Fuzzy Intelligent Systems E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Artificial Intelligence and Soft Computing for Industrial Transformation
• Sprache: Englisch

Seitenzahl: 508

Veröffentlichungsjahr: 2021

Beschreibung

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.

Leseprobe

Table of Contents

Cover

Title Page

Copyright

Preface

1 Fuzzy Fractals in Cervical Cancer

1.1 Introduction

1.2 Methods

1.3 Maximum Modulus Theorem

1.4 Results

1.5 Conclusion

References

2 Emotion Detection in IoT-Based E-Learning Using Convolution Neural Network

2.1 Introduction

2.2 Related Works

2.3 Proposed Methodology

2.4 Experimental Results

2.5 Conclusions

References

3 Fuzzy Quotient-3 Cordial Labeling of Some Trees of Diameter 5—Part III

3.1 Introduction

3.2 Related Work

3.3 Definition

3.4 Notations

3.5 Main Results

3.6 Conclusion

References

4 Classifying Fuzzy Multi-Criterion Decision Making and Evolutionary Algorithm

4.1 Introduction

4.2 Multiple Criteria That is Used for Decision Making (MCDM)

4.3 Conclusion

References

5 Fuzzy Tri-Magic Labeling of Isomorphic Caterpillar Graph of Diameter 5

5.1 Introduction

5.2 Main Result

5.3 Conclusion

References

6 Fuzzy Tri-Magic Labeling of Isomorphic Caterpillar Graph of Diameter 5

6.1 Introduction

6.2 Main Result

6.3 Conclusion

References

7 Ceaseless Rule-Based Learning Methodology for Genetic Fuzzy Rule-Based Systems

7.1 Introduction

7.2 Existing Technology and its Review

7.3 Research Design

7.4 Findings or Result Discussion so for in the Area of GFS Hybridization

7.5 Conclusion

References

8 Using Fuzzy Technique Management of Configuration and Status of VM for Task Distribution in Cloud System

8.1 Introduction

8.2 Literature Review

8.3 Logic System for Fuzzy

8.4 Proposed Algorithm

8.5 Results of Simulation

8.6 Conclusion

References

9 Theorems on Fuzzy Soft Metric Spaces

9.1 Introduction

9.2 Preliminaries

9.3 FSMS

9.4 Main Results

9.5 Fuzzy Soft –Contractive Type Mappings and – Admissible Mappings

References

10 Synchronization of Time-Delay Chaotic System with Uncertainties in Terms of Takagi–Sugeno Fuzzy System

10.1 Introduction

10.2 Statement of the Problem and Notions

10.3 Main Result

10.4 Numerical Illustration

10.5 Conclusion

References

11 Trapezoidal Fuzzy Numbers (TrFN) and its Application in Solving Assignment Problem by Hungarian Method: A New Approach

11.1 Introduction

11.2 Preliminary

11.3 Theoretical Part

11.4 Application With Discussion

11.5 Conclusion and Further Work

References

12 The Connectedness of Fuzzy Graph and the Resolving Number of Fuzzy Digraph

12.1 Introduction

12.2 Definitions

12.3 An Algorithm to Find the Super Resolving Matrix

12.4 An Application of the Connectedness of the Modified Fuzzy Graph in Rescuing Human Life From Fire Accident

12.5 Resolving Number Fuzzy Graph and Fuzzy Digraph

12.6 Conclusion

References

13 A Note on Fuzzy Edge Magic Total Labeling Graphs

13.1 Introduction

13.2 Preliminaries

13.3 Theorem

13.4 Theorem

13.5 Theorem

13.6 Theorem

13.7 Theorem

13.8 Theorem

13.9 Theorem

13.10 Application of Fuzzy Edge Magic Total Labeling

13.11 Conclusion

References

14 The Synchronization of Impulsive Time-Delay Chaotic Systems with Uncertainties in Terms of Takagi–Sugeno Fuzzy System

14.1 Introduction

14.2 Problem Description and Preliminaries

14.3 The T–S Fuzzy Model

14.4 Designing of Fuzzy Impulsive Controllers

14.5 Main Result

14.6 Numerical Example

14.7 Conclusion

References

15 Theorems on Soft Fuzzy Metric Spaces by Using Control Function

15.1 Introduction

15.2 Preliminaries and Definition

15.3 Main Results

15.4 Conclusion

References

16 On Soft

α

(

γ,β

)

-Continuous Functions in Soft Topological Spaces

16.1 Introduction

16.2 Preliminaries

16.3 Soft

α

(

γ,β

)

-Continuous Functions in Soft Topological Spaces

16.4 Conclusion

References

Index

End User License Agreement

List of Tables

Chapter 1

Table 1.1 Analysis of normal cervical cancer.

Table 1.2 Analysis of abnormal cervical cancer.

Table 1.3 Matrix of normal cervix cell and abnormal cervix cell.

Table 1.4 Eigen values, Eigen vectors of normal cells of cervix.

Table 1.5 Eigen values and Eigen vector of abnormal cell of cervix.

Table 1.6 Eigen values and Eigen vector of fuzzy matrix.

Table 1.7 Normal cervix cell.

Table 1.8 Abnormal cervix cell.

Table 1.9 Regression line for cancer cell image.

Table 1.10 Regression lines for normal, abnormal cervical cells.

Table 1.11a Maximum modulus theorem of normal cancer cells.

Table 1.11b Maximum modulus theorem of abnormal cancer cells.

Chapter 2

Table 2.1 Accuracy of algorithms for face recognition.

Table 2.2 Eye gaze detection algorithm accuracy.

Table 2.3 Processing time of eye gaze algorithm.

Table 2.4 Face recognition accuracy across feature descriptors.

Table 2.5 Iris recognition accuracy across feature descriptors.

Table 2.6 Comparison of head movement accuracy across feature descriptors.

Table 2.7 Comparison of FBET with SVM.

Table 2.8 Comparison of FBET model with CNN.

Chapter 3

Table 3.1

v

σ

(

i

) and

e

μ

(

i

) for the tree .

Table 3.2

v

σ

(

i

) and

e

μ

(

i

) for the tree 𝒯

32

5

Table 3.3

v

σ

(

i

) and

e

μ

(

i

) for the tree 𝒯

33

5

.

Table 3.4

v

σ

(

i

) and

e

μ

(

i

) for the tree 𝒯

34

5

.

Table 3.5

v

σ

(

i

) and

e

μ

(

i

) for the tree

𝒯

35

5

.

Table 3.6

v

σ

(

i

) and

e

μ

(

i

) for the tree

𝒯

36

5

.

Table 3.7

v

σ

(

i

) and

e

μ

(

i

) for the tree

𝒯

37

5

.

Table 3.8

v

σ

(

i

) and

e

μ

(

i

) for the tree .

Table 3.9

v

σ

(

i

) and

e

μ

(

i

) for the tree .

Chapter 4

Table 4.1 Comparison between classical constructive and generative techniques.

Table 4.2 Pairwise Comparison Scales (presented by Saaty, 1980 [19]).

Chapter 5

Table 5.1 MMVs K

i

’s, their corresponding edges and the number of K

i

’s (1 ≤

i

≤ 3).

Table 5.2 MMVs K

i

’s, their corresponding edges and the number of K

i

’s (1 ≤

i

≤ 3).

Table 5.3 MMVs K

i

’s, their corresponding edges and the number of K

i

’s (1 ≤

i

≤ 3).

Table 5.4 MMVs K

i

’s, their corresponding edges and the number of K

i

’s (1 ≤

i

≤ 3).

Table 5.5 MMVs K

i

’s, their corresponding edges and the number of K

i

’s (1 ≤

i

≤ 3).

Table 5.6 MMVs K

i

’s, their corresponding edges and the number of K

i

’s (1 ≤

i

≤ 3).

Table 5.7 MMVs K

i

’s, their corresponding edges and the number of K

i

’s (1 ≤

i

≤ 3).

Table 5.8 MMVs K

i

’s, their corresponding edges and the number of K

i

’s (1 ≤

i

≤ 3).

Table 5.9 MMVs K

i

’s, their corresponding edges and the number of K

i

’s (1 ≤

i

≤ 3).

Chapter 6

Table 6.1 MMVs K

i

’s, their corresponding edges and the number of K

i

’s (1 ≤

i

≤ 3).

Table 6.2 MMVs K

i

’s, their corresponding edges and the number of K

i

’s (1 ≤

i

≤ 3).

Table 6.3 MMVs K

i

’s, their corresponding edges and the number of K

i

’s (1 ≤

i

≤ 3).

Table 6.4 MMVs K

i

’s, their corresponding edges and the number of K

i

’s (1 ≤

i

≤ 3).

Table 6.5 MMVs K

i

’s, their corresponding edges and the number of K

i

’s (1 ≤

i

≤ 3).

Table 6.6 MMVs K

i

’s, their corresponding edges and the number of K

i

’s (1 ≤

i

≤ 3).

Table 6.7 MMVs K

i

’s, their corresponding edges and the number of K

i

’s (1 ≤

i

≤ 3).

Table 6.8 MMVs K

i

’s, their corresponding edges and the number of K

i

’s (1 ≤

i

≤ 3).

Chapter 8

Table 8.1 Terminology of models.

Table 8.2 Fuzzy controllers for the fuzzy rules and surf plots.

Table 8.3 The parameters of simulation and their values.

Table 8.4 Different work load conditions in comparison to resource utilization efficiency (%).

Table 8.5 With different work load comparison of SLO failure or SLO deadline violation (%).

Table 8.6 With different average task length comparison of power consumption in percentage of 100% resource utilization.

Chapter 12

Table 12.1 The safety index of each country is given below.

Table 12.2 Accident per million departure.

Chapter 13

Table 13.1 Strength between two person using FEMT labeling.

Chapter 14

Table 14.1 Training data for impulsive control genesio–Tesi chaotic system.

Table 14.2 Checking data for impulsive control Genesio–Tesi chaotic system.

List of Illustrations

Chapter 1

Figure 1.1 Examples of fractals.

Figure 1.2 Cells of cervix.

Figure 1.3 Pap smear test of the cervical cancer.

Figure 1.4 Normal cervix cell images.

Figure 1.5 Abnormal cervix cell images.

Figure 1.6 Graphical representation of fuzzy Eigen vectors.

Figure 1.7 Human Papiloma Virus leads to cervical cancer [5].

Figure 1.8 Linear regression lines of normal cervix cell (even scaling).

Figure 1.9 Linear regression lines of normal cervix cell (odd scaling).

Figure 1.10 Linear regression lines of abnormal cervix cell (even scaling).

Figure 1.11 Linear regression lines of abnormal cervix cell (odd scaling).

Chapter 2

Figure 2.1 Adaptive E-Learning system.

Figure 2.2 Proposed e-learning architecture.

Figure 2.3 Face recognition results of UMIST dataset.

Figure 2.4 Pupil detection, Starburst, Haar cascade comparison chart.

Figure 2.5 Pooling Techniques.

Figure 2.6 Pooling techniques.

Figure 2.7 Typical CNN architecture.

Figure 2.8 Facial emotion recognition—surprise, neutral, happy, angry and sad.

Figure 2.9 Eye gaze movement detection—center, left, right, top and bottom.

Figure 2.10 Face movement detection—up, down, right and left.

Figure 2.11 Face recognition accuracy across feature descriptors.

Figure 2.12 Iris recognition accuracy across feature descriptors.

Figure 2.13 Comparison of head movement accuracy across feature descriptors.

Figure 2.14 Comparison of FBET using SVM with accuracy of 73.

Figure 2.15 Comparison of FBET using SVM with accuracy of 81.5.

Chapter 4

Figure 4.1 Classification of optimization techniques.

Figure 4.2 Hierarchy of nature-inspired algorithms.

Figure 4.3 Components of bio-inspired computing.

Figure 4.4 Applications of (ACO).

Figure 4.5 Hierarchical structure of MCDM.

Figure 4.6 Input/output measures of AHP.

Chapter 7

Figure 7.1 Fundamental Structure of Genetic Fuzzy Rule Based (GFRB) System.

Figure 7.2 Strategies for GA based FLC optimization.

Figure 7.3 Rule encoding styles in genetic fuzzy hybrid systems.

Figure 7.4 Methods for Genetic Fuzzy System.

Figure 7.5 ES and CS differences.

Figure 7.6 Classifier System (CS) subsystems.

Figure 7.7 Pittsburgh rule learning approach.

Figure 7.8 Michigan approach versus Pittsburg approach.

Figure 7.9 CRL stages.

Figure 7.10 CRL Sub Components.

Chapter 8

Figure 8.1 Fuzzy Logic Controller (FLC) system representation [2].

Figure 8.2 In triangular membership function process of fuzzification [13].

Figure 8.3 Representation of blocks of different functions and their internal connection [7].

Figure 8.4 Fuzzy estimators based membership function shown in graphs. Graph (a) is based on triangular function, (b) is based on two-sided Gaussian Function and (c) is based on Gaussian [23].

Figure 8.5 Structure of convolution neural network [10].

Figure 8.6 Structure of recurrent neural network [13].

Figure 8.7 The proposed algorithm flow chart [11].

Chapter 10

Figure 10.1 The chaotic nature of Jerk system with uncertainties.

Figure 10.2 The chaotic nature of Jerk system with uncertainties between

x

1

and

x

2

.

Figure 10.3 The chaotic nature of Jerk system with uncertainties between

x

1

and

x

3

.

Figure 10.4 The chaotic nature of Jerk system with uncertainties between

x

2

and

x

3

.

Figure 10.5 Synchronization between

x

1

and .

Figure 10.6 Synchronization between

x

2

and .

Figure 10.7 Synchronization between

x

3

and .

Figure 10.8 Error dynamics of chaotic Jerk system.

Figure 10.9 Input membership function Sprott time-delay chaotic Jerk systems with uncertainties.

Figure 10.10 Output membership function Sprott time-delay chaotic Jerk systems with uncertainties.

Figure 10.11 Fuzzy rules for the synchronization of chaotic Jerk system with uncertainties.

Figure 10.12 Output for fuzzy rules.

Figure 10.13 Surface of the fuzzy rules.

Chapter 11

Figure 11.1 Flow chart of Hungarian method.

Figure 11.2 Matrix 1.

Figure 11.3 Matrix 2.

Figure 11.4 Matrix 3.

Figure 11.5 Matrix 4.

Figure 11.6 Matrix 1.

Figure 11.7 Matrix 2.

Figure 11.8 Matrix 3.

Figure 11.9 Matrix 4.

Figure 11.10 Matrix 1.

Figure 11.11 Matrix 2.

Figure 11.12 Matrix 3.

Figure 11.13 Matrix 4.

Figure 11.14 Matrix 5.

Figure 11.15 Matrix 6.

Chapter 12

Figure 12.1 Example of a fuzzy graph.

Figure 12.2 Fuzzy Graph

G.

Figure 12.3 Homomorphic fuzzy graphs

G

and

G’

.

Figure 12.4 Example of an Isomorphic fuzzy graphs G and G′.

Figure 12.5 Fuzzy digraph.

Figure 12.6 Fuzzy graph

G

(

V, σ, μ

).

Figure 12.7

G

(

V, σ, μ

).

Figure 12.8 Fuzzy graph on life risk rate.

Figure 12.9

G

(

V, σ, μ

).

Figure 12.10 Hospital map.

Figure 12.11 Graphical representation of the hospital.

Figure 12.12 Modified fuzzy graph representing the safety level.

Figure 12.13 Fuzzy digraph.

Figure 12.14 The fuzzy digraph and are isomorphic.

Figure 13.1 Bistar B (4, 3) is FEMT labeling.

Chapter 13

Figure 13.2 Bistar B (3, 4) is FEMT labeling.

Figure 13.3 Bistar B (3,3) is FEMT labeling.

Figure 13.4 Unicyclic U(5,3) is FEMT labeling.

Figure 13.5 Star graph S(1,9) is FEMT labeling.

Figure 13.6 Friendship graph

F

5

is FEMT labeling.

Figure 13.7 Triangular snake graph

T

4

is FEMT labeling.

Figure 13.8 Tadpole graph T(5,3) is FEMT labeling.

Figure 13.9 Tadpole graph T(3,4) is FEMT labeling.

Figure 13.10 Jelly fish J(m,n) is FEMT labeling.

Figure 13.11 The graph

C

5

+

F

2

is FEMT labeling.

Chapter 14

Figure 14.1 Chaotic portait of Genesio–Tesi system.

Figure 14.2 Chaotic nature between

x

1

and

x

2

.

Figure 14.3 Chaotic nature between

x

1

and

x

3

.

Figure 14.4 Chaotic nature between

x

2

and

x

3

.

Figure 14.5 Impulsive control of Genesio–Tesi chaotic system.

Figure 14.6 Training and checking data of x_1.

Figure 14.7 Training and checking data of x_2.

Figure 14.8 Training and checking data of x_3.

Figure 14.9 Initial fuzzy membership function for ANFIS.

Figure 14.10 Initial fuzzy membership function for ANFIS.

Figure 14.11 Initial fuzzy membership function for ANFIS.

Chapter 16

Figure 16.3.6.1 Relationship between soft continuous functions.

Figure 16.3.6.2 Association between soft open (closed) functions.

Figure 16.3.7.1 Association between soft contra-continuous functions.

Guide

Cover

Table of Contents

Title Page

Copyright

Preface

Index

End User License Agreement

Pages

v

ii

iii

iv

xiii

xiv

xv

xvi

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

217

218

219

220

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

241

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

272

273

274

275

276

277

278

279

280

281

282

283

285

286

287

288

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

307

308

309

310

311

312

313

315

316

317

318

319

320

321

322

323

324

325

326

327

328

329

330

331

332

333

335

336

337

338

339

340

341

342

343

344

345

346

347

348

349

350

351

352

353

354

355

356

357

358

359

360

361

362

363

365

366

367

368

369

370

371

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

439

440

441

442

443

444

445

446

447

448

449

450

451

452

453

454

455

456

457

458

459

460

461

462

463

464

465

Scrivener Publishing100 Cummings Center, Suite 541JBeverly, MA 01915-6106

Artificial Intelligence and Soft Computing for Industrial Transformation

Series Editor: Dr S. Balamurugan ([email protected])

Scope: Artificial Intelligence and Soft Computing Techniques play an impeccable role in industrial transformation. The topics to be covered in this book series include Artificial Intelligence, Machine Learning, Deep Learning, Neural Networks, Fuzzy Logic, Genetic Algorithms, Particle Swarm Optimization, Evolutionary Algorithms, Nature Inspired Algorithms, Simulated Annealing, Metaheuristics, Cuckoo Search, Firefly Optimization, Bio-inspired Algorithms, Ant Colony Optimization, Heuristic Search Techniques, Reinforcement Learning, Inductive Learning, Statistical Learning, Supervised and Unsupervised Learning, Association Learning and Clustering, Reasoning, Support Vector Machine, Differential Evolution Algorithms, Expert Systems, Neuro Fuzzy Hybrid Systems, Genetic Neuro Hybrid Systems, Genetic Fuzzy Hybrid Systems and other Hybridized Soft Computing Techniques and their applications for Industrial Transformation. The book series is aimed to provide comprehensive handbooks and reference books for the benefit of scientists, research scholars, students and industry professional working towards next generation industrial transformation.

Publishers at ScrivenerMartin Scrivener ([email protected])Phillip Carmical ([email protected])

Fuzzy Intelligent Systems

Methodologies, Techniques, and Applications

Edited by

E. Chandrasekaran,

R. Anandan,

G. Suseendran,

S. Balamurugan

and

Hanaa Hachimi

This edition first published 2021 by John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA and Scrivener Publishing LLC, 100 Cummings Center, Suite 541J, Beverly, MA 01915, USA

© 2021 Scrivener Publishing LLC

For more information about Scrivener publications please visit www.scrivenerpublishing.com.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

Wiley Global Headquarters

111 River Street, Hoboken, NJ 07030, USA

For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com.

Limit of Liability/Disclaimer of Warranty

While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials, or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read.

Library of Congress Cataloging-in-Publication Data

ISBN 978-1-119-76045-0

Cover image: Pixabay.Com

Cover design by Russell Richardson

Preface

It is with immense pleasure that we introduce this book. Our objective in writing it 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.

The format of the book was designed to match the self-contained approach to fuzzy mathematics and fuzzy control systems theory that even students with no prior knowledge can easily understand. It enables both classroom and self-directed learners to create a strong foundation in fuzzy systems by being open and straightforward; following a brief introduction to the subject, the authors dive right into real-world applications of fuzzy logic revealing its practical flavor. The book is mainly intended to familiarize systems and control subjects for both senior undergraduate and first-year graduate students, with the fundamental mathematical theory and design methodology needed to understand and use fuzzy control systems. This self-contained textbook will provide a solid framework for designing and evaluating fuzzy control systems under unpredictable and irregular conditions. Students can gain a thorough understanding of fuzzy control systems theory by mastering its contents.

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 attempts to showcase the combination of fuzzy logic and neural networks known as a neuro-fuzzy system, which should result in a hybrid intelligent system by combining a human-like reasoning style of neural networks.

Listed below is a brief description of the subjects covered in each chapter of the book.

Chapter 1 explains the uncertain growth of cervical cancer. Cancer cells keep developing and apparently unpredictable behavior arises in a deterministic system because of great sensitivity to initial conditions. Images of cancer-based cell formation in the tissue are represented in this chapter and a fuzzy matrix method and sausage method are used along with the maximum modulus theorem to explain the complexity of these cancer cell (CC) images.

Chapter 2 deals with the use of a fuzzy convolutional neural network in a virtual classroom environment to detect students’ emotions. Here, different feature extraction techniques are used for the face, eye and head (PCA for face, HAAR cascade for eye and LBP for head) and then emotion detection is carried out. The experimental results of the proposed method achieve an accuracy of 81.5%.

Chapter 3 presents a new labeling concept known as fuzzy quotient-3 cordial labeling, in which notations for some trees of diameter 5 are defined. The authors analyzed the existence of fuzzy quotient-3 cordial labeling of some trees of diameter 5 denoted by , 31 ≤ s ≤ 39 and the existence of fuzzy quotient-3 cordial labeling was established and the work presented.

Chapter 4 introduces hybrid computational intelligence. After a brief review of optimization and meta-heuristic algorithms, the scope of swarm intelligence in overcoming the limitations of traditional methods is examined. Ant colony optimization and swarm optimization are also thoroughly covered. Next, multi-criteria decision problems and various tools for these problems, such as WSM, WPM, AHP, TOPSIS, ELECTRE and VIKOR, are covered along with their behavior and application.

Chapter 5 examines finite, simple, undirected graphs without loops or multiple edges. Graph labeling, which is an assignment of integers to the vertices or edges or both, has a well-developed broad range of applications. Graph labeling introduces the concept of fuzzy tri-magic and proves that some graphs are fuzzy tri-magic. In this chapter, we take the isomorphic caterpillar of diameter 5 and prove that it is fuzzy tri-magic. We also give the magic membership values, their corresponding edges and the number of magic membership values with various natures of m, n and a as tables.

Chapter 6 defines fuzzy tri-magic labeling and proves that the isomorphic caterpillar of diameter 5 graph admits fuzzy tri-magic by proving that the maximum difference between the number of Ki’s and Kj’s (1 ≤ i ≤ 3) differs by at most 1 and for 1≤ i, j ≤ 3, r ≥ 2.

Chapter 7 characterizes the three significant approaches of GFS hybridization: Michigan, Pittsburgh and CRL. This chapter clarifies each of these methodologies along with subcomponents, working style, points of interest and confinements. It likewise contrasts qualities of a conventional master framework and classifier system for genetic-fuzzy hybridization and subsequently presents the significance of structuring GFS. A similar assessment of every one of the mixture techniques prompts the CRL plan. The chapter also describes different points of interest of the ceaseless rule learning approach.

Chapter 8 discusses the design of a fuzzy technique-based system for a given task. In any given task, to make a decision by fuzzy logic, either a number is used with a combination of VMs or is created with a fresh VM based on current operational conditions such as task requirement, load and available resources, etc. In this era, service of the internet or implementation of cloud applications work by using virtual machines (VMs) in the cloud system.

Chapter 9 deals with the basic notation of fixed-point theory in fuzzy soft metric spaces. The common fixed-point result is proved for (α − β) − ψ − functions of the contractive type mappings. Another result is proved for fuzzy soft – contractive type mappings and – admissible mappings in fuzzy soft metric space. The obtained results are very useful for uncertainty and decision-making problems.

Chapter 10 analyzes the asymptotic mean-square stability of an observer-based chaos synchronization with time-delay fuzzy stochastic systems. Utilizing the Lyapunov stability theory, a fuzzy-based stochastic system with time delay is designed, which is assumed to have asymptotic mean-square stability. Fuzzy-based chaotic synchronization has been the main focus of propagation delay and system uncertainties.

Chapter 11 discusses solving assignment problems using trapezoidal fuzzy numbers. Here, some arithmetic operations of TrFN are represented. Some assignment problems are fully solved by fuzzy numbers using the Hungarian method.

Chapter 12 discusses the connectedness of fuzzy graph with a real-life application on firefighting humanoid robots and resolving the matrix. The left resolving set and the right resolving set are defined for fuzzy digraph. Some theorems and corollaries are also proved in determining the set of the fuzzy digraph.

Chapter 13 proposes that some fuzzy graph families have a fuzzy edgemagic total labeling, which is discussed here with a brief example and extended with an application that finds a stronger friendship between two people using fuzzy edge-magic labeling.

Chapter 14 investigates the control of impulsive chaotic systems based on the Takagi-Sugeno (TS) fuzzy model. The asymptotic mean-square stability criterion is designed and a robust supervisory control is proposed. When fuzzy-based impulsive chaotic systems are subjected to system uncertainties and external disturbance, the supervisory control can induce the designed system’s convergence speed. The Genesio-Tesi chaotic model is utilized and the fuzzy logic toolbox in MATLAB is invoked, forgetting results.

Chapter 15 discusses ways to solve uncertainty problems, which are real-world problems that often turn out to be complex due to inserting an element of uncertainty either in parameters that define the problem or the situation in which the problem occurs. Because of various uncertainties arising in real-world situations, classical mathematics methods may not be successfully applied to solve them. However, fuzzy set theory (FST) and soft set theory (SST) can solve these uncertainty problems. As presented in this chapter, the application of mathematics is used to solve uncertainty. We prove some common fixed-points theorems in φ − ψ weak contraction on soft fuzzy metric spaces by using control function or altering distance function. Here, we define mapping by using some proven results and obtain a result on the actuality of fixed points. To confirm the results, the basic concepts of soft sets and fuzzy sets are used.

The final chapter is devoted to On Soft α(γ,β)-Continuous Functions in Soft Topological Spaces.

Finally, we would like to thank all chapter authors for their valuable time and effort.

E. Chandrasekaran

R. Anandan

G. Suseendran

S. Balamurugan Hanaa Hachimi

Editors

July 2021