4.5 Applications of Intuitionistic Fuzzy Rough Sets 116
4.5.1 Attribute Reduction 116
4.5.2 Decision Making 118
4.5.3 Other Applications 119
4.6 Work Distribution of IFRS Country-Wise and Year-Wise 123
4.6.1 Country-Wise Work Distribution 123
4.6.2 Year-Wise Work Distribution 124
4.6.3 Limitations of Intuitionistic Fuzzy Rough Set Theory 124
4.7 Conclusion 125
Acknowledgement 125
References 125
5 Satellite-Based Estimation of Ambient Particulate Matters (pm 2.5) Over a Metropolitan City in Eastern India 135 Tamanna Nasrin, Sharadia Dey and Sabyasachi Mondal
5.1 Introduction 136
5.2 Methodology 137
5.3 Result and Discussions 138
5.4 Conclusion 143
References 144
6 Computational Simulation Techniques in Inventory Management 147 Dr. Abhijit Pandit and Dr. Pulak Konar
6.1 Introduction 147
6.1.1 Inventory Management 147
6.1.2 Simulation 148
6.2 Conclusion 164
References 165
7 Workability of Cement Mortar Using Nano Materials and PVA 167 Dr. Mohan Kantharia and Dr. Pankaj Mishra
7.1 Introduction 167
7.2 Literature Survey 168
7.3 Materials and Methods 171
7.4 Results and Discussion 171
7.5 Conclusion 177
References 178
8 Distinctive Features of Semiconducting and Brittle Half-Heusler Alloys; LiXP (X=Zn, Cd) 181 Madhu Sarwan, Abdul Shukoor V. and Sadhna Singh
8.1 Introduction 182
8.2 Computation Method 183
8.3 Result and Discussion 183
8.3.1 Structural Properties 183
8.3.2 Elastic Properties 185
8.3.3 Electronic Properties 187
8.3.4 Thermodynamic Properties 190
8.4 Conclusions 195
Acknowledgement 196
References 196
9 Fixed Point Results with Fuzzy Sets 199 Qazi Aftab Kabir, Sanath Kumar H.G. and Ramakant Bhardwaj
9.1 Introduction 199
9.2 Definitions and Preliminaries 200
9.3 Main Results 201
References 208
10 Role of Mathematics in Novel Artificial Intelligence Realm 211 Kavita Rawat and Manas Kumar Mishra
10.1 Introduction 212
10.2 Mathematical Concepts Applied in Artificial Intelligence 212
10.2.1 Linear Algebra 213
10.2.1.1 Matrix and Vectors 213
10.2.1.2 Eigen Value and Eigen Vector 214
10.2.1.3 Matrix Operations 217
10.2.1.4 Artificial Intelligence Algorithms That Use Linear Algebra 217
10.2.2 Calculus 218
10.2.2.1 Objective Function 219
10.2.2.2 Loss Function & Cost Function 219
10.2.2.3 Artificial Intelligence Algorithms That Use Calculus 222
10.2.3 Probability and Statistics 222
10.2.3.1 Population Versus Sample 224
10.2.3.2 Descriptive Statistics 224
10.2.3.3 Distributions 225
10.2.3.4 Probability 225
10.2.3.5 Correlation 226
10.2.3.6 Data Visualization Using Statistics 226
10.2.3.7 Artificial Intelligence Algorithms That Use Probability and Statistics 227
10.3 Work Flow of Artificial Intelligence & Application Areas 227
10.3.1 Application Areas 229
10.3.2 Trending Areas 229
10.4 Conclusion 230
References 231
11 Study of Corona Epidemic: Predictive Mathematical Model 233 K. Sruthila Gopala Krishnan, Ramakant Bhardwaj, Amit Kumar Mishra and Rakesh Mohan Shrraf
11.1 Mathematical Modelling 234
11.2 Need of Mathematical Modelling 235
11.3 Methods of Construction of Mathematical Models 236
11.3.1 Mathematical Modelling with the Help of Geometry 236
11.3.2 Mathematical Modelling with the Help of Algebra 237
11.3.3 Mathematical Modelling Using Trigonometry 239
11.3.4 Mathematical Modelling with the Help of Ordinary Differential Equation (ODE) 239
11.3.5 Mathematical Modelling Using Partial Differential Equation (PDE) 240
11.3.6 Mathematical Modelling Using Difference Equation 240
11.4 Comparative Study of Mathematical Model in the Time of Covid-19 – A Review 241
11.4.1 Review 241
11.4.2 Case Study 246
11.5 Corona Epidemic in the Context of West Bengal: Predictive Mathematical Model 247
11.5.1 Overview 247
11.5.2 Case Study 248
11.5.3 Methodology 250
11.5.3.1 Exponential Model 250
11.5.3.2 Model Based on Geometric Progression (g.p.) 252
11.5.3.3 Model for Stay At Home 253
11.5.4 Discussion 255
References 255
12 Application of Mathematical Modeling in Various Fields in Light of Fuzzy Logic 257 Dr. Dhirendra Kumar Shukla
12.4.2 Usage of Fuzzy Logic in a Washing Machine 270
12.4.3 Air Conditioner 271
12.4.4 Aeronautics 272
12.4.5 Automotive Field 272
12.4.6 Business 274
12.4.7 Finance 275
12.4.8 Chemical Engineering 276
12.4.9 Defence 278
12.4.10 Electronics 279
12.4.11 Medical Science and Bioinformatics 280
12.4.12 Robotics 282
12.4.13 Signal Processing and Wireless Communication 283
12.4.14 Transportation Problems 283
12.5 Conclusion 285
References 285
13 A Mathematical Approach Using Set & Sequence Similarity Measure for Item Recommendation Using Sequential Web Data 287 Vishal Paranjape, Dr. Neelu Nihalani, Dr. Nishchol Mishra and Dr. Jyoti Mishra
13.1 Introduction 288
13.2 Measures of Assessment for Recommendation Engines 294
13.3 Related Work 295
13.4 Methodology/Research Design 296
13.4.1 Web Data Collection Through Web Logs 296
13.4.2 Web User Sessions Classification 300
13.5 Finding or Result 305
13.6 Conclusion and Future Work 306
References 307
14 Neural Network and Genetic Programming Based Explicit Formulations for Shear Capacity Estimation of Adhesive Anchors 311 Tawfik Kettanah and Satyendra Narayan
14.1 General Introduction 312
14.2 Research Significance 313
14.3 Biological Nervous System 314
14.4 Constructing Artificial Neural Network Model 317
14.5 Genetic Programming (GP) 320
14.6 Administering Genetic Programming Scheme 320
14.7 Genetic Programming In Details 320
14.8 Genetic Expression Programming 322
14.9 Developing Model With Genexpo Software 322
14.10 Comparing NN and GEP Results 325
14.11 Conclusions 326
References 327
15 Adaptive Heuristic - Genetic Algorithms 329 R. Anandan
15.1 Introduction 329
15.2 Genetic Algorithm 330
15.3 The Genetic Algorithm 331
15.4 Evaluation Module 331
15.5 Populace Module 331
15.5.1 Introduction 331
15.5.2 Initialisation Technique 331
15.5.3 Deletion Technique 332
15.5.4 Parent Selection Procedure 332
15.5.5 Fitness Technique 333
15.5.6 Populace Size 333
15.5.7 Elitism 334
15.6 Reproduction Module 334
15.6.1 Introduction 334
15.6.2 Operators 334
15.6.3 Mutation 338
15.6.4 Mutation Rate 338
15.6.5 Crossover Rate 338
15.6.6 Dynamic Mutation and Crossover Rates 338
15.7 Example 339
15.8 Schema Theorem 341
15.8.1 Introduction 341
15.9 Conclusion 342
15.10 Future Scope 342
References 342
16 Mathematically Enhanced Corrosion Detection 343 SeyedBijan Mahbaz, Giovanni Cascante, Satyendra Narayan, Maurice B. Dusseault and Philippe Vanheeghe
16.1 Introduction 344
16.1.1 Mathematics in NDT 346
16.1.2 Principal Component Analysis (PCA) 347
16.2 Case Study: PCA Applied to PMI Data for Defect Detection 347
16.3 PCA Feature Extraction for PMI Method 349
16.4 Experimental Setup and Test 351
16.5 Results 352
16.6 Conclusions 355
References 355
17 Dynamics of Malaria Parasite with Effective Control Analysis 359 Nagadevi Bala Nagaram and Suresh Rasappan
17.1 Introduction 359
17.2 The Mathematical Structure of EGPLC 361
17.3 The Modified EGPLC Model 363
17.4 Equilibria and Local Stability Analysis 364
17.5 Analysis of Global Stability 365
17.6 Global Stability Analysis with Back Propagation 367
17.7 Stability Analysis of Non-Deterministic EGPLC Model 373
17.8 Discussion on Numerical Simulation 378
17.9 Conclusion 381
17.10 Future Scope of the Work 381
References 381
18 Dynamics, Control, Stability, Diffusion and Synchronization of Modified Chaotic Colpitts Oscillator with Triangular Wave Non-Linearity Depending on the States 383 Suresh Rasappan and Niranjan Kumar K.A.
18.1 Introduction 384
18.2 The Mathematical Model of Chaotic Colpitts Oscillator 385
18.3 Adaptive Backstepping Control of the Modified Colpitts Oscillator with Unknown Parameters 395
18.3.1 Proposed System 395
18.3.2 Numerical Simulation 400
18.4 Synchronization of Modified Chaotic Colpitts Oscillator 400
18.4.1 Synchronization of Modified Chaotic Colpitts Oscillator using Non-Linear Feedback Method 402
18.4.2 Numerical Simulation 404
18.5 The Synchronization of Colpitts Oscillator via Backstepping Control 405
18.5.1 Analysis of the Error Dynamics 405
18.5.2 Numerical Simulation 408
18.6 Circuit Implementation 409
18.7 Conclusion 412
References 412
Index 415
About the Authors Ramakant Bhardwaj, PhD, is an associate professor of mathematics in Amity University, Kolkata, India with 15 years of teaching experience. He has published 135 research papers in reputed journals. He is also the co-author of six mathematics books, which are not only for mathematicians but written for practical applications for engineers and scientists.
Satyendra Narayan, PhD, is a professor of applied computing at the Sheridan Institute of Technology and Advanced Learning in Oakville, Ontario, Canada. He has more than 35 years of teaching experience and has published several research papers in the field of computing in reputed journals. He is also the co-author of several books.
Jyoti Mishra, PhD, is an associate professor in the Department of Mathematics, Gyan Ganga Institute of Technology, Jabalpur, India. She has more than ten years of teaching and research experience and has published close to 50 research papers in reputed journals. She is also the co-author of several books.