This monograph belongs to the broader area of Fuzzy Mathematics and it is the first one in Fuzzy Approximation Theory. The chapters are self-contained with lots of applications to teach several advanced courses and th...
ISBN:
(数字)9783642112201
ISBN:
(纸本)9783642112195
This monograph belongs to the broader area of Fuzzy Mathematics and it is the first one in Fuzzy Approximation Theory. The chapters are self-contained with lots of applications to teach several advanced courses and the topics covered are very diverse. An extensive background of fuzziness and Fuzzy Real Analysis is given. The author covers Fuzzy Differentiation and Integration Theory followed by Fuzzy Ostrowski inequalities. Then results on classical algebraic and trigonometric polynomial Fuzzy Approximation are presented. The author develops a complete theory of convergence with rates of Fuzzy Positive linear operators to Fuzzy unit operator, the so-called Fuzzy Korovkin Theory. The related Fuzzy Global Smoothness is included. Then follows the study of Fuzzy Wavelet type operators and their convergence with rates to Fuzzy unit operator. Similarly the Fuzzy Neural Network Operators are discussed followed by Fuzzy Random Korovkin approximation theory and Fuzzy Random Neural Network approximations. The author continues with Fuzzy Korovkin approximations in the sense of Summability. Finally fuzzy sense differences of Fuzzy Wavelet type operators are estimated. The monograph's approach is quantitative and the main results are given via Fuzzy inequalities, involving Fuzzy moduli of continuity, that is Fuzzy Jackson type inequalities. The exposed theory is destined and expected to find applications to all aspects of fuzziness from theoretical to practical in almost all sciences, technology, finance and industry. Also it has its interest within Pure Mathematics. So this monograph is suitable for researchers, graduate students and seminars of theoretical and applied mathematics, computer science, statistics and engineering.
This book is organized in five chapters. In Chapter 1, some basic concepts are explained to completely understand the contribution of the algorithms developed in this research work. The evaluation of how motion is pre...
ISBN:
(数字)9783642106958
ISBN:
(纸本)9783642106941
This book is organized in five chapters. In Chapter 1, some basic concepts are explained to completely understand the contribution of the algorithms developed in this research work. The evaluation of how motion is present and how it influences on de-interlacing is studied in Chapter 2. The design options of the proposed fuzzy motion-adaptive de-interlacing algorithm is studied in Chapter 3. A spatial interpolator that adapts the interpolation to the presence of edges in a fuzzy way is developed in Chapter 4. A temporal interpolator that adapts the strategy of the interpolation to possible repetition of areas of fields is presented in Chapter 5. Using both interpolators in the fuzzy motion-adaptive algorithm described in Chapter 3 clearly improves the de-interlaced results.
The book contains ten chapters as follows, Prepare Knowledge, Regression and Self-regression Models with Fuzzy Coefficients; Regression and Self-regression Models with Fuzzy Variables, Fuzzy Input/output Model, Fuzzy ...
ISBN:
(数字)9783642107122
ISBN:
(纸本)9783642107108
The book contains ten chapters as follows, Prepare Knowledge, Regression and Self-regression Models with Fuzzy Coefficients; Regression and Self-regression Models with Fuzzy Variables, Fuzzy Input/output Model, Fuzzy Cluster Analysis and Fuzzy Recognition, Fuzzy Linear Programming, Fuzzy Geometric Programming, Fuzzy Relative Equation and Its Optimizing, Interval and Fuzzy Differential Equations and Interval and Fuzzy Functional and Their Variation. It can not only be used as teaching materials or reference books for under-graduates in higher education, master graduates and doctor graduates in the courses of applied mathematics, computer science, artificial intelligence, fuzzy information process and automation, operations research, system science and engineering, and the like, but also serves as a reference book for researchers in these fields, particularly, for researchers in soft science.
Many problems in decision making, monitoring, fault detection, and control require the knowledge of state variables and time-varying parameters that are not directly measured by sensors. In such situations, observers,...
ISBN:
(纸本)9783642167751
Many problems in decision making, monitoring, fault detection, and control require the knowledge of state variables and time-varying parameters that are not directly measured by sensors. In such situations, observers, or estimators, can be employed that use the measured input and output signals along with a dynamic model of the system in order to estimate the unknown states or parameters. An essential requirement in designing an observer is to guarantee the convergence of the estimates to the true values or at least to a small neighborhood around the true values. However, for nonlinear, large-scale, or time-varying systems, the design and tuning of an observer is generally complicated and involves large computational costs. This book provides a range of methods and tools to design observers for nonlinear systems represented by a special type of a dynamic nonlinear model -- the Takagi--Sugeno (TS) fuzzy model. The TS model is a convex combination of affine linear models, which facilitates its stability analysis and observer design by using effective algorithms based on Lyapunov functions and linear matrix inequalities. Takagi--Sugeno models are known to be universal approximators and, in addition, a broad class of nonlinear systems can be exactly represented as a TS system. Three particular structures of large-scale TS models are considered: cascaded systems, distributed systems, and systems affected by unknown disturbances. The reader will find in-depth theoretic analysis accompanied by illustrative examples and simulations of real-world systems. Stability analysis of TS fuzzy systems is addressed in detail. The intended audience are graduate students and researchers both from academia and industry. For newcomers to the field, the book provides a concise introduction dynamic TS fuzzy models along with two methods to construct TS models for a given nonlinear system
The theory of cognitive maps was developed in 1976. Its main aim was the representation of (causal) relationships among concepts also known as factors or nodes. Concepts could be assigned values. Causal relationships ...
ISBN:
(数字)9783642032202
ISBN:
(纸本)9783642032196
The theory of cognitive maps was developed in 1976. Its main aim was the representation of (causal) relationships among concepts also known as factors or nodes. Concepts could be assigned values. Causal relationships between two concepts could be of three types: positive, negative or neutral. Increase in the value of a concept would yield a corresponding positive or negative increase at the concepts connected to it via relationships. In 1986 Bart Kosko introduced the notion of fuzziness to cognitive maps and created the theory of Fuzzy Cognitive Maps (FCMs). The relationship between two concepts in (FCMs) can take a value in the interval [-1,1]. This relationship value is called weight. For the last twenty years extensive research in the theory of FCMs has been performed that provided major improvements and enhancements in its theoretical underpinning. New methodologies and approaches have been developed. FCMs have also been applied to many different sectors. New software tools have been developed that automate FCM creation and management. The aim of this book is to present recent advances and state of the art in FCM theory, methodologies, applications and tools that exist to date scattered in journal papers, in a concrete and integrated manner.
This monograph is a second in the series of treatment on fuzzy rationality as an enveloping of decision-choice rationalities where limited information, vagueness, ambiguities and inexactnes are essential characteristi...
ISBN:
(数字)9783540880851
ISBN:
(纸本)9783540880844
This monograph is a second in the series of treatment on fuzzy rationality as an enveloping of decision-choice rationalities where limited information, vagueness, ambiguities and inexactnes are essential characteristics of our knowledge structure and reasoning process. The volume is devoted to a unified epistemic models and theories of decision-choice under total uncertainties.
In our new century, the theory of fuzzy sets and systems is in the core of "softcomputing" and "Computational Intelligence" and has become a normal scientific theory in the fields of exact science...
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ISBN:
(数字)9783540938026
ISBN:
(纸本)9783540938019
In our new century, the theory of fuzzy sets and systems is in the core of "softcomputing" and "Computational Intelligence" and has become a normal scientific theory in the fields of exact sciences and engineering and it is well on its way to becoming normal in the soft sciences as well. This book is a collection of the views of numerous scholars in different parts of the world who are involved in various research projects concerning fuzziness in science, technology, economic systems, social sciences, logics and philosophy. This volume demonstrates that there are many different views of the theory of fuzzy sets and systems and of their interpretation and applications in diverse areas of our cultural and social life.
Biological systems are inherently stochastic and uncertain. Thus, research in bioinformatics, biomedical engineering and computational biology has to deal with a large amount of uncertainties. Fuzzy logic has shown to...
ISBN:
(数字)9783540899686
ISBN:
(纸本)9783540899679
Biological systems are inherently stochastic and uncertain. Thus, research in bioinformatics, biomedical engineering and computational biology has to deal with a large amount of uncertainties. Fuzzy logic has shown to be a powerful tool in capturing different uncertainties in engineering systems. In recent years, fuzzy logic based modeling and analysis approaches are also becoming popular in analyzing biological data and modeling biological systems. Numerous research and application results have been reported that demonstrated the effectiveness of fuzzy logic in solving a wide range of biological problems found in bioinformatics, biomedical engineering, and computational biology. Contributed by leading experts world-wide, this edited book contains 16 chapters presenting representative research results on the application of fuzzy systems to genome sequence assembly, gene expression analysis, promoter analysis, cis-regulation logic analysis and synthesis, reconstruction of genetic and cellular networks, as well as biomedical problems, such as medical image processing, electrocardiogram data classification and anesthesia monitoring and control. This volume is a valuable reference for researchers, practitioners, as well as graduate students working in the field of bioinformatics, biomedical engineering and computational biology.
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