempts us to discuss fuzzy sets in comparison with probabilities. However, such a direct comparison must fail. The concept of fuzzy sets (precisely speaking, fuzzy subsets of an ordinary set) is nothing but an extended concept of ordinary sets. We have to notice that the concept of probabilities is absolutely different from that of sets. To discuss our problem in detail, let us consider probabilities for the time being. There are a number of interpretations for probabilities: classical probabilities (originated by Laplace); measure theoretical probabilities (by Kolmogorov); subjective probabilities in Bayesian statistics; probabilities as logics and so on.
889 citations
01 Sep 1993
TL;DR: Simulation results demonstrate that better control performance can be achieved in comparison with Ziegler-Nichols controllers and Kitamori's PID controllers.
Abstract: This paper describes the development of a fuzzy gain scheduling scheme of PID controllers for process control. Fuzzy rules and reasoning are utilized online to determine the controller parameters based on the error signal and its first difference. Simulation results demonstrate that better control performance can be achieved in comparison with Ziegler-Nichols controllers and Kitamori's PID controllers. >
773 citations
Book•
28 Feb 1993
TL;DR: This monograph is the first to integrate ambiguous parameters in problem-formulation with fuzzy goals for multiobjective optimization into a unified methodology.
Abstract: This monograph is the first to integrate ambiguous parameters in problem-formulation with fuzzy goals for multiobjective optimization into a unified methodology. Including ''real-world'' applications illustrated by interactive computer programs (written in C, version 6.0 for Ibm Pcs), the work is intended for advanced undergraduate and graduate students and specialists in systems analysis in such fields as public decision-making, administrative planning, and managerial decision-making.
731 citations
TL;DR: Algorithms which enable forecasting attainable periods are developed which look valid and applicable to further analyses of other questions and items on questionnaires and using these methods simultaneously as well as the traditional Delphi method may prove a really effective result.
640 citations
TL;DR: This paper will provide some background concerning the development of the fuzzy min-max clustering neural network and provide a comparison with similar work that has recently emerged and a brief description of fuzzy sets, pattern clustering, and their synergistic combination is presented.
Abstract: In an earlier companion paper (56) a supervised learning neural network pattern classifier called the fuzzy min- max classification neural network was described. In this sequel, the unsupervised learning pattern clustering sibling called the fuzzy min-max clustering neural network is presented. Pattern clusters are implemented here as fuzzy sets using a membership function with a hyperbox core that is constructed from a min point and a max point. The min-max points are determined using the fuzzy min-max learning algorithm, an expansion-contraction process that refines the author's earlier Fuzzy Adaptive Reso- nance Theory neural network (50). The fuzzy min-max clustering neural network stabilizes into pattern clusters in only a few passes through a data set; it can be reduced to hard cluster boundaries that are easily examined without sacrificing the fuzzy boundaries; it provides the ability to incorporate new data and add new clusters without retraining; and it inherently provides degree of membership information that is extremely useful in higher level decision making and information processing. This paper will provide some background concerning the development of the fuzzy min-max clustering neural network and provide a comparison with similar work that has recently emerged. A brief description of fuzzy sets, pattern clustering, and their synergistic combination is presented. The fuzzy min- max clustering neural network will be explained in detail and examples of its clustering performance will be given. The paper will conclude with a description of problems that need to be addressed and a list of some potential applications.
541 citations
TL;DR: A family of objective functions called fuzzy c-regression models, which can be used too fit switching regression models to certain types of mixed data, is presented and a general optimization approach is given and corresponding theoretical convergence results are discussed.
Abstract: A family of objective functions called fuzzy c-regression models, which can be used too fit switching regression models to certain types of mixed data, is presented. Minimization of particular objective functions in the family yields simultaneous estimates for the parameters of c regression models, together with a fuzzy c-partitioning of the data. A general optimization approach for the family of objective functions is given and corresponding theoretical convergence results are discussed. The approach is illustrated by two numerical examples that show how it can be used to fit mixed data to coupled linear and nonlinear models. >
534 citations
TL;DR: A survey of fuzzy set theory applied in cluster analysis in three categories: the fuzzy clustering based on fuzzy relation, the fuzzy generalized k-nearest neighbor rule, and an overview of a nonparametric classifier.
TL;DR: The properties of several measures of similarity of fuzzy values are presented and compared and it is shown that several properties are common to all measures but some properties do not hold for all of them.
01 Jan 1993
TL;DR: An automatic fuzzy system design method that uses a genetic algorithm and integrates three design stages that was applied to the classic inverted-pendulum control problem and has been shown to be practical through a comparison with another method.
Abstract: The authors propose an automatic fuzzy system design method that uses a genetic algorithm and integrates three design stages. The method determines membership functions, the number of fuzzy rules, and the rule-consequent 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 method was applied to the classic inverted-pendulum control problem and has been shown to be practical through a comparison with another method. >
01 Jan 1993
TL;DR: The problem of converting possibility measures into probability measures has received attention in the past, but not by so many scholars, and has roots at least as much in the possibility/probability consistency principle of Zadeh (1978), that he proposed in the paper founding possibility theory.
Abstract: The problem of converting possibility measures into probability measures has received attention in the past, but not by so many scholars. This question is philosophically interesting as part of the debate between probability and fuzzy sets. The imbedding of fuzzy sets into random set theory as done by Goodman and Nguyen (1985), Wang Peizhuang (1983), among others, has solved this question in principle. However the conversion problem has roots at least as much in the possibility/probability consistency principle of Zadeh (1978), that he proposed in the paper founding possibility theory.
TL;DR: A new informative measure for discrimination between two fuzzy sets is introduced and it is shown that this discriminating measure reduces to the nonprobabilistic entropy of Deluca and Termini under a special condition.
TL;DR: A fuzzy linguistic model is defined, starting from an existing weighted Boolean retrieval model, a linguistic extension, formalized within fuzzy set theory, in which numeric query weights are replaced by linguistic descriptors which specify the degree of importance of the terms.
Abstract: The generalization of Boolean Information Retrieval Systems (IRS) is still an open research field; in fact, though such systems are diffused on the market, they present some limitations; one of the main features lacking in these systems is the ability to deal with the “imprecision” and “subjectivity” characterizing retrieval activity. However, the replacement of such systems would be much more costly than their evolution through the incorporation of new features to enhance their efficiency and effectiveness. Previous efforts in this area have led to the introduction of numeric weights to improve both document representation and query language. By attaching a numeric weight to a term in a query, a user can provide a quantitative description of the “importance” of that term in the documents he or she is looking for. However, the use of weights requires a clear knowledge of their semantics for translating a fuzzy concept into a precise numeric value. Our acquaintance with these problems led us to define, starting from an existing weighted Boolean retrieval model, a linguistic extension, formalized within fuzzy set theory, in which numeric query weights are replaced by linguistic descriptors which specify the degree of importance of the terms. This fuzzy linguistic model is defined and an evaluation is made of its implementation on a Boolean IRS. © 1993 John Wiley & Sons, Inc.
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.
TL;DR: A prototype expert system based on the dissolved gas analysis (DGA) technique for diagnosis of suspected transformer faults and their maintenance actions is developed and a synthetic method is proposed to assist the gas ratio method.
Abstract: A prototype expert system based on the dissolved gas analysis (DGA) technique for diagnosis of suspected transformer faults and their maintenance actions is developed. A synthetic method is proposed to assist the gas ratio method. The uncertainties of key gas analysis, norms threshold, and gas ratio boundaries, are managed by using a fuzzy set concept. The expert system is implemented on a PC-AT using KES with rule-based knowledge representation. The system has been tested to show its effectiveness in transformer diagnosis. >
18 Sep 1993
TL;DR: Fuzzy cognitive maps are applied to an undersea virtual world of dolphins and change as causal patterns change with differential Hebbian learning.
Abstract: Fuzzy cognitive maps (FCMs) can structure virtual worlds. FCMs link causal events, values, goals, and trends in a fuzzy feedback dynamical system. They direct actors in virtual worlds as the actors react to events and to one another. In nested FCMs each causal concept can control its own FCM. This combines levels of fuzzy systems that can choose goals or move objects. Adaptive FCMs change as causal patterns change. They adapt with differential Hebbian learning. FCMs are applied to an undersea virtual world of dolphins. >
TL;DR: A new definition of consistency is introduced that allows us to locate the roots of inconsistency and is easy to interpret and forms a better basis than the old eigenvalue consistency for selecting a threshold based on common sense.
28 Mar 1993
TL;DR: The authors address some classical misunderstandings between fuzzy sets and probabilities, and consider probabilistic interpretations of membership functions that may help in membership function assessment.
Abstract: One of the most controversial issues in uncertainty modeling and information sciences is the relationship between probability theory and fuzzy sets The literature pertaining to this debate is surveyed The authors address some classical misunderstandings between fuzzy sets and probabilities They consider probabilistic interpretations of membership functions that may help in membership function assessment Nonprobabilistic interpretations of fuzzy sets are identified The literature on possibility-probability transformations is examined, and some lurking controversies on that topic are clarified Several subfields of fuzzy set research where fuzzy sets and probability are conjointly used are discussed >
TL;DR: The proposed two-phase approach guarantees both nondominated and balanced solutions for solving both the crisp and the fuzzy multiple objective decision making problems.
TL;DR: It is proposed in the present paper that the indicator for set inclusion must be two-valued for crisp sets, and the investigation results in a very general class of indicators based on the bold union operation, and in a complete measure-theoretic characterization of this class.
Book•
01 Aug 1993
TL;DR: This book makes available significant articles on fuzzy sets related to intelligent systems and fundamental notions in fuzzy sets, fuzzy control, fuzzy logic and approximate reasoning, information processing, decision sciences, connections with operations research, and knowledge acquisition.
Abstract: From the Publisher:
In recent years, fuzzy sets have become an important field, the development of which has been accelerated by the emergence of fuzzy control as a commercially successful methodology. This book makes available significant articles on fuzzy sets related to intelligent systems.
The papers in this volume cover fundamental notions in fuzzy sets, fuzzy control, fuzzy logic and approximate reasoning, information processing, decision sciences, connections with operations research, and knowledge acquisition. Each chapter is introduced by the editors, who describe the relevance of each article and provide pointers to other literature and a short list of further readings.
This collection will be of interest to researchers and professionals in artificial intelligence, engineering, decision sciences, and other fields concerned with management of uncertainty.
02 Oct 1993
TL;DR: In this paper, a rule-based fuzzy logic controller is proposed to control the output power of a PWM inverter used in a stand-alone wind energy conversion scheme (SAWECS).
Abstract: The paper presents a rule-based fuzzy logic controller to control the output power of a pulse width modulated (PWM) inverter used in a stand-alone wind energy conversion scheme (SAWECS). The self-excited induction generator used in SAWECS has the inherent problem of fluctuations in the magnitude and frequency of its terminal voltage with changes in wind velocity and load. To overcome this drawback the variable magnitude, variable frequency voltage at the generator terminals is rectified and the DC power is transferred to the load through a PWM inverter. The objective is to track and extract maximum power from the wind energy system and transfer this power to the local isolated load, This is achieved by using the fuzzy logic controller which regulates the modulation index of the PWM inverter based on the input signals: the power error; and its rate of change. These input signals are fuzzified, that is defined by a set of linguistic labels characterized by their membership functions predefined for each class. Using a set of 49 rules which relate the fuzzified input signals to the fuzzy controller output, fuzzy set theory and associated fuzzy logic operations, the fuzzy controller's output is obtained. The fuzzy set describing the controller's output (in terms of linguistic labels) is defuzzified to obtain the actual analog (numerical) output signal which is then used to control the PWM inverter and ensure complete utilization of the available wind energy. The proposed rule-based fuzzy logic controller is simulated and the results are experimentally verified on a scaled down laboratory prototype of the SAWECS.
01 Jul 1993
TL;DR: An approach is described that utilizes fuzzy sets to develop a fuzzy qualitative simulation algorithm that allows a semiquantitative extension to qualitative simulation, providing three significant advantages over existing techniques.
Abstract: An approach is described that utilizes fuzzy sets to develop a fuzzy qualitative simulation algorithm that allows a semiquantitative extension to qualitative simulation, providing three significant advantages over existing techniques. Firstly, it allows a more detailed description of physical variables, through an arbitrary, but finite, discretisation of the quantity space. The adoption of fuzzy sets also allows common-sense knowledge to be represented in defining values through the use of graded membership, enabling the subjective element in system modelling to be incorporated and reasoned with in a formal way. Secondly, the fuzzy quantity space allows more detailed description of functional relationships in that both strength and sign information can be represented by fuzzy relations holding against two or multivariables. Thirdly, the quantity space allows ordering information on rates of change to be used to compute temporal durations of the state and the possible transitions. Thus, an ordering of the evolution of the states and the associated temporal durations are obtained. This knowledge is used to develop an effective temporal filter that significantly reduces the number of spurious behaviors. >
TL;DR: A new index that is useful for ordering (ranking) of fuzzy numbers is proposed and its relationship to the 1981 Yager's index is explained.
TL;DR: It is argued that there is a method, Saaty's Analytic Hierarchy Process (AHP), that is compatible with both fuzzy set theory and multi-criteria methodology, and can deal operationally with fuzziness, factor diversity and complexity in problems of land evaluation involving the location of a public facility.
Abstract: Recent developments in geographical information systems have drawn upon concepts of fuzzy set theory and multi-criteria methodology. In this paper we argue that there is a method, Saaty’s Analytic Hierarchy Process (AHP), that is compatible with both these research directions. The contributions of the AHP are highlighted in the light of recent developments in GIS, with particular attention to the concept of fuzzy set theory. An example of a GIS application is provided to show how the AHP can deal operationally with fuzziness, factor diversity and complexity in problems of land evaluation involving the location of a public facility.
TL;DR: Relationships between conceptual and computational platforms of fuzzy sets and neurocomputations and the proposed architecture of logic processors implements the paradigm of distributed processing with the aid of logic-driven neurons is discussed.
01 Jan 1993
TL;DR: Using the structural forms supplied by fuzzy set theory and approximate reasoning, a new method is presented for solving multiple-objective decision problems for which the decision maker can supply only ordinal information on his preferences and the importance of the individual objectives.
Abstract: Using the structural forms supplied by fuzzy set theory and approximate reasoning, a new method is presented for solving multiple-objective decision problems for which the decision maker can supply only ordinal information on his preferences and the importance of the individual objectives.