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Fuzzy Logic Foundations and Industrial Applications is an organized edited collection of contributed chapters covering basic fuzzy logic theory, fuzzy linear programming, and applications. Special emphasis has been given to coverage of recent research results, and to industrial applications of fuzzy logic.
The chapters are new works that have been written exclusively for this book by many of the leading and prominent researchers (such as Ronald Yager, Ellen Hisdal, Etienne Kerre, and others) in this field. The contributions are original and each chapter is self-contained. The authors have been careful to indicate direct links between fuzzy set theory and its industrial applications.
Fuzzy Logic Foundations and Industrial Applications is an invaluable work that provides researchers and industrial engineers with up-to-date coverage of new results on fuzzy logic and relates these results to their industrial use.



Fuzzy Logic Foundations


1. A Unified View of Case Based Reasoning and Fuzzy Modeling

The fuzzy systems modeling technique and the case based reasoning methodology are briefly described. It is then shown that these two approaches can be viewed in a unified way as essentially involving the same process, a matching step and a solution composition step. It is noted that in the typical case based reasoning application the solution composition step is more difficult because of the complexity of the associated action space. Two techniques are then suggested to help in the solution composition task in case based reasoning. The first, the weighted median, is shown to be useful in domains in which the action space consists of an ordered collection of alternatives. The second, a variation of reinforcement learning, is shown to be useful in domains in which the resulting actions involve a sequence of steps.
Ronald R. Yager

2. Open-Mindedness and Probabilities Versus Possibilities

A probabilistic interpretation of grades of membership is described.
Ellen Hisdal

3. Fuzzy Derivatives and Fuzzy Cauchy Problems Using LP Metric

A new approach for defining a fuzzy derivative is introduced and a comparison with a previous approach illustrates the advantages of the new method. A first order fuzzy differential equation and a fuzzy Cauchy problem are defined and sufficient conditions for existence and uniqueness of solutions to fuzzy initial value problems are given. Solutions are calculated for simple examples.
Menahem Friedman, Ming Ma, Abraham Kandel

4. On the Classification and the Dependencies of the Ordering Methods

In this paper, we classify all the approaches to order fuzzy quantities into three classes. Then we focus our attention on the investigation of dependency among the elements of the first class of ordering approaches.
Xuzhu Wang, Etienne Kerre

Fuzzy Logic Systems


5. Possibility Model and its Applications

In this paper, we give some basic principle of possibility models and its applications. We briefly review possibility analysis based on the max-min operator and explain possibility analysis based on exponential possibility distributions in contrast to statistical analysis. Using possibility analysis, we show an identification method of possibility distributions and fuzzy data analysis such as regression analysis.
Hideo Tanaka

6. Interactive Fuzzy Programming for Multiobjective 0–1 Programming Problems Through Genetic Algorithms with Double Strings

In this paper, interactive fuzzy programming for multiobjective 0-1 programming problems is proposed by incorporating the desirable features of both the interactive fuzzy programming methods and genetic algorithms with double strings. By considering the vague nature of human judgments, fuzzy goals of the decision maker (DM) for objective functions are quantified by eliciting linear membership functions. If the DM specifies a reference membership level for each of the membership functions, the corresponding (local) Pareto optimal solution, which is nearest to the requirement in the minimax sense, can be obtained by solving the formulated minimax problem through a genetic algorithm with double strings. For obtaining an optimal solution not dominated by the solutions before interaction, the algorithm is revised by introducing some new mechanism for forming an initial population. An application to multiobjective project selection problems demonstrate both feasibility and efficiency of the proposed method.
Masatoshi Sakawa, Toshihiro Shibano

7. The Handling of Fuzzy Objective Functions in (Multicriteria) Linear Programs

For calculating a solution of a linear program where coefficients of the objective function(s) may be fuzzy, we have to explain how the maximization of a fuzzy objective can be interpreted. In the literature of fuzzy optimization, a lot of procedures for substituting fuzzy objectives by crisp ones are proposed. In this paper, a critical survey of these different methods is given.
Heinrich J. Rommelfanger

8. Making Decisions on Fuzzy Integer Linear Programming Problems

Integer Linear Programming problems with fuzzy constraints are considered, and an algorithm to solve them, which provides a fuzzy solution, is proposed. It is shown how this algorithm also serves to solve conventional parametric Integer Linear Programming problems. Additionally the algorithm is accommodated to deal with Fuzzy Boolean Programming problems. The problem of choosing a point solution from the fuzzy optimal solution obtained in each case is approached and discussed.
Francisco Herrera, José Luis Verdegay

9. Information Diffusion Principle and Application in Fuzzy Neuron

In this paper, we demonstrate that the fuzziness of fuzzy information can come not only from the measuring scale, but also from the incompleteness of sample knowledge. Fundamentally, by developing the method of information distribution to information diffusion principle, we establish the embryonic form of the theory of fuzzy information optimization processing, which is connected with incompleteness. An application in fuzzy neuron to estimate earthquake intensity shows that information diffusion methods have obvious advantages and future applications.
Chongfu Huang, Da Ruan

Fuzzy Logic Industrial Applications


10. Some Application Examples of Fuzzy Set Theory

We describe some applications from fuzzy set theory in the areas: automobile technology, domestic appliances, power plants, traffic technology, and telecommunications.
Hans Hellendoorn

11. Recent Successful Fuzzy Logic Applications in Industrial Automation

In this paper I review 8 recent applications of fuzzy logic in industrial automation. All applications used the so-called “fuzzyPLC,” an innovative hardware platform that merges fuzzy logic and traditional automation techniques. Following a quick overview on the fuzzyPLC, I discuss the 8 applications and focus on how fuzzy logic enabled a superior solution compared to conventional techniques. Whenever possible, I quantify the benefit in cost saving or quality improvement. For detailed information on the reviewed applications, I reference the respective papers.
Constantin von Altrock

12. FIPS—Foundations of a New Tool for Process Control Problems

FIPS denotes a Fuzzy Instrumented Process Control System geared to the special features of reversal processes, which especially occur during the start-up and shut-down control of industrial plants. Its fundamental architecture contains four modules: a basic module, a model-building module, a logic module and a simulation module. The basic features and properties of the first three modules are outlined below.
Siegfried Gottwald, Manfred Locke

13. Industrial Applications of Fuzzy Logic and Neural Networks in China

Fuzzy logic development in the People’s Republic of China started in the end of 1970s, but most work lay just on theory in the early time. About ten years later, the government of China began aware of the significance of fuzzy logic application in industry. In 1988 a national key laboratory on fuzzy logic research and development was established in Beijing Normal University, supported by the Department of Education of China. In the mean time, “fuzzy information processing and machine intelligence” was determined as a major national project supported by the Natural Science Foundation of China, led by Prof. P. Z. Wang who is a leading figure in China’s fuzzy logic and also the director of the key lab mentioned above. From then on, a lot of researchers turned to fuzzy application. So far, fuzzy technology has been successfully widely applied in China to computer science, automatic control, earthquake engineering, system engineering, civil engineering, environmental protection, machinery, management science, thinking science, social science, medical science, weather forecast, literature, art, sports and psychology.
Xiaozhong Li

14. The Potential of Fuzzy Logic Applications in Industry

In this paper an overview is given of the various ways fuzzy logic can be used in industry. The application of fuzzy logic in control is illustrated by four case studies. The first example shows how fuzzy logic, incorporated in the hardware of an industrial controller, helps to improve a classical linear PID controller by reducing its overshoot. In the second example the overshoot of a PID controller is drastically reduced by scheduling of the set-point by means of fuzzy logic. A third study describes how fuzzy logic may be used to fine-tune a PID controller, without the operator having any a priori knowledge of the system to be controlled. The last example in the field of control is from process industry. Here, fuzzy logic supervisory control is implemented in software and enhances the operation of a sintering oven through a subtle combination of priority management and deviation-controlled timing. Finally the key areas of research in fuzzy logic control are discussed. First the paper discusses how fuzzy logic control can be combined with other methods. By properly separating the a priori model knowledge of the process under control, a hierarchy of non-linear control methods is established. After a short discussion of how to optimise an intuitive fuzzy rule base, we show that it is possible to derive conditions for asymptotic stability and robustness for fuzzy logic controllers, using classical non-linear analysis. Next, a completely different application area of fuzzy logic is discussed: sensor fusion. After a short overview on the various types of sensor fusion methods two case studies in this field are treated: the fuzzy human body detector and the earth quake detector. The review of the main industrial application fields of fuzzy logic is concluded with a case study on a fuzzy Health Management expert systems.
Ariën J. van der Wal

15. Fuzzy Logic Applications in Nuclear Industry

Fuzzy logic applications in nuclear industry present a tremendous challenge. The main reason for this is the public awareness of the risks of nuclear industry and the very strict safety regulations in force for nuclear power plants. The very same regulations prevent a researcher from quickly introducing novel fuzzy-logic methods into this field. On the other hand, the application of fuzzy logic has, despite the ominous sound of the word “fuzzy” to nuclear engineers, a number of very desirable advantages over classical methods, e.g., its robustness and the capability to include human experience into the controller.
In this chapter, we review the available literature on fuzzy logic applications in nuclear industry, then present the initiative and progress of FLINS (Fuzzy Logic and Intelligent technologies in Nuclear Science) at the Belgian Nuclear Research Centre (SCK · CEN), and finally provide up-to-date coverage of new references on the subject from the first and second FLINS international workshops.
Da Ruan


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