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Soft Numerical Computing in Uncertain Dynamic Systems is intended for system specialists interested in dynamic systems that operate at different time scales. The book discusses several types of errors and their propagation, covering numerical methods—including convergence and consistence properties and characteristics—and proving of related theorems within the setting of soft computing. Several types of uncertainty representation like interval, fuzzy, type 2 fuzzy, granular, and combined uncertain sets are discussed in detail. The book can be used by engineering students in control and finite element fields, as well as all engineering, applied mathematics, economics, and computer science students.
One of the important topics in applied science is dynamic systems and their applications. The authors develop these models and deliver solutions with the aid of numerical methods. Since they are inherently uncertain, soft computations are of high relevance here. This is the reason behind investigating soft numerical computing in dynamic systems. If these systems are involved with complex-uncertain data, they will be more practical and important. Real-life problems work with this type of data and most of them cannot be solved exactly and easily—sometimes they are impossible to solve.
Clearly, all the numerical methods need to consider error of approximation. Other important applied topics involving uncertain dynamic systems include image processing and pattern recognition, which can benefit from uncertain dynamic systems as well. In fact, the main objective is to determine the coefficients of a matrix that acts as the frame in the image. One of the effective methods exhibiting high accuracy is to use finite differences to fill the cells of the matrix.
- Explores dynamic models, how time is fundamental to the structure of the model and data, and how a process unfolds
- Investigates the dynamic relationships between multiple components of a system in modeling using mathematical models and the concept of stability in uncertain environments
- Exposes readers to many soft numerical methods to simulate the solution function’s behavior
Researchers, professionals, and graduate students in computer science & engineering, bioinformatics, and electrical engineering
1.1. Importance of the subjects of the book
1.3. The structure of the book
2. Uncertain sets
2.1. Introduction to aspects of uncertainty
2.2.1. Distribution functions
2.2.2. Uncertainty distribution functions
2.2.3. Uncertain variable
2.2.4. Uncertain set
2.2.5. Function of uncertain set
2.2.6. Membership function
2.2.7. Interval parametric form
2.2.8. Distance between uncertain sets
2.2.9. Combined uncertain sets
2.2.10. Level wise parametric format of a Combined uncertain set
3. Soft computing with uncertain sets
3.1. Introduction to soft computing
3.2. Computing with uncertain sets
3.2.1. Extension principle-based operations
3.2.2. Computations with combined uncertain sets
3.2.3. Computations with interval parametric form
3.2.4. Difference between uncertain sets
4. Continuous numerical solution of uncertain differential equations
4.2. Uncertain differential equations
4.2.1. First order uncertain differential equations
18.104.22.168. Uncertain Taylor expansion methods
22.214.171.124. Uncertain Homotopy perturbation method
126.96.36.199. Uncertain Homotopy analysis perturbation method
188.8.131.52. Uncertain differential transform method
4.2.2. High order uncertain differential equation
184.108.40.206. Uncertain Taylor expansion methods
220.127.116.11. Uncertain Homotopy perturbation method
18.104.22.168. Uncertain Homotopy analysis perturbation method
22.214.171.124. Uncertain differential transform method
5. Discrete numerical solution of uncertain differential equations
5.2. First order uncertain differential equations
5.2.1. Uncertain difference methods
126.96.36.199. Uncertain Euler’s method
188.8.131.52. Uncertain Runge-Kutta’s method ….
5.2.2. Uncertain multi-step methods
184.108.40.206. Uncertain explicit methods
220.127.116.11. Uncertain implicit methods
6. Numerical solution of uncertain fractional differential equations
6.2. Uncertain fractional differential equations
6.3. Numerical solution of uncertain fractional differential equations
6.4. Convergence, Consistence and stability of the methods
7. Numerical solution of uncertain partial differential equations
7.2. Uncertain partial differential equations
7.3. Numerical solutions of uncertain partial differential equations
7.4. Convergence, Consistence and stability
- No. of pages:
- © Academic Press 2021
- 1st September 2020
- Academic Press
- Paperback ISBN:
Dr. Allahviranloo is professor in Bahcesehir International university. As a trained mathematician and computer scientist, Tofigh has developed a passion for multi- and interdisciplinary research. He is not only deeply involved in fundamental research in fuzzy applied mathematics, especially fuzzy differential equations, but he also aims at innovative applications in the applied biological sciences. Over the past 22 years, 70 Ph.D. students have graduated under his co- supervision. Tofigh is a prolific writer, with a bibliography comprising over 200 peer-reviewed journal papers, eleven books in Farsi as an author, three book chapters and 20 contributions to conference proceedings. Dr. Allahviranloo actively serves the research community, in particular as editor-in-chief of Int. J. of Industrial Mathematics and as member in charge of the editorial board of several other journals, including the Fuzzy Sets and Systems, Journal of Intelligent and Fuzzy Systems, and Mathematical Science. , Witold Pedrycz (IEEE Fellow, 1998) is Professor and Canada Research Chair (CRC) in Computational Intelligence in the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada. He is also with the Systems Research Institute of the Polish Academy of Sciences, Warsaw, Poland. In 2009, Dr. Pedrycz was elected a foreign member of the Polish Academy of Sciences. In 2012 he was elected a Fellow of the Royal Society of Canada. In 2007 he received a prestigious Norbert Wiener award from the IEEE Systems, Man, and Cybernetics Society. He is a recipient of the IEEE Canada Computer Engineering Medal, a Cajastur Prize for Soft Computing from the European Centre for Soft Computing, a Killam Prize, and a Fuzzy Pioneer Award from the IEEE Computational Intelligence Society. His main research directions involve Computational Intelligence, fuzzy modeling and Granular Computing, knowledge discovery and data science, pattern recognition, data science, knowledge-based neural networks, and control engineering.
Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey
Witold Pedrycz (IEEE Fellow, 1998) is Professor and Canada Research Chair (CRC) in Computational Intelligence in the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada. He is also with the Systems Research Institute of the Polish Academy of Sciences, Warsaw, Poland. In 2009, Dr. Pedrycz was elected a foreign member of the Polish Academy of Sciences. In 2012 he was elected a Fellow of the Royal Society of Canada. In 2007 he received a prestigious Norbert Wiener award from the IEEE Systems, Man, and Cybernetics Society. He is a recipient of the IEEE Canada Computer Engineering Medal, a Cajastur Prize for Soft Computing from the European Centre for Soft Computing, a Killam Prize, and a Fuzzy Pioneer Award from the IEEE Computational Intelligence Society. His main research directions involve Computational Intelligence, fuzzy modeling and Granular Computing, knowledge discovery and data science, pattern recognition, data science, knowledge-based neural networks, and control engineering. He has published numerous papers in these areas; the current h-index is 107 (Google Scholar) and 82 on the list top-h scientists for computer science and electronics http://www.guide2research.com/scientists/. He is also an author of 18 research monographs and edited volumes covering various aspects of Computational Intelligence, data mining, and Software Engineering. Dr. Pedrycz is vigorously involved in editorial activities. He is an Editor-in-Chief of Information Sciences (Elsevier), Editor-in-Chief of WIREs Data Mining and Knowledge Discovery (Wiley), and Co-editor-in-Chief of Int. J. of Granular Computing (Springer) and J. of Data Information and Management (Springer). He serves on an Advisory Board of IEEE Transactions on Fuzzy Systems and is a member of a number of editorial boards of international journals.
Department of Electrical and Computer Engineering, University of Alberta, Canada
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