Soft computing is an emerging discipline which aims to exploit tolerance for imprecision, approximate reasoning, and uncertainty to achieve robustness, tractability, and cost effectiveness for building intelligent machines. Soft computing methodologies include neural networks, fuzzy sets, genetic algorithms, Bayesian networks, and rough sets, among others. In this regard, neural networks are widely used for modeling dynamic solvers, classification of data, and prediction of solutions, whereas fuzzy sets provide a natural framework for dealing with uncertainty. Artificial Neural Networks and Type-2 Fuzzy Set: Elements of Soft Computing and Its Applications covers the fundamental concepts and the latest research on variants of Artificial Neural Networks (ANN), including scientific machine learning and Type-2 Fuzzy Set (T2FS). In addition, the book also covers different applications for solving real-world problems along with various examples and case studies. It may be noted that quite a bit of research has been done on ANN and Fuzzy Set theory/ Fuzzy logic. However, Artificial Neural Networks and Type-2 Fuzzy Set is the first book to cover the use of ANN and fuzzy set theory with regards to Type-2 Fuzzy Set in static and dynamic problems in one place. Artificial Neural Networks and Type-2 Fuzzy Sets are two of the most widely used computational intelligence techniques for solving complex problems in various domains. Both ANN and T2FS have unique characteristics that make them suitable for different types of problems. This book provides the reader with in-depth understanding of how to apply these computational intelligence techniques in various fields of science and engineering in general and static and dynamic problems in particular. Further, for validation purposes of the ANN and fuzzy models, the obtained solutions of each model in the book is compared with already existing solutions that have been obtained with numerical or analytical methods.

Dr. Snehashish Chakraverty has over thirty years of experience as a teacher and researcher. Currently, he is a Senior Professor in the Department of Mathematics (Applied Mathematics Group) at the National Institute of Technology Rourkela, Odisha, India. He has a Ph.D. from IIT Roorkee in Computer Science. Thereafter he did his post-doctoral research at Institute of Sound and Vibration Research (ISVR), University of Southampton, U.K. and at the Faculty of Engineering and Computer Science, Concordia University, Canada. He was also a visiting professor at Concordia and McGill Universities, Canada, and visiting professor at the University of Johannesburg, South Africa. He has authored/co-authored 14 books, published 315 research papers in journals and conferences, and has four more books in development. Dr. Chakraverty is on the Editorial Boards of various International Journals, Book Series and Conferences. Dr. Chakraverty is the Chief Editor of the International Journal of Fuzzy Computation and Modelling (IJFCM), Associate Editor of Computational Methods in Structural Engineering, Frontiers in Built Environment, and is the Guest Editor for several other journals. He was the President of the Section of Mathematical sciences (including Statistics) of the Indian Science Congress. His present research area includes Differential Equations (Ordinary, Partial and Fractional), Soft Computing and Machine Intelligence (Artificial Neural Network, Fuzzy and Interval Computations), Numerical Analysis, Mathematical Modeling, Uncertainty Modelling, Vibration and Inverse Vibration Problems.

1. Introduction to Soft Computing
Part I: Artificial Neural Network
2. Artificial Neural Network: An Overview
3. Mathematical Formulation of Neural network for Differential Equations
4. Recent Trends in Activation Functions for Solving Differential Equations
5. Curriculum Learning for Artificial Neural Network
6. Symplectic Artificial Neural Network
7. Wavelet Neural Network
8. Physics Informed Neural Network
Part II: Type-2 Fuzzy Uncertainty
9. Fuzzy Set Theory: An Overview
10. Preliminaries of Type-2 Fuzzy Set
11. Uncertain Static Engineering Problems
12. Linear Dynamical Problems with Uncertainty
13. Non-Linear Dynamical Problems with Uncertainty
14. Type-2 Fuzzy Initial Value Problems with Applications
15. Type-2 Fuzzy Fractional Differential Equations with Applications