Fuzzy Intelligent Systems
Methodologies, Techniques, and Applications
Artificial Intelligence and Soft Computing for Industrial Transformation
1. Edition November 2021
480 Pages, Hardcover
Wiley & Sons Ltd
ISBN:
978-1-119-76045-0
John Wiley & Sons
Further versions
FUZZY INTELLIGENT SYSTEMS
A comprehensive guide to Expert Systems and Fuzzy Logic that is the backbone of artificial intelligence.
The objective in writing the book is to foster advancements in the field and help disseminate results concerning recent applications and case studies in the areas of fuzzy logic, intelligent systems, and web-based applications among working professionals and those in education and research covering a broad cross section of technical disciplines.
Fuzzy Intelligent Systems: Methodologies, Techniques, and Applications comprises state-of-the-art chapters detailing how expert systems are built and how the fuzzy logic resembling human reasoning, powers them. Engineers, both current and future, need systematic training in the analytic theory and rigorous design of fuzzy control systems to keep up with and advance the rapidly evolving field of applied control technologies. As a consequence, expert systems with fuzzy logic capabilities make for a more versatile and innovative handling of problems. This book showcases the combination of fuzzy logic and neural networks known as a neuro-fuzzy system, which results in a hybrid intelligent system by combining a human-like reasoning style of neural networks.
Audience
Researchers and students in computer science, Internet of Things, artificial intelligence, machine learning, big data analytics and information and communication technology-related fields. Students will gain a thorough understanding of fuzzy control systems theory by mastering its contents.
Preface xiii
1 Fuzzy Fractals in Cervical Cancer 1
T. Sudha and G. Jayalalitha
1.1 Introduction 2
1.1.1 Fuzzy Mathematics 2
1.1.1.1 Fuzzy Set 2
1.1.1.2 Fuzzy Logic 2
1.1.1.3 Fuzzy Matrix 3
1.1.2 Fractals 3
1.1.2.1 Fractal Geometry 4
1.1.3 Fuzzy Fractals 4
1.1.4 Cervical Cancer 5
1.2 Methods 7
1.2.1 Fuzzy Method 7
1.2.2 Sausage Method 11
1.3 Maximum Modulus Theorem 15
1.4 Results 18
1.4.1 Fuzzy Method 19
1.4.2 Sausage Method 20
1.5 Conclusion 21
References 23
2 Emotion Detection in IoT-Based E-Learning Using Convolution Neural Network 27
Latha Parthiban and S. Selvakumara Samy
2.1 Introduction 28
2.2 Related Works 30
2.3 Proposed Methodology 31
2.3.1 Students Emotion Recognition Towards the Class 31
2.3.2 Eye Gaze-Based Student Engagement Recognition 31
2.3.3 Facial Head Movement-Based Student Engagement Recognition 34
2.4 Experimental Results 35
2.4.1 Convolutional Layer 35
2.4.2 ReLU Layer 35
2.4.3 Pooling Layer 36
2.4.4 Fully Connected Layer 36
2.5 Conclusions 42
References 42
3 Fuzzy Quotient-3 Cordial Labeling of Some Trees of Diameter 5--Part III 45
P. Sumathi and J. Suresh Kumar
3.1 Introduction 46
3.2 Related Work 46
3.3 Definition 47
3.4 Notations 47
3.5 Main Results 48
3.6 Conclusion 71
References 71
4 Classifying Fuzzy Multi-Criterion Decision Making and Evolutionary Algorithm 73
Kirti Seth and Ashish Seth
4.1 Introduction 74
4.1.1 Classical Optimization Techniques 74
4.1.2 The Bio-Inspired Techniques Centered on Optimization 75
4.1.2.1 Swarm Intelligence 77
4.1.2.2 The Optimization on Ant Colony 78
4.1.2.3 Particle Swarm Optimization (PSO) 82
4.1.2.4 Summary of PSO 83
4.2 Multiple Criteria That is Used for Decision Making (MCDM) 83
4.2.1 WSM Method 86
4.2.2 WPM Method 86
4.2.3 Analytic Hierarchy Process (AHP) 87
4.2.4 TOPSIS 89
4.2.5 VIKOR 90
4.3 Conclusion 91
References 91
5 Fuzzy Tri-Magic Labeling of Isomorphic Caterpillar Graph J¯62,3,4 of Diameter 5 93
P. Sumathi and C. Monigeetha
5.1 Introduction 93
5.2 Main Result 95
5.3 Conclusion 154
References 154
6 Fuzzy Tri-Magic Labeling of Isomorphic Caterpillar Graph J¯6 2,3,5 of Diameter 5 155
P. Sumathi and C. Monigeetha
6.1 Introduction 155
6.2 Main Result 157
6.3 Conclusion 215
References 215
7 Ceaseless Rule-Based Learning Methodology for Genetic Fuzzy Rule-Based Systems 217
B. Siva Kumar Reddy, R. Balakrishna and R. Anandan
7.1 Introduction 218
7.1.1 Integration of Evolutionary Algorithms and Fuzzy Logic 219
7.1.2 Fuzzy Logic-Aided Evolutionary Algorithm 220
7.1.3 Adaptive Genetic Algorithm That Adapt Manage Criteria 220
7.1.4 Genetic Algorithm With Fuzzified Genetic Operators 220
7.1.5 Genetic Fuzzy Systems 220
7.1.6 Genetic Learning Process 223
7.2 Existing Technology and its Review 223
7.2.1 Techniques for Rule-Based Understanding with Genetic Algorithm 223
7.2.2 Strategy A: GA Primarily Based Optimization for Computerized Built FLC 223
7.2.3 Strategy B: GA-Based Optimization of Manually Created FLC 224
7.2.4 Methods of Hybridization for GFS 225
7.2.4.1 The Michigan Strategy--Classifier System 226
7.2.4.2 The Pittsburgh Method 229
7.3 Research Design 233
7.3.1 The Ceaseless Rule Learning Approach (CRL) 233
7.3.2 Multistage Processes of Ceaseless Rule Learning 234
7.3.3 Other Approaches of Genetic Rule Learning 236
7.4 Findings or Result Discussion so for in the Area of GFS Hybridization 237
7.5 Conclusion 239
References 240
8 Using Fuzzy Technique Management of Configuration and Status of VM for Task Distribution in Cloud System 243
Yogesh Shukla, Pankaj Kumar Mishra and Ramakant Bhardwaj
8.1 Introduction 244
8.2 Literature Review 244
8.3 Logic System for Fuzzy 246
8.4 Proposed Algorithm 248
8.4.1 Architecture of System 248
8.4.2 Terminology of Model 250
8.4.3 Algorithm Proposed 252
8.4.4 Explanations of Proposed Algorithm 254
8.5 Results of Simulation 257
8.5.1 Cloud System Numerical Model 257
8.5.2 Evaluation Terms Definition 258
8.5.3 Environment Configurations Simulation 259
8.5.4 Outcomes of Simulation 259
8.6 Conclusion 260
References 266
9 Theorems on Fuzzy Soft Metric Spaces 269
Qazi Aftab Kabir, Ramakant Bhardwaj and Ritu Shrivastava
9.1 Introduction 269
9.2 Preliminaries 270
9.3 FSMS 271
9.4 Main Results 273
9.5 Fuzzy Soft Contractive Type Mappings and Admissible Mappings 278
References 282
10 Synchronization of Time-Delay Chaotic System with Uncertainties in Terms of Takagi-Sugeno Fuzzy System 285
Sathish Kumar Kumaravel, Suresh Rasappan and Kala Raja Mohan
10.1 Introduction 285
10.2 Statement of the Problem and Notions 286
10.3 Main Result 291
10.4 Numerical Illustration 302
10.5 Conclusion 312
References 312
11 Trapezoidal Fuzzy Numbers (TrFN) and its Application in Solving Assignment Problem by Hungarian Method: A New Approach 315
Rahul Kar, A.K. Shaw and J. Mishra
11.1 Introduction 316
11.2 Preliminary 317
11.2.1 Definition 317
11.2.2 Some Arithmetic Operations of Trapezoidal Fuzzy Number 318
11.3 Theoretical Part 319
11.3.1 Mathematical Formulation of an Assignment Problem 319
11.3.2 Method for Solving an Assignment Problem 320
11.3.2.1 Enumeration Method 320
11.3.2.2 Regular Simplex Method 321
11.3.2.3 Transportation Method 321
11.3.2.4 Hungarian Method 321
11.3.3 Computational Processor of Hungarian Method (For Minimization Problem) 323
11.4 Application With Discussion 325
11.5 Conclusion and Further Work 331
References 332
12 The Connectedness of Fuzzy Graph and the Resolving Number of Fuzzy Digraph 335
Mary Jiny D. and R. Shanmugapriya
12.1 Introduction 336
12.2 Definitions 336
12.3 An Algorithm to Find the Super Resolving Matrix 341
12.3.1 An Application on Resolving Matrix 344
12.3.2 An Algorithm to Find the Fuzzy Connectedness Matrix 347
12.4 An Application of the Connectedness of the Modified Fuzzy Graph in Rescuing Human Life From Fire Accident 349
12.4.1 Algorithm to Find the Safest and Shortest Path Between Two Landmarks 352
12.5 Resolving Number Fuzzy Graph and Fuzzy Digraph 356
12.5.1 An Algorithm to Find the Resolving Set of a Fuzzy Digraph 360
12.6 Conclusion 362
References 362
13 A Note on Fuzzy Edge Magic Total Labeling Graphs 365
R. Shanmugapriya and P.K. Hemalatha
13.1 Introduction 365
13.2 Preliminaries 366
13.3 Theorem 367
13.3.1 Example 368
13.4 Theorem 370
13.4.1 Example 371
13.4.1.1 Lemma 374
13.4.1.2 Lemma 374
13.4.1.3 Lemma 374
13.5 Theorem 374
13.5.1 Example as Shown in Figure 13.5 Star Graph S(1,9) is FEMT Labeling 374
13.6 Theorem 376
13.7 Theorem 377
13.7.1 Example 378
13.8 Theorem 380
13.9 Theorem 381
13.10 Application of Fuzzy Edge Magic Total Labeling 383
13.11 Conclusion 385
References 385
14 The Synchronization of Impulsive Time-Delay Chaotic Systems with Uncertainties in Terms of Takagi-Sugeno Fuzzy System 387
Balaji Dharmalingam, Suresh Rasappan, V. Vijayalakshmi and G. Suseendran
14.1 Introduction 387
14.2 Problem Description and Preliminaries 389
14.2.1 Impulsive Differential Equations 389
14.3 The T-S Fuzzy Model 391
14.4 Designing of Fuzzy Impulsive Controllers 393
14.5 Main Result 394
14.6 Numerical Example 400
14.7 Conclusion 410
References 410
15 Theorems on Soft Fuzzy Metric Spaces by Using Control Function 413
Sneha A. Khandait, Chitra Singh, Ramakant Bhardwaj and Amit Kumar Mishra
15.1 Introduction 413
15.2 Preliminaries and Definition 414
15.3 Main Results 415
15.4 Conclusion 429
References 429
16 On Soft alpha(gamma,ß)-Continuous Functions in Soft Topological Spaces 431
N. Kalaivani, E. Chandrasekaran and K. Fayaz Ur Rahman
16.1 Introduction 432
16.2 Preliminaries 432
16.2.1 Outline 432
16.2.2 Soft alphagamma-Open Set 432
16.2.3 Soft alphagamma Ti Spaces 434
16.2.4 Soft (alphagamma, ßs)-Continuous Functions 436
16.3 Soft alpha(gamma,ß)-Continuous Functions in Soft Topological Spaces 438
16.3.1 Outline 438
16.3.2 Soft alpha(gamma,ß)-Continuous Functions 438
16.3.3 Soft alpha(gamma,ß)-Open Functions 444
16.3.4 Soft alpha(gamma,ß)-Closed Functions 447
16.3.5 Soft alpha(gamma,ß)-Homeomorphism 450
16.3.6 Soft (alphagamma, ßs)-Contra Continuous Functions 450
16.3.7 Soft alpha(gamma,ß)-Contra Continuous Functions 455
16.4 Conclusion 459
References 459
Index 461
1 Fuzzy Fractals in Cervical Cancer 1
T. Sudha and G. Jayalalitha
1.1 Introduction 2
1.1.1 Fuzzy Mathematics 2
1.1.1.1 Fuzzy Set 2
1.1.1.2 Fuzzy Logic 2
1.1.1.3 Fuzzy Matrix 3
1.1.2 Fractals 3
1.1.2.1 Fractal Geometry 4
1.1.3 Fuzzy Fractals 4
1.1.4 Cervical Cancer 5
1.2 Methods 7
1.2.1 Fuzzy Method 7
1.2.2 Sausage Method 11
1.3 Maximum Modulus Theorem 15
1.4 Results 18
1.4.1 Fuzzy Method 19
1.4.2 Sausage Method 20
1.5 Conclusion 21
References 23
2 Emotion Detection in IoT-Based E-Learning Using Convolution Neural Network 27
Latha Parthiban and S. Selvakumara Samy
2.1 Introduction 28
2.2 Related Works 30
2.3 Proposed Methodology 31
2.3.1 Students Emotion Recognition Towards the Class 31
2.3.2 Eye Gaze-Based Student Engagement Recognition 31
2.3.3 Facial Head Movement-Based Student Engagement Recognition 34
2.4 Experimental Results 35
2.4.1 Convolutional Layer 35
2.4.2 ReLU Layer 35
2.4.3 Pooling Layer 36
2.4.4 Fully Connected Layer 36
2.5 Conclusions 42
References 42
3 Fuzzy Quotient-3 Cordial Labeling of Some Trees of Diameter 5--Part III 45
P. Sumathi and J. Suresh Kumar
3.1 Introduction 46
3.2 Related Work 46
3.3 Definition 47
3.4 Notations 47
3.5 Main Results 48
3.6 Conclusion 71
References 71
4 Classifying Fuzzy Multi-Criterion Decision Making and Evolutionary Algorithm 73
Kirti Seth and Ashish Seth
4.1 Introduction 74
4.1.1 Classical Optimization Techniques 74
4.1.2 The Bio-Inspired Techniques Centered on Optimization 75
4.1.2.1 Swarm Intelligence 77
4.1.2.2 The Optimization on Ant Colony 78
4.1.2.3 Particle Swarm Optimization (PSO) 82
4.1.2.4 Summary of PSO 83
4.2 Multiple Criteria That is Used for Decision Making (MCDM) 83
4.2.1 WSM Method 86
4.2.2 WPM Method 86
4.2.3 Analytic Hierarchy Process (AHP) 87
4.2.4 TOPSIS 89
4.2.5 VIKOR 90
4.3 Conclusion 91
References 91
5 Fuzzy Tri-Magic Labeling of Isomorphic Caterpillar Graph J¯62,3,4 of Diameter 5 93
P. Sumathi and C. Monigeetha
5.1 Introduction 93
5.2 Main Result 95
5.3 Conclusion 154
References 154
6 Fuzzy Tri-Magic Labeling of Isomorphic Caterpillar Graph J¯6 2,3,5 of Diameter 5 155
P. Sumathi and C. Monigeetha
6.1 Introduction 155
6.2 Main Result 157
6.3 Conclusion 215
References 215
7 Ceaseless Rule-Based Learning Methodology for Genetic Fuzzy Rule-Based Systems 217
B. Siva Kumar Reddy, R. Balakrishna and R. Anandan
7.1 Introduction 218
7.1.1 Integration of Evolutionary Algorithms and Fuzzy Logic 219
7.1.2 Fuzzy Logic-Aided Evolutionary Algorithm 220
7.1.3 Adaptive Genetic Algorithm That Adapt Manage Criteria 220
7.1.4 Genetic Algorithm With Fuzzified Genetic Operators 220
7.1.5 Genetic Fuzzy Systems 220
7.1.6 Genetic Learning Process 223
7.2 Existing Technology and its Review 223
7.2.1 Techniques for Rule-Based Understanding with Genetic Algorithm 223
7.2.2 Strategy A: GA Primarily Based Optimization for Computerized Built FLC 223
7.2.3 Strategy B: GA-Based Optimization of Manually Created FLC 224
7.2.4 Methods of Hybridization for GFS 225
7.2.4.1 The Michigan Strategy--Classifier System 226
7.2.4.2 The Pittsburgh Method 229
7.3 Research Design 233
7.3.1 The Ceaseless Rule Learning Approach (CRL) 233
7.3.2 Multistage Processes of Ceaseless Rule Learning 234
7.3.3 Other Approaches of Genetic Rule Learning 236
7.4 Findings or Result Discussion so for in the Area of GFS Hybridization 237
7.5 Conclusion 239
References 240
8 Using Fuzzy Technique Management of Configuration and Status of VM for Task Distribution in Cloud System 243
Yogesh Shukla, Pankaj Kumar Mishra and Ramakant Bhardwaj
8.1 Introduction 244
8.2 Literature Review 244
8.3 Logic System for Fuzzy 246
8.4 Proposed Algorithm 248
8.4.1 Architecture of System 248
8.4.2 Terminology of Model 250
8.4.3 Algorithm Proposed 252
8.4.4 Explanations of Proposed Algorithm 254
8.5 Results of Simulation 257
8.5.1 Cloud System Numerical Model 257
8.5.2 Evaluation Terms Definition 258
8.5.3 Environment Configurations Simulation 259
8.5.4 Outcomes of Simulation 259
8.6 Conclusion 260
References 266
9 Theorems on Fuzzy Soft Metric Spaces 269
Qazi Aftab Kabir, Ramakant Bhardwaj and Ritu Shrivastava
9.1 Introduction 269
9.2 Preliminaries 270
9.3 FSMS 271
9.4 Main Results 273
9.5 Fuzzy Soft Contractive Type Mappings and Admissible Mappings 278
References 282
10 Synchronization of Time-Delay Chaotic System with Uncertainties in Terms of Takagi-Sugeno Fuzzy System 285
Sathish Kumar Kumaravel, Suresh Rasappan and Kala Raja Mohan
10.1 Introduction 285
10.2 Statement of the Problem and Notions 286
10.3 Main Result 291
10.4 Numerical Illustration 302
10.5 Conclusion 312
References 312
11 Trapezoidal Fuzzy Numbers (TrFN) and its Application in Solving Assignment Problem by Hungarian Method: A New Approach 315
Rahul Kar, A.K. Shaw and J. Mishra
11.1 Introduction 316
11.2 Preliminary 317
11.2.1 Definition 317
11.2.2 Some Arithmetic Operations of Trapezoidal Fuzzy Number 318
11.3 Theoretical Part 319
11.3.1 Mathematical Formulation of an Assignment Problem 319
11.3.2 Method for Solving an Assignment Problem 320
11.3.2.1 Enumeration Method 320
11.3.2.2 Regular Simplex Method 321
11.3.2.3 Transportation Method 321
11.3.2.4 Hungarian Method 321
11.3.3 Computational Processor of Hungarian Method (For Minimization Problem) 323
11.4 Application With Discussion 325
11.5 Conclusion and Further Work 331
References 332
12 The Connectedness of Fuzzy Graph and the Resolving Number of Fuzzy Digraph 335
Mary Jiny D. and R. Shanmugapriya
12.1 Introduction 336
12.2 Definitions 336
12.3 An Algorithm to Find the Super Resolving Matrix 341
12.3.1 An Application on Resolving Matrix 344
12.3.2 An Algorithm to Find the Fuzzy Connectedness Matrix 347
12.4 An Application of the Connectedness of the Modified Fuzzy Graph in Rescuing Human Life From Fire Accident 349
12.4.1 Algorithm to Find the Safest and Shortest Path Between Two Landmarks 352
12.5 Resolving Number Fuzzy Graph and Fuzzy Digraph 356
12.5.1 An Algorithm to Find the Resolving Set of a Fuzzy Digraph 360
12.6 Conclusion 362
References 362
13 A Note on Fuzzy Edge Magic Total Labeling Graphs 365
R. Shanmugapriya and P.K. Hemalatha
13.1 Introduction 365
13.2 Preliminaries 366
13.3 Theorem 367
13.3.1 Example 368
13.4 Theorem 370
13.4.1 Example 371
13.4.1.1 Lemma 374
13.4.1.2 Lemma 374
13.4.1.3 Lemma 374
13.5 Theorem 374
13.5.1 Example as Shown in Figure 13.5 Star Graph S(1,9) is FEMT Labeling 374
13.6 Theorem 376
13.7 Theorem 377
13.7.1 Example 378
13.8 Theorem 380
13.9 Theorem 381
13.10 Application of Fuzzy Edge Magic Total Labeling 383
13.11 Conclusion 385
References 385
14 The Synchronization of Impulsive Time-Delay Chaotic Systems with Uncertainties in Terms of Takagi-Sugeno Fuzzy System 387
Balaji Dharmalingam, Suresh Rasappan, V. Vijayalakshmi and G. Suseendran
14.1 Introduction 387
14.2 Problem Description and Preliminaries 389
14.2.1 Impulsive Differential Equations 389
14.3 The T-S Fuzzy Model 391
14.4 Designing of Fuzzy Impulsive Controllers 393
14.5 Main Result 394
14.6 Numerical Example 400
14.7 Conclusion 410
References 410
15 Theorems on Soft Fuzzy Metric Spaces by Using Control Function 413
Sneha A. Khandait, Chitra Singh, Ramakant Bhardwaj and Amit Kumar Mishra
15.1 Introduction 413
15.2 Preliminaries and Definition 414
15.3 Main Results 415
15.4 Conclusion 429
References 429
16 On Soft alpha(gamma,ß)-Continuous Functions in Soft Topological Spaces 431
N. Kalaivani, E. Chandrasekaran and K. Fayaz Ur Rahman
16.1 Introduction 432
16.2 Preliminaries 432
16.2.1 Outline 432
16.2.2 Soft alphagamma-Open Set 432
16.2.3 Soft alphagamma Ti Spaces 434
16.2.4 Soft (alphagamma, ßs)-Continuous Functions 436
16.3 Soft alpha(gamma,ß)-Continuous Functions in Soft Topological Spaces 438
16.3.1 Outline 438
16.3.2 Soft alpha(gamma,ß)-Continuous Functions 438
16.3.3 Soft alpha(gamma,ß)-Open Functions 444
16.3.4 Soft alpha(gamma,ß)-Closed Functions 447
16.3.5 Soft alpha(gamma,ß)-Homeomorphism 450
16.3.6 Soft (alphagamma, ßs)-Contra Continuous Functions 450
16.3.7 Soft alpha(gamma,ß)-Contra Continuous Functions 455
16.4 Conclusion 459
References 459
Index 461
E. Chandresekaran, PhD is a Professor of Mathematics at Veltech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai India.
R. Anandan, PhD is a IBMS/390 Mainframe professional, a Chartered Engineer from the Institution of Engineers in India and received a fellowship from Bose Science Society, India. He is currently a Professor in the Department of Computer Science and Engineering, School of Engineering, Vels Institute of Science, Technology & Advanced Studies (VISTAS), Chennai.
G. Suseendran, PhD was an assistant professor in the Department of Information Technology, School of Computing Sciences, Vels Institute of Science, Technology & Advanced Studies (VISTAS), Chennai and passed away as this book was being prepared.
S. Balamurugan, PhD is the Director of Research and Development, Intelligent Research Consultancy Services(iRCS), Coimbatore, Tamilnadu, India. He is also Director of the Albert Einstein Engineering and Research Labs (AEER Labs), as well as Vice-Chairman, Renewable Energy Society of India(RESI), India.
Hanaa Hachimi, PhD is an associate professor at the Ibn Tofail University, in the National School of Applied Sciences ENSA in Kenitra, Morocco. She is President of the Moroccan Society of Engineering Sciences and Technology (MSEST).
R. Anandan, PhD is a IBMS/390 Mainframe professional, a Chartered Engineer from the Institution of Engineers in India and received a fellowship from Bose Science Society, India. He is currently a Professor in the Department of Computer Science and Engineering, School of Engineering, Vels Institute of Science, Technology & Advanced Studies (VISTAS), Chennai.
G. Suseendran, PhD was an assistant professor in the Department of Information Technology, School of Computing Sciences, Vels Institute of Science, Technology & Advanced Studies (VISTAS), Chennai and passed away as this book was being prepared.
S. Balamurugan, PhD is the Director of Research and Development, Intelligent Research Consultancy Services(iRCS), Coimbatore, Tamilnadu, India. He is also Director of the Albert Einstein Engineering and Research Labs (AEER Labs), as well as Vice-Chairman, Renewable Energy Society of India(RESI), India.
Hanaa Hachimi, PhD is an associate professor at the Ibn Tofail University, in the National School of Applied Sciences ENSA in Kenitra, Morocco. She is President of the Moroccan Society of Engineering Sciences and Technology (MSEST).
