Details

<p>Preface xiii</p> <p><b>1 Fuzzy Fractals in Cervical Cancer 1<br /></b><i>T. Sudha and G. Jayalalitha</i></p> <p>1.1 Introduction 2</p> <p>1.1.1 Fuzzy Mathematics 2</p> <p>1.1.1.1 Fuzzy Set 2</p> <p>1.1.1.2 Fuzzy Logic 2</p> <p>1.1.1.3 Fuzzy Matrix 3</p> <p>1.1.2 Fractals 3</p> <p>1.1.2.1 Fractal Geometry 4</p> <p>1.1.3 Fuzzy Fractals 4</p> <p>1.1.4 Cervical Cancer 5</p> <p>1.2 Methods 7</p> <p>1.2.1 Fuzzy Method 7</p> <p>1.2.2 Sausage Method 11</p> <p>1.3 Maximum Modulus Theorem 15</p> <p>1.4 Results 18</p> <p>1.4.1 Fuzzy Method 19</p> <p>1.4.2 Sausage Method 20</p> <p>1.5 Conclusion 21</p> <p>References 23</p> <p><b>2 Emotion Detection in IoT-Based E-Learning Using Convolution Neural Network 27<br /></b><i>Latha Parthiban and S. Selvakumara Samy</i></p> <p>2.1 Introduction 28</p> <p>2.2 Related Works 30</p> <p>2.3 Proposed Methodology 31</p> <p>2.3.1 Students Emotion Recognition Towards the Class 31</p> <p>2.3.2 Eye Gaze-Based Student Engagement Recognition 31</p> <p>2.3.3 Facial Head Movement-Based Student Engagement Recognition 34</p> <p>2.4 Experimental Results 35</p> <p>2.4.1 Convolutional Layer 35</p> <p>2.4.2 ReLU Layer 35</p> <p>2.4.3 Pooling Layer 36</p> <p>2.4.4 Fully Connected Layer 36</p> <p>2.5 Conclusions 42</p> <p>References 42</p> <p><b>3 Fuzzy Quotient-3 Cordial Labeling of Some Trees of Diameter 5—Part III 45<br /></b><i>P. Sumathi and J. Suresh Kumar</i></p> <p>3.1 Introduction 46</p> <p>3.2 Related Work 46</p> <p>3.3 Definition 47</p> <p>3.4 Notations 47</p> <p>3.5 Main Results 48</p> <p>3.6 Conclusion 71</p> <p>References 71</p> <p><b>4 Classifying Fuzzy Multi-Criterion Decision Making and Evolutionary Algorithm</b> <b>73</b><br /><i>Kirti Seth and Ashish Seth</i></p> <p>4.1 Introduction 74</p> <p>4.1.1 Classical Optimization Techniques 74</p> <p>4.1.2 The Bio-Inspired Techniques Centered on Optimization 75</p> <p>4.1.2.1 Swarm Intelligence 77</p> <p>4.1.2.2 The Optimization on Ant Colony 78</p> <p>4.1.2.3 Particle Swarm Optimization (PSO) 82</p> <p>4.1.2.4 Summary of PSO 83</p> <p>4.2 Multiple Criteria That is Used for Decision Making (MCDM) 83</p> <p>4.2.1 WSM Method 86</p> <p>4.2.2 WPM Method 86</p> <p>4.2.3 Analytic Hierarchy Process (AHP) 87</p> <p>4.2.4 TOPSIS 89</p> <p>4.2.5 VIKOR 90</p> <p>4.3 Conclusion 91</p> <p>References 91</p> <p><b>5 Fuzzy Tri-Magic Labeling of Isomorphic Caterpillar Graph J⁶_2,3,4 of Diameter 5 93<br /></b><i>P. Sumathi and C. Monigeetha</i></p> <p>5.1 Introduction 93</p> <p>5.2 Main Result 95</p> <p>5.3 Conclusion 154</p> <p>References 154</p> <p><b>6 Fuzzy Tri-Magic Labeling of Isomorphic Caterpillar Graph J⁶_2,3,5 of Diameter 5 155<br /></b><i>P. Sumathi and C. Monigeetha</i></p> <p>6.1 Introduction 155</p> <p>6.2 Main Result 157</p> <p>6.3 Conclusion 215</p> <p>References 215</p> <p><b>7 Ceaseless Rule-Based Learning Methodology for Genetic Fuzzy Rule-Based Systems 217<br /></b><i>B. Siva Kumar Reddy, R. Balakrishna and R. Anandan</i></p> <p>7.1 Introduction 218</p> <p>7.1.1 Integration of Evolutionary Algorithms and Fuzzy Logic 219</p> <p>7.1.2 Fuzzy Logic-Aided Evolutionary Algorithm 220</p> <p>7.1.3 Adaptive Genetic Algorithm That Adapt Manage Criteria 220</p> <p>7.1.4 Genetic Algorithm With Fuzzified Genetic Operators 220</p> <p>7.1.5 Genetic Fuzzy Systems 220</p> <p>7.1.6 Genetic Learning Process 223</p> <p>7.2 Existing Technology and its Review 223</p> <p>7.2.1 Techniques for Rule-Based Understanding with Genetic Algorithm 223</p> <p>7.2.2 Strategy A: GA Primarily Based Optimization for Computerized Built FLC 223</p> <p>7.2.3 Strategy B: GA-Based Optimization of Manually Created FLC 224</p> <p>7.2.4 Methods of Hybridization for GFS 225</p> <p>7.2.4.1 The Michigan Strategy—Classifier System 226</p> <p>7.2.4.2 The Pittsburgh Method 229</p> <p>7.3 Research Design 233</p> <p>7.3.1 The Ceaseless Rule Learning Approach (CRL) 233</p> <p>7.3.2 Multistage Processes of Ceaseless Rule Learning 234</p> <p>7.3.3 Other Approaches of Genetic Rule Learning 236</p> <p>7.4 Findings or Result Discussion so for in the Area of GFS Hybridization 237</p> <p>7.5 Conclusion 239</p> <p>References 240</p> <p><b>8 Using Fuzzy Technique Management of Configuration and Status of VM for Task Distribution in Cloud System 243<br /></b><i>Yogesh Shukla, Pankaj Kumar Mishra and Ramakant Bhardwaj</i></p> <p>8.1 Introduction 244</p> <p>8.2 Literature Review 244</p> <p>8.3 Logic System for Fuzzy 246</p> <p>8.4 Proposed Algorithm 248</p> <p>8.4.1 Architecture of System 248</p> <p>8.4.2 Terminology of Model 250</p> <p>8.4.3 Algorithm Proposed 252</p> <p>8.4.4 Explanations of Proposed Algorithm 254</p> <p>8.5 Results of Simulation 257</p> <p>8.5.1 Cloud System Numerical Model 257</p> <p>8.5.2 Evaluation Terms Definition 258</p> <p>8.5.3 Environment Configurations Simulation 259</p> <p>8.5.4 Outcomes of Simulation 259</p> <p>8.6 Conclusion 260</p> <p>References 266</p> <p><b>9 Theorems on Fuzzy Soft Metric Spaces 269<br /></b><i>Qazi Aftab Kabir, Ramakant Bhardwaj and Ritu Shrivastava</i></p> <p>9.1 Introduction 269</p> <p>9.2 Preliminaries 270</p> <p>9.3 FSMS 271</p> <p>9.4 Main Results 273</p> <p>9.5 Fuzzy Soft Contractive Type Mappings and Admissible Mappings 278</p> <p>References 282</p> <p><b>10 Synchronization of Time-Delay Chaotic System with Uncertainties in Terms of Takagi–Sugeno Fuzzy System 285<br /></b><i>Sathish Kumar Kumaravel, Suresh Rasappan and Kala Raja Mohan</i></p> <p>10.1 Introduction 285</p> <p>10.2 Statement of the Problem and Notions 286</p> <p>10.3 Main Result 291</p> <p>10.4 Numerical Illustration 302</p> <p>10.5 Conclusion 312</p> <p>References 312</p> <p><b>11 Trapezoidal Fuzzy Numbers (TrFN) and its Application in Solving Assignment Problem by Hungarian Method: A New Approach 315<br /></b><i>Rahul Kar, A.K. Shaw and J. Mishra</i></p> <p>11.1 Introduction 316</p> <p>11.2 Preliminary 317</p> <p>11.2.1 Definition 317</p> <p>11.2.2 Some Arithmetic Operations of Trapezoidal Fuzzy Number 318</p> <p>11.3 Theoretical Part 319</p> <p>11.3.1 Mathematical Formulation of an Assignment Problem 319</p> <p>11.3.2 Method for Solving an Assignment Problem 320</p> <p>11.3.2.1 Enumeration Method 320</p> <p>11.3.2.2 Regular Simplex Method 321</p> <p>11.3.2.3 Transportation Method 321</p> <p>11.3.2.4 Hungarian Method 321</p> <p>11.3.3 Computational Processor of Hungarian Method (For Minimization Problem) 323</p> <p>11.4 Application With Discussion 325</p> <p>11.5 Conclusion and Further Work 331</p> <p>References 332</p> <p><b>12 The Connectedness of Fuzzy Graph and the Resolving Number of Fuzzy Digraph 335<br /></b><i>Mary Jiny D. and R. Shanmugapriya</i></p> <p>12.1 Introduction 336</p> <p>12.2 Definitions 336</p> <p>12.3 An Algorithm to Find the Super Resolving Matrix 341</p> <p>12.3.1 An Application on Resolving Matrix 344</p> <p>12.3.2 An Algorithm to Find the Fuzzy Connectedness Matrix 347</p> <p>12.4 An Application of the Connectedness of the Modified Fuzzy Graph in Rescuing Human Life From Fire Accident 349</p> <p>12.4.1 Algorithm to Find the Safest and Shortest Path Between Two Landmarks 352</p> <p>12.5 Resolving Number Fuzzy Graph and Fuzzy Digraph 356</p> <p>12.5.1 An Algorithm to Find the Resolving Set of a Fuzzy Digraph 360</p> <p>12.6 Conclusion 362</p> <p>References 362</p> <p><b>13 A Note on Fuzzy Edge Magic Total Labeling Graphs 365<br /></b><i>R. Shanmugapriya and P.K. Hemalatha</i></p> <p>13.1 Introduction 365</p> <p>13.2 Preliminaries 366</p> <p>13.3 Theorem 367</p> <p>13.3.1 Example 368</p> <p>13.4 Theorem 370</p> <p>13.4.1 Example 371</p> <p>13.4.1.1 Lemma 374</p> <p>13.4.1.2 Lemma 374</p> <p>13.4.1.3 Lemma 374</p> <p>13.5 Theorem 374</p> <p>13.5.1 Example as Shown in Figure 13.5 Star Graph S(1,9) is FEMT Labeling 374</p> <p>13.6 Theorem 376</p> <p>13.7 Theorem 377</p> <p>13.7.1 Example 378</p> <p>13.8 Theorem 380</p> <p>13.9 Theorem 381</p> <p>13.10 Application of Fuzzy Edge Magic Total Labeling 383</p> <p>13.11 Conclusion 385</p> <p>References 385</p> <p><b>14 The Synchronization of Impulsive Time-Delay Chaotic Systems with Uncertainties in Terms of Takagi–Sugeno Fuzzy System 387<br /></b><i>Balaji Dharmalingam, Suresh Rasappan, V. Vijayalakshmi and G. Suseendran</i></p> <p>14.1 Introduction 387</p> <p>14.2 Problem Description and Preliminaries 389</p> <p>14.2.1 Impulsive Differential Equations 389</p> <p>14.3 The T–S Fuzzy Model 391</p> <p>14.4 Designing of Fuzzy Impulsive Controllers 393</p> <p>14.5 Main Result 394</p> <p>14.6 Numerical Example 400</p> <p>14.7 Conclusion 410</p> <p>References 410</p> <p><b>15 Theorems on Soft Fuzzy Metric Spaces by Using Control Function 413<br /></b><i>Sneha A. Khandait, Chitra Singh, Ramakant Bhardwaj and Amit Kumar Mishra</i></p> <p>15.1 Introduction 413</p> <p>15.2 Preliminaries and Definition 414</p> <p>15.3 Main Results 415</p> <p>15.4 Conclusion 429</p> <p>References 429</p> <p><b>16 On Soft <i>α</i>₍</b><i>_γ,β</i><b>₎-Continuous Functions in Soft Topological Spaces 431<br /></b><i>N. Kalaivani, E. Chandrasekaran and K. Fayaz Ur Rahman</i></p> <p>16.1 Introduction 432</p> <p>16.2 Preliminaries 432</p> <p>16.2.1 Outline 432</p> <p>16.2.2 Soft <i>α_γ</i>-Open Set 432</p> <p>16.2.3 Soft <i>α_γ </i>T_i Spaces 434</p> <p>16.2.4 Soft (<i>α_γ</i>, <i>β_s</i>)-Continuous Functions 436</p> <p>16.3 Soft <i>α</i>_{(<i>γ,β</i>)}-Continuous Functions in Soft Topological Spaces 438</p> <p>16.3.1 Outline 438</p> <p>16.3.2 Soft <i>α</i>_{(<i>γ,β</i>)}-Continuous Functions 438</p> <p>16.3.3 Soft <i>α</i>_{(<i>γ,β</i>)}-Open Functions 444</p> <p>16.3.4 Soft α_(γ,β)-Closed Functions 447</p> <p>16.3.5 Soft <i>α</i>_{(<i>γ,β</i>)}-Homeomorphism 450</p> <p>16.3.6 Soft (<i>α_γ</i>, <i>β_s</i>)-Contra Continuous Functions 450</p> <p>16.3.7 Soft <i>α</i>_{(<i>γ,β</i>)}-Contra Continuous Functions 455</p> <p>16.4 Conclusion 459</p> <p>References 459</p> <p>Index 461</p>

<p><b>E. Chandresekaran, PhD</b> is a Professor of Mathematics at Veltech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai India. </p> <p><b>R. Anandan, PhD</b> 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. <p><b>G. Suseendran, PhD</b> 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. <p><b>S. Balamurugan, PhD</b> 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. <p><b>Hanaa Hachimi, PhD</b> 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).

<p><b>A comprehensive guide to Expert Systems and Fuzzy Logic that is the backbone of artificial intelligence.</b></p> <p>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. <p><i>Fuzzy Intelligent Systems: Methodologies, Techniques, and Applications</i> 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. <p><b>Audience</b> <p>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.

US