Fuzzy Intelligent Systems

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