Table of Contents
1. Introduction to Soft ComputingPart 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
Authors
Snehashish Chakraverty HAG Professor, Department of Mathematics, Applied Mathematics Group, National Institute of Technology Rourkela, Rourkela, Odisha, India. Differential Equations (ordinary, partial, and fractional), Numerical Analysis, Computational Methods, Structural Dynamics (FGM, Nano), Fluid Dynamics, Mathematical and Uncertainty Modelling, Soft Computing and Machine Intelligence (Artificial Neural Network, Fuzzy, Interval, and Affine Computations)..Snehashish Chakraverty has thirty-one years of experience as a researcher and teacher. Presently, he is working in the Department of Mathematics (Applied Mathematics Group), National Institute of Technology Rourkela, Odisha, as a senior (Higher Administrative Grade) professor. Dr Chakraverty received his PhD in Mathematics from IIT-Roorkee in 1993. Thereafter, he did his post-doctoral research at the Institute of Sound and Vibration Research (ISVR), University of Southampton, UK, and at the Faculty of Engineering and Computer Science, Concordia University, Canada. He was also a visiting professor at Concordia and McGill Universities, Canada, during 1997-1999 and visiting professor at the University of Johannesburg, Johannesburg, South Africa, during 2011-2014. He has authored/co-authored/edited 33 books, published 482 research papers (till date) in journals and conferences. He was the president of the section of mathematical sciences of Indian Science Congress (2015-2016) and was the vice president of Orissa Mathematical Society (2011-2013). Prof. Chakraverty is a recipient of prestigious awards, viz. "Careers360 2nd Faculty Research Award� for the Most Outstanding Researcher in the country in the field of Mathematics, Indian National Science Academy (INSA) nomination under International Collaboration/Bilateral Exchange Program (with the Czech Republic), Platinum Jubilee ISCA Lecture Award (2014), CSIR Young Scientist Award (1997), BOYSCAST Fellow. (DST), UCOST Young Scientist Award (2007, 2008), Golden Jubilee Director's (CBRI) Award (2001), INSA International Bilateral Exchange Award (2015), Roorkee University Gold Medals (1987, 1988) for first positions in MSc and MPhil (Computer Application). He is in the list of 2% world scientists (2020 to 2024) in the Artificial Intelligence and Image Processing category based on an independent study done by Stanford University scientists.
Arup Kumar Sahoo Assistant Professor, Department of Computer Science and Engineering, Siksha "O� Anusandhan (Deemed to be University), Odisha, India. Artificial Intelligence, Scientific Machine Learning, Artificial Neural Networks, Advanced Navigation Algorithm, Autonomous Vehicles and Differential Equations..Arup Kumar Sahoo is currently working as an Assistant Professor in the Department of Computer Science and Engineering at Siksha "O� Anusandhan (Deemed to be University), Odisha, India. He has joined as a postdoctoral research fellow at the Autonomous Navigation and Sensor Fusion Lab (ANSFL), The Hatter Department of Marine Technologies, University of Haifa, Israel. Dr. Sahoo holds a PhD from the Department of Mathematics, National Institute of Technology Rourkela, Odisha, India. He earned his MPhil in Mathematics from Utkal University, Bhubaneswar, Odisha, India, and MSc in Mathematics and Computing from Biju Patnaik University of Technology, Rourkela, Odisha, India. Dr Sahoo has authored and co-authored 13 research papers and book chapters published in journals and conferences. In 2023, he received the Best Paper Presenter Award at an IEEE Conference.
Dhabaleswar Mohapatra Assistant Professor, Department of Mathematics, Siksha "O� Anusandhan (Deemed to be University), Odisha, India. Type-2 Fuzzy Uncertainty, Static and Dynamic Problems with Uncertainty, Numerical and Analytical Methods, and Fuzzy Differential and Fractional Differential Equations..Dhabaleswar Mohapatra is currently working as an Assistant Professor in the Department of Mathematics at the Institute of Technical Education and Research, Siksha 'O' Anusandhan (Deemed to be University), Odisha, India. He received his PhD from the National Institute of Technology, Rourkela, Odisha, India. To date, he has published 12 research articles in journals and book chapters.
