Fuzzy Fractional Differential Equations and Applications
Author: Snehashish Chakraverty,Smita Tapaswini,Diptiranjan Behera
Publisher: John Wiley & Sons
Presents a systematic treatment of fuzzy fractional differential equations as well as newly developed computational methods to model uncertain physical problems Complete with comprehensive results and solutions, Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications details newly developed methods of fuzzy computational techniquesneeded to model solve uncertainty. Fuzzy differential equations are solved via various analytical andnumerical methodologies, and this book presents their importance for problem solving, prototypeengineering design, and systems testing in uncertain environments. In recent years, modeling of differential equations for arbitrary and fractional order systems has been increasing in its applicability, and as such, the authors feature examples from a variety of disciplines to illustrate the practicality and importance of the methods within physics, applied mathematics, engineering, and chemistry, to name a few. The fundamentals of fractional differential equations and the basic preliminaries of fuzzy fractional differential equations are first introduced, followed by numerical solutions, comparisons of various methods, and simulated results. In addition, fuzzy ordinary, partial, linear, and nonlinear fractional differential equations are addressed to solve uncertainty in physical systems. In addition, this book features: Basic preliminaries of fuzzy set theory, an introduction of fuzzy arbitrary order differential equations, and various analytical and numerical procedures for solving associated problems Coverage on a variety of fuzzy fractional differential equations including structural, diffusion, and chemical problems as well as heat equations and biomathematical applications Discussions on how to model physical problems in terms of nonprobabilistic methods and provides systematic coverage of fuzzy fractional differential equations and its applications Uncertainties in systems and processes with a fuzzy concept Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications is an ideal resource for practitioners, researchers, and academicians in applied mathematics, physics, biology, engineering, computer science, and chemistry who need to model uncertain physical phenomena and problems. The book is appropriate for graduate-level courses on fractional differential equations for students majoring in applied mathematics, engineering, physics, and computer science.
This book addresses the basics of interval/fuzzy set theory, artificial neural networks (ANN) and computational methods. It presents step-by-step modeling for application problems along with simulation and numerical solutions. In general, every science and engineering problem is inherently biased by uncertainty, and there is often a need to model, solve and interpret problems in the world of uncertainty. At the same time, exact information about models and parameters of practical applications is usually not known and precise values do not exist. This book discusses uncertainty in both data and models. It consists of seven chapters covering various aspects of fuzzy uncertainty in application problems, such as shallow water wave equations, static structural problems, robotics, radon diffusion in soil, risk of invasive alien species and air quality quantification. These problems are handled by means of advanced computational and fuzzy theory along with machine intelligence when the uncertainties involved are fuzzy. The proposed computational methods offer new fuzzy computing methods that help other areas of knowledge construction where inexact information is present.
Author: Management Association, Information Resources
Publisher: IGI Global
There are a myriad of mathematical problems that cannot be solved using traditional methods. The development of fuzzy expert systems has provided new opportunities for problem-solving amidst uncertainties. Fuzzy Systems: Concepts, Methodologies, Tools, and Applications is a comprehensive reference source on the latest scholarly research and developments in fuzzy rule-based methods and examines both theoretical foundations and real-world utilization of these logic sets. Featuring a range of extensive coverage across innovative topics, such as fuzzy logic, rule-based systems, and fuzzy analysis, this is an essential publication for scientists, doctors, engineers, physicians, and researchers interested in emerging perspectives and uses of fuzzy systems in various sectors.
Conventional model-based data processing methods are computationally expensive and require experts knowledge for the modelling of a system; neural networks provide a model-free, adaptive, parallel-processing solution. Neural Networks in a Softcomputing Framework presents a thorough review of the most popular neural-network methods and their associated techniques.This concise but comprehensive textbook provides a powerful and universal paradigm for information processing. Each chapter provides state-of-the-art descriptions of the important major research results of the respective neural-network methods. A range of relevant computational intelligence topics, such as fuzzy logic and evolutionary algorithms, are introduced. These are powerful tools for neural-network learning. Array signal processing problems are discussed in order to illustrate the applications of each neural-network model.Neural Networks in a Softcomputing Framework is an ideal textbook for graduate students and researchers in this field because in addition to grasping the fundamentals, they can discover the most recent advances in each of the popular models. The systematic survey of each neural-network model and the exhaustive list of references will enable researchers and students to find suitable topics for future research. The important algorithms outlined also make this textbook a valuable reference for scientists and practitioners working in pattern recognition, signal processing, speech and image processing, data analysis and artificial intelligence.
This book provides comprehensive introduction to a consortium of technologies underlying soft computing, an evolving branch of computational intelligence. The constituent technologies discussed comprise neural networks, fuzzy logic, genetic algorithms, and a number of hybrid systems which include classes such as neuro-fuzzy, fuzzy-genetic, and neuro-genetic systems. The hybridization of the technologies is demonstrated on architectures such as Fuzzy-Back-propagation Networks (NN-FL), Simplified Fuzzy ARTMAP (NN-FL), and Fuzzy Associative Memories. The book also gives an exhaustive discussion of FL-GA hybridization. Every architecture has been discussed in detail through illustrative examples and applications. The algorithms have been presented in pseudo-code with a step-by-step illustration of the same in problems. The applications, demonstrative of the potential of the architectures, have been chosen from diverse disciplines of science and engineering. This book with a wealth of information that is clearly presented and illustrated by many examples and applications is designed for use as a text for courses in soft computing at both the senior undergraduate and first-year post-graduate engineering levels. It should also be of interest to researchers and technologists desirous of applying soft computing technologies to their respective fields of work.
Evolutionary Tuning and Learning of Fuzzy Knowledge Bases
Author: Oscar Cord¢n
Publisher: World Scientific
In recent years, a great number of publications have explored the use of genetic algorithms as a tool for designing fuzzy systems. Genetic Fuzzy Systems explores and discusses this symbiosis of evolutionary computation and fuzzy logic. The book summarizes and analyzes the novel field of genetic fuzzy systems, paying special attention to genetic algorithms that adapt and learn the knowledge base of a fuzzy-rule-based system. It introduces the general concepts, foundations and design principles of genetic fuzzy systems and covers the topic of genetic tuning of fuzzy systems. It also introduces the three fundamental approaches to genetic learning processes in fuzzy systems: the Michigan, Pittsburgh and Iterative-learning methods. Finally, it explores hybrid genetic fuzzy systems such as genetic fuzzy clustering or genetic neuro-fuzzy systems and describes a number of applications from different areas. Genetic Fuzzy System represents a comprehensive treatise on the design of the fuzzy-rule-based systems using genetic algorithms, both from a theoretical and a practical perspective. It is a valuable compendium for scientists and engineers concerned with research and applications in the domain of fuzzy systems and genetic algorithms.
a practitioner's guide to building, using, and maintaining fuzzy systems
Author: Earl Cox
Publisher: Morgan Kaufmann Pub
This new edition provides a comprehensive introduction to fuzzy logic, and leads the reader through the complete process of designing, constructing, implementing, verifying and maintaining a platform-independent fuzzy system model. The book has been extensively revised to bring the subject up-to-date, and features two new chapters: "Building and Using Fuzzy Cognitive Map Models" and "Building ME-OWA Models."The multiplatform CD-ROM contains all the C++ source code from the book’s examples – but its real value is the robust package of fuzzy system related tools and utilities, featuring two notable components. First: Metus Systems’ basic fuzzy modeling software, which includes complete C/C++ source code for creating and executing fuzzy models, a Visual Basic shell that can be used to create fuzzy sets and generate the C/C++ include files, and code for models for pricing, project management, risk assessment, and more. Second: The ME-OWA (Minimum-Entropy, Ordered Weighted Aggregation) decision modeling software from Fuzzy Logic, Inc. This software is used to focus on a single objective function from a set of alternatives given a fuzzy ranking among various alternatives. It is not only an important technique as a stand-alone tool, but is an important methodology in parameter selection (and parameterization ordering) for genetic algorithms and various data mining techniques. It is also an important technique used to establish rule and policy level peer weights in fuzzy models.
The book provides an introduction to basic concepts as well as some recent advancements in fuzzy set theory, approximate reasoning, artificial neural networks & clustering methods. These methodologies create together the so-called soft computing, which is part of a computational approach to system intelligence. The book deals with an overview of fuzzy set theory, foundations for approximate reasoning principles, specific equivalence of inference results using logical conjunctive interpretations of if-then rules, supervised & unsupervised artificial neural networks, a new generalized conditional fuzzy clustering method, artificial neural networks based fuzzy inference system with parameterized consequences in if-then rules, MATLAB(R) m-files implementation of neuro-fuzzy systems, detailed study of neuro-fuzzy systems applications.
The analysis and control of complex systems have been the main motivation for the emergence of fuzzy set theory since its inception. It is also a major research field where many applications, especially industrial ones, have made fuzzy logic famous. This unique handbook is devoted to an extensive, organized, and up-to-date presentation of fuzzy systems engineering methods. The book includes detailed material and extensive bibliographies, written by leading experts in the field, on topics such as: Use of fuzzy logic in various control systems. Fuzzy rule-based modeling and its universal approximation properties. Learning and tuning techniques for fuzzy models, using neural networks and genetic algorithms. Fuzzy control methods, including issues such as stability analysis and design techniques, as well as the relationship with traditional linear control. Fuzzy sets relation to the study of chaotic systems, and the fuzzy extension of set-valued approaches to systems modeling through the use of differential inclusions. Fuzzy Systems: Modeling and Control is part of The Handbooks of Fuzzy Sets Series. The series provides a complete picture of contemporary fuzzy set theory and its applications. This volume is a key reference for systems engineers and scientists seeking a guide to the vast amount of literature in fuzzy logic modeling and control.
One of the attractions of fuzzy logic is its utility in solving many real engineering problems. As many have realised, the major obstacles in building a real intelligent machine involve dealing with random disturbances, processing large amounts of imprecise data, interacting with a dynamically changing environment, and coping with uncertainty. Neural-fuzzy techniques help one to solve many of these problems. Fuzzy Logic and Intelligent Systems reflects the most recent developments in neural networks and fuzzy logic, and their application in intelligent systems. In addition, the balance between theoretical work and applications makes the book suitable for both researchers and engineers, as well as for graduate students.
Fuzzy Control Systems explores one of the most active areas of research involving fuzzy set theory. The contributors address basic issues concerning the analysis, design, and application of fuzzy control systems. Divided into three parts, the book first devotes itself to the general theory of fuzzy control systems. The second part deals with a variety of methodologies and algorithms used in the analysis and design of fuzzy controllers. The various paradigms include fuzzy reasoning models, fuzzy neural networks, fuzzy expert systems, and genetic algorithms. The final part considers current applications of fuzzy control systems. This book should be required reading for researchers, practitioners, and students interested in fuzzy control systems, artificial intelligence, and fuzzy sets and systems.
Author: S. Chakraverty,Smita Tapaswini,Diptiranjan Behera
Publisher: CRC Press
Differential equations play a vital role in the modeling of physical and engineering problems, such as those in solid and fluid mechanics, viscoelasticity, biology, physics, and many other areas. In general, the parameters, variables and initial conditions within a model are considered as being defined exactly. In reality there may be only vague, imprecise or incomplete information about the variables and parameters available. This can result from errors in measurement, observation, or experimental data; application of different operating conditions; or maintenance induced errors. To overcome uncertainties or lack of precision, one can use a fuzzy environment in parameters, variables and initial conditions in place of exact (fixed) ones, by turning general differential equations into Fuzzy Differential Equations ("FDEs"). In real applications it can be complicated to obtain exact solution of fuzzy differential equations due to complexities in fuzzy arithmetic, creating the need for use of reliable and efficient numerical techniques in the solution of fuzzy differential equations. These include fuzzy ordinary and partial, fuzzy linear and nonlinear, and fuzzy arbitrary order differential equations. This unique work?provides a new direction for the reader in the use of basic concepts of fuzzy differential equations, solutions and its applications. It can serve as an essential reference work for students, scholars, practitioners, researchers and academicians in engineering and science who need to model uncertain physical problems.
This book is devoted to reporting innovative and significant progress in fuzzy system engineering. Given the maturation of fuzzy logic, this book is dedicated to exploring the recent breakthroughs in fuzziness and soft computing in favour of intelligent system engineering. This monograph presents novel developments of the fuzzy theory as well as interesting applications of the fuzzy logic exploiting the theory to engineer intelligent systems.
Neural Fuzzy Systems provides a comprehensive, up-to-date introduction to the basic theories of fuzzy systems and neural networks, as well as an exploration of how these two fields can be integrated to create Neural-Fuzzy Systems. It includes Matlab software, with a Neural Network Toolkit, and a Fuzzy System Toolkit.
IEEE Neural Networks Council (New York, NY),Institute of Electrical and Electronics Engineers. Computational Intelligence Society,International Conference on Fuzzy Systems,World Congress on Computational Intelligence (1994, Orlando, Fla),World Congress on Computational Intelligence (1998, Anchorage, Alas.)
Author: IEEE Neural Networks Council (New York, NY),Institute of Electrical and Electronics Engineers. Computational Intelligence Society,International Conference on Fuzzy Systems,World Congress on Computational Intelligence (1994, Orlando, Fla),World Congress on Computational Intelligence (1998, Anchorage, Alas.)
Fuzzy theory has become a subject that generates much interest among the courses for graduate students. However, it was not easy to find a suitable textbook to use in the introductory course and to recommend to the students who want to self-study. The main purpose of this book is just to meet that need. The author has given lectures on the fuzzy theory and its applications for ten years and continuously developed lecture notes on the subject. This book is a publication of the modification and summary of the lecture notes. The fundamental idea of the book is to provide basic and concrete concepts of the fuzzy theory and its applications, and thus the author focused on easy illustrations of the basic concepts. There are numerous examples and figures to help readers to understand and also added exercises at the end of each chapter. This book consists of two parts: a theory part and an application part. The first part (theory part) includes chapters from 1 to 8. Chapters 1 and 2 introduce basic concepts of fuzzy sets and operations, and Chapters 3 and 4 deal with the multi-dimensional fuzzy sets. Chapters 5 and 6 are extensions of the fuzzy theory to the number and function, and Chapters 7 and 8 are developments of fuzzy properties on the probability and logic theories.
Fuzzy modeling has become one of the most productive and successful results of fuzzy logic. Among others, it has been applied to knowledge discovery, automatic classification, long-term prediction, or medical and engineering analysis. The research developed in the topic during the last two decades has been mainly focused on exploiting the fuzzy model flexibility to obtain the highest accuracy. This approach usually sets aside the interpretability of the obtained models. However, we should remember the initial philosophy of fuzzy sets theory directed to serve the bridge between the human understanding and the machine processing. In this challenge, the ability of fuzzy models to express the behavior of the real system in a comprehensible manner acquires a great importance. This book collects the works of a group of experts in the field that advocate the interpretability improvements as a mechanism to obtain well balanced fuzzy models.