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).

• Preface xiii1 Fuzzy Fractals in Cervical Cancer 1T. Sudha and G. Jayalalitha1.1 Introduction 21.1.1 Fuzzy Mathematics 21.1.1.1 Fuzzy Set 21.1.1.2 Fuzzy Logic 21.1.1.3 Fuzzy Matrix 31.1.2 Fractals 31.1.2.1 Fractal Geometry 41.1.3 Fuzzy Fractals 41.1.4 Cervical Cancer 51.2 Methods 71.2.1 Fuzzy Method 71.2.2 Sausage Method 111.3 Maximum Modulus Theorem 151.4 Results 181.4.1 Fuzzy Method 191.4.2 Sausage Method 201.5 Conclusion 21References 232 Emotion Detection in IoT-Based E-Learning Using Convolution Neural Network 27Latha Parthiban and S. Selvakumara Samy2.1 Introduction 282.2 Related Works 302.3 Proposed Methodology 312.3.1 Students Emotion Recognition Towards the Class 312.3.2 Eye Gaze-Based Student Engagement Recognition 312.3.3 Facial Head Movement-Based Student Engagement Recognition 342.4 Experimental Results 352.4.1 Convolutional Layer 352.4.2 ReLU Layer 352.4.3 Pooling Layer 362.4.4 Fully Connected Layer 362.5 Conclusions 42References 423 Fuzzy Quotient-3 Cordial Labeling of Some Trees of Diameter 5—Part III 45P. Sumathi and J. Suresh Kumar3.1 Introduction 463.2 Related Work 463.3 Definition 473.4 Notations 473.5 Main Results 483.6 Conclusion 71References 714 Classifying Fuzzy Multi-Criterion Decision Making and Evolutionary Algorithm 73Kirti Seth and Ashish Seth4.1 Introduction 744.1.1 Classical Optimization Techniques 744.1.2 The Bio-Inspired Techniques Centered on Optimization 754.1.2.1 Swarm Intelligence 774.1.2.2 The Optimization on Ant Colony 784.1.2.3 Particle Swarm Optimization (PSO) 824.1.2.4 Summary of PSO 834.2 Multiple Criteria That is Used for Decision Making (MCDM) 834.2.1 WSM Method 864.2.2 WPM Method 864.2.3 Analytic Hierarchy Process (AHP) 874.2.4 TOPSIS 894.2.5 VIKOR 904.3 Conclusion 91References 915 Fuzzy Tri-Magic Labeling of Isomorphic Caterpillar Graph J6 2,3,4 of Diameter 5 93P. Sumathi and C. Monigeetha5.1 Introduction 935.2 Main Result 955.3 Conclusion 154References 1546 Fuzzy Tri-Magic Labeling of Isomorphic Caterpillar Graph J6 2,3,5 of Diameter 5 155P. Sumathi and C. Monigeetha6.1 Introduction 1556.2 Main Result 1576.3 Conclusion 215References 2157 Ceaseless Rule-Based Learning Methodology for Genetic Fuzzy Rule-Based Systems 217B. Siva Kumar Reddy, R. Balakrishna and R. Anandan7.1 Introduction 2187.1.1 Integration of Evolutionary Algorithms and Fuzzy Logic 2197.1.2 Fuzzy Logic-Aided Evolutionary Algorithm 2207.1.3 Adaptive Genetic Algorithm That Adapt Manage Criteria 2207.1.4 Genetic Algorithm With Fuzzified Genetic Operators 2207.1.5 Genetic Fuzzy Systems 2207.1.6 Genetic Learning Process 2237.2 Existing Technology and its Review 2237.2.1 Techniques for Rule-Based Understanding with Genetic Algorithm 2237.2.2 Strategy A: GA Primarily Based Optimization for Computerized Built FLC 2237.2.3 Strategy B: GA-Based Optimization of Manually Created FLC 2247.2.4 Methods of Hybridization for GFS 2257.2.4.1 The Michigan Strategy—Classifier System 2267.2.4.2 The Pittsburgh Method 2297.3 Research Design 2337.3.1 The Ceaseless Rule Learning Approach (CRL) 2337.3.2 Multistage Processes of Ceaseless Rule Learning 2347.3.3 Other Approaches of Genetic Rule Learning 2367.4 Findings or Result Discussion so for in the Area of GFS Hybridization 2377.5 Conclusion 239References 2408 Using Fuzzy Technique Management of Configuration and Status of VM for Task Distribution in Cloud System 243Yogesh Shukla, Pankaj Kumar Mishra and Ramakant Bhardwaj8.1 Introduction 2448.2 Literature Review 2448.3 Logic System for Fuzzy 2468.4 Proposed Algorithm 2488.4.1 Architecture of System 2488.4.2 Terminology of Model 2508.4.3 Algorithm Proposed 2528.4.4 Explanations of Proposed Algorithm 2548.5 Results of Simulation 2578.5.1 Cloud System Numerical Model 2578.5.2 Evaluation Terms Definition 2588.5.3 Environment Configurations Simulation 2598.5.4 Outcomes of Simulation 2598.6 Conclusion 260References 2669 Theorems on Fuzzy Soft Metric Spaces 269Qazi Aftab Kabir, Ramakant Bhardwaj and Ritu Shrivastava9.1 Introduction 2699.2 Preliminaries 2709.3 FSMS 2719.4 Main Results 2739.5 Fuzzy Soft Contractive Type Mappings and Admissible Mappings 278References 28210 Synchronization of Time-Delay Chaotic System with Uncertainties in Terms of Takagi–Sugeno Fuzzy System 285Sathish Kumar Kumaravel, Suresh Rasappan and Kala Raja Mohan10.1 Introduction 28510.2 Statement of the Problem and Notions 28610.3 Main Result 29110.4 Numerical Illustration 30210.5 Conclusion 312References 31211 Trapezoidal Fuzzy Numbers (TrFN) and its Application in Solving Assignment Problem by Hungarian Method: A New Approach 315Rahul Kar, A.K. Shaw and J. Mishra11.1 Introduction 31611.2 Preliminary 31711.2.1 Definition 31711.2.2 Some Arithmetic Operations of Trapezoidal Fuzzy Number 31811.3 Theoretical Part 31911.3.1 Mathematical Formulation of an Assignment Problem 31911.3.2 Method for Solving an Assignment Problem 32011.3.2.1 Enumeration Method 32011.3.2.2 Regular Simplex Method 32111.3.2.3 Transportation Method 32111.3.2.4 Hungarian Method 32111.3.3 Computational Processor of Hungarian Method (For Minimization Problem) 32311.4 Application With Discussion 32511.5 Conclusion and Further Work 331References 33212 The Connectedness of Fuzzy Graph and the Resolving Number of Fuzzy Digraph 335Mary Jiny D. and R. Shanmugapriya12.1 Introduction 33612.2 Definitions 33612.3 An Algorithm to Find the Super Resolving Matrix 34112.3.1 An Application on Resolving Matrix 34412.3.2 An Algorithm to Find the Fuzzy Connectedness Matrix 34712.4 An Application of the Connectedness of the Modified Fuzzy Graph in Rescuing Human Life From Fire Accident 34912.4.1 Algorithm to Find the Safest and Shortest Path Between Two Landmarks 35212.5 Resolving Number Fuzzy Graph and Fuzzy Digraph 35612.5.1 An Algorithm to Find the Resolving Set of a Fuzzy Digraph 36012.6 Conclusion 362References 36213 A Note on Fuzzy Edge Magic Total Labeling Graphs 365R. Shanmugapriya and P.K. Hemalatha13.1 Introduction 36513.2 Preliminaries 36613.3 Theorem 36713.3.1 Example 36813.4 Theorem 37013.4.1 Example 37113.4.1.1 Lemma 37413.4.1.2 Lemma 37413.4.1.3 Lemma 37413.5 Theorem 37413.5.1 Example as Shown in Figure 13.5 Star Graph S(1,9) is FEMT Labeling 37413.6 Theorem 37613.7 Theorem 37713.7.1 Example 37813.8 Theorem 38013.9 Theorem 38113.10 Application of Fuzzy Edge Magic Total Labeling 38313.11 Conclusion 385References 38514 The Synchronization of Impulsive Time-Delay Chaotic Systems with Uncertainties in Terms of Takagi–Sugeno Fuzzy System 387Balaji Dharmalingam, Suresh Rasappan, V. Vijayalakshmi and G. Suseendran14.1 Introduction 38714.2 Problem Description and Preliminaries 38914.2.1 Impulsive Differential Equations 38914.3 The T–S Fuzzy Model 39114.4 Designing of Fuzzy Impulsive Controllers 39314.5 Main Result 39414.6 Numerical Example 40014.7 Conclusion 410References 41015 Theorems on Soft Fuzzy Metric Spaces by Using Control Function 413Sneha A. Khandait, Chitra Singh, Ramakant Bhardwaj and Amit Kumar Mishra15.1 Introduction 41315.2 Preliminaries and Definition 41415.3 Main Results 41515.4 Conclusion 429References 42916 On Soft α( γ,β ) -Continuous Functions in Soft Topological Spaces 431N. Kalaivani, E. Chandrasekaran and K. Fayaz Ur Rahman16.1 Introduction 43216.2 Preliminaries 43216.2.1 Outline 43216.2.2 Soft αγ -Open Set 43216.2.3 Soft αγ Ti Spaces 43416.2.4 Soft (αγ , βs )-Continuous Functions 43616.3 Soft α(γ,β) -Continuous Functions in Soft Topological Spaces 43816.3.1 Outline 43816.3.2 Soft α(γ,β) -Continuous Functions 43816.3.3 Soft α(γ,β) -Open Functions 44416.3.4 Soft α(γ,β) -Closed Functions 44716.3.5 Soft α(γ,β) -Homeomorphism 45016.3.6 Soft (αγ , βs )-Contra Continuous Functions 45016.3.7 Soft α(γ,β) -Contra Continuous Functions 45516.4 Conclusion 459References 459Index 461