Soft Numerical Computing in Uncertain Dynamic Systems - Softcover

Allahviranloo, Tofigh; Pedrycz, Witold

Softcover

ISBN 10: 0128228555 ISBN 13: 9780128228555

Publisher: Academic Press, 2020

Synopsis

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

About this title

About the Authors

Tofigh Allahviranloo is a full professor of applied mathematics at Istinye University, Turkey. As a trained mathematician and computer scientist, Prof. Allahviranloo 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. He is the author of several books and many papers published by Elsevier and Springer. He actively serves the research community, as Editor-in-Chief of the International J. of Industrial Mathematics, and Associate Editor or editorial board member of several other journals, including Information Sciences, Fuzzy Sets and Systems, Journal of Intelligent and Fuzzy Systems, Iranian J. of Fuzzy Systems and Mathematical Sciences.

Dr. 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. In 2012 he was elected a fellow of the Royal Society of Canada. 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 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 the editor-in-chief of Information Sciences, editor-in-chief of WIREs Data Mining and Knowledge Discovery, and co-editor-in-chief of International Journal of Granular Computing, and Journal of Data Information and Management. He serves on the advisory board of IEEE Transactions on Fuzzy Systems.

From the Back Cover

One of the important topics in applied science is dynamic systems and their applications. If these systems are involved with complex-uncertain data then they will be more important and practical; real-life problems work with this type of data and most of them cannot be solved exactly and easily and sometimes they are impossible to solve.

In Soft Numerical Computing in Uncertain Dynamic Systems, the authors develop these models and deliver solutions to them with the aid of numerical methods. Since they are inherently uncertain, so uncertain and soft computations are of high relevance here. This is the reason behind investigating soft numerical computing in dynamic systems. Clearly, all the numerical methods need to consider error of approximation. Having this in mind, the books aims to discuss several types of errors and their propagation. Moreover, numerical methods complete with convergence and consistence properties and characteristics, so the other main objectives involve considerations, discussion and proving 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 along with their pertinent computing. Other important applied topics involving uncertain dynamic systems include image processing and pattern recognition; they can benefit from the 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.

This book is intended for system specialists who are interested in dynamic systems that operate at different time scales. 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, interested in dynamic and uncertain systems. Graduate courses offered at MSc and PhD level in applied sciences like control and optimal control include uncertain dynamic systems.

Edition details

• Publisher: Academic Press
• Publication date: 2020
• ISBN 10: 0128228555
• ISBN 13: 9780128228555
• Binding: Paperback
• Language: English
• Number of pages: 388