Fuzzy Information and Engineering (eBook)

Title Page 1
Preface 5
Organization 7
Contents 10
Part I Fuzzy Information 19
Contrast Enhancement for Image by WNN and GA Combining PSNR with Information Entropy 20
Introduction 20
IBT 21
Contrast Classification for Image Based on Histogram 22
Transform Parameters Optimization by GA 22
IBT Calculation with WNN 25
Local Contrast Enhancement by Non-linear Operator 26
Algorithm Steps 27
Experimental Results 27
Conclusion 31
References 31
A Generalized Decision Logic Language for Information Tables 33
Introduction 33
Decision Logic Language 34
Generalized Decision Logic Language 36
Conclusions 38
References 38
New Similarity Measures on Intuitionistic Fuzzy Sets 39
Introduction 39
Basic Notions and Definitions of Intuitionistic Fuzzy Sets 40
New Approaches to Calculating Similarity Measures 41
Application to Pattern Recognition Problem 44
Conclusions 46
References 46
Information Source Entropy Based Fuzzy Integral Decision Model on Radiodiagnosis of Congenital Heart Disease 48
Introduction 48
Medical Expert Diagnosis System Model 49
Conformation of Attaching Function of Each Symptom 50
Information Analysis of Radiodiagnosis Value and Weight of Each Symptom 52
Fuzzy Integral Decision-Making 53
Example Analysis and Optimization Processing 54
Example Analysis 54
Optimization Processing 56
References 57
The Design and Research of Controller in Fuzzy PETRI NET 58
Introduction 58
The Definition of Fuzzy PETRI NET 58
The Definition of Fuzzy PETRI NET 58
The Rules of Activation 59
Place Invariant 59
Design of Controller 59
A Synthetical Algorithm Aiming at the Dead Lock Phenomenon 62
Dealing with Dead Lock Phenomenon 63
Summary 65
References 65
Fuzzy Tracing the Source of Net-Virus 67
Introduction 67
Source Tracing Modeling 68
Solutions to the Equations 71
Simulation Tests 72
Conclusion and Acknowledgements 74
References 75
Uncertain Temporal Knowledge Reasoning of Train Group Operation Based on Extended Fuzzy-Timing Petri Nets 76
Introduction 76
EFTN and Relative Computations 77
Updating Fuzzy Timestamps 77
Possibility Computation 78
Analysis of Temporal Uncertainty 78
Comparing Analysis 79
Conclusion 80
References 81
An Improved FMM Neural Network for Classification of Gene Expression Data 82
Introduction 82
Improving FMM Neural Network Classifier 84
Original FMM Neural Network 84
Drawbacks of FMM Neural Network 85
Improvement of FMM Neural Network 86
Gene Selection 87
Experiment Evaluation 89
Conclusion 90
References 90
Using Assignment Matrix on Incomplete Information Systems Reduction of Attributes 92
Introduction 92
Incomplete Information System and Tolerance Relation 93
Assignment Matrix and Measurement of Conditional Attributes’ Significance to Decision 94
Assignment Matrix Based Attribute Reduction Algorithm 96
Example and Analysis 97
Summary 99
References 99
An Image Compression Algorithm with Controllable Compression Rate 100
Introduction 100
The Fuzzy Neural Network 101
The Technical Details 101
Performance 103
Conclusions 104
References 104
A Novel Approach for Fuzzy Connected Image Segmentation 106
Introduction 106
Preliminaries 107
A Framework for Fuzzy Connectedness, Relative Fuzzy Connectedness 107
Fuzzy k -Object 109
Algorithm 109
Original Algorithm 109
Proposed Algorithm 109
Algorithm Complexity Analysis 110
Experimental and Evaluation 111
Experimental Result 111
Evaluation 111
Conculsion 113
References 114
Knowledge Mass and Automatic Reasoning System in Similarity Logic $C_Q$ 115
Introduction and Preliminary 115
Type V Knowledge Mass, Type V Knowledge Universe, Type V Knowledge Base and Type V $Q$-Automatic Reasoning System 119
Type V True Level k Knowledge Circle, Extended Type V Knowledge Base and Extended Type V $Q$-Automatic Reasoning System 122
The Type V Level (k,j) Perfection of Extended Type V Knowledge Base $K^V$ 126
Conclusion 128
References 128
Image Segmentation by Multi-level Thresholding Based on C-Means Clustering Algorithms and Fuzzy Entropy 130
Introduction 130
Image Segmentation Based on C-Means Clustering Algorithms 131
C-Means Clustering Algorithms 131
C-Means Clustering Algorithms for Image Segmentation 132
Perform Post Process Using Fuzzy Entropy 133
Fuzzy Entropy and Membership Function 133
Perform Post Process Using Fuzzy Entropy 133
Experimental Results 134
Conclusion 138
References 138
Part II Fuzzy Sets and Systems 139
Extension Principle of Interval-Valued Fuzzy Set 140
Introduction 140
Preliminaries 141
Maximal Extension Principle of Interval-Valued Fuzzy Set 144
Minimal Extension Principle of Interval-Valued Fuzzy Set 146
Generalized Extension Principle of Interval-Valued Fuzzy Set 150
Conclusion 151
References 152
On Vague Subring and Its Structure 153
Introduction 153
Preliminaries 153
Vague Ring and Its Substructures 154
The Homomorphism of Vague Ring 157
References 158
A Common Generalization of Smooth Group and Vague Group 159
Introduction 159
Common Generalization of Smooth Group and Vague Group 159
The Relationships Among Fuzzy Groups Based on Fuzzy Equalities 161
Conclusion 163
References 163
Sequences of Fuzzy-Valued Choquet Integrable Functions 164
Introduction 164
Preliminaries and Propositions 164
Uniform Integrability, Uniform Absolute Continuity and Uniform Boundedness 166
Some Convergence Theorems 170
Conclusions 172
References 173
Generalized Root of Theories in Propositional Fuzzy Logical Systems 174
Introduction 174
Preliminaries 175
Logic Systems: ${/L}uk$, $G/ddot{o}d$, $/Pi$ and$L^{/ast}$} /label 175
Generalized Deduction Theorems in ${/L}uk$, $G/ddot{o}d$, $/Pi$ and 177
Basic Definitions and Properties 178
Results in the n-Valued ukasiewicz Logic System 180
Results in the $G/ddot{o}del$ Fuzzy Logic System 181
Results in the R_o -- Fuzzy Logic System 182
Conclusion Remarks 183
References 184
Countable Dense Subsets and Countable Nested Sets 185
Introduction 185
Countable Decomposition Theorems 186
Countable Representation Theorems 190
Conclusion 194
References 195
The Construction of Power Ring 196
Introduction 196
Concepts of HX Ring and Power Ring 196
Construction of HX Ring and Power Ring 198
References 202
On Fuzzy Ideals in BCH-Algebras 203
Introduction 203
Preliminaries 203
Fuzzy Quasi-associate Ideals of BCH-Algebras 204
References 207
Minimization of Lattice Automata 209
Introduction 209
Lattice Automata 209
Refining Congruence and Quotient Automata 210
Equivalent and Minimal Automata 213
Minimization Algorithm 215
An Example 217
Conclusions 220
References 220
Fixed Points in $M$-Fuzzy Metric Spaces 221
Introduction 221
Compatible Mappings of Type (*) 224
Common Fixed Point Theorems 226
References 229
Common Fixed Points of Maps on Intuitionistic Fuzzy Metric Spaces 231
Introduction 231
Preliminaries 232
Result 233
References 240
Generalized Fuzzy $B$-Algebras 241
Introduction 241
Preliminary 241
($/alpha,/beta$,)-Fuzzy $B$-Algebras 243
References 248
Fuzzy Set Theory Applied to $QS$-Algebras 249
Introduction 249
Preliminary 249
Fuzzy $QS$-Subalgebra 251
Fuzzy Topological $QS$-Algebra 256
References 257
$L$-Topological Dynamical System and Its Asymptotic Properties 258
Introduction 258
Dynamical Systems on F-Lattice 259
Systems 260
Subsystems 262
Asymptotic Properties 263
Recurrence 263
$ /omega $ -Limit Sets 264
Topological Conjugacy 265
Conclusion 266
References 266
Integrating Probability and Quotient Space Theory: Quotient Probability 267
Introduction 267
Quotient Probability and Some Results 268
Probability Update and Spaces Fusion 269
Distance Between Two Different Quotient Probabilities 271
Conclusion 273
References 273
.-Convergence Theory of Filters in L.-Spaces 275
Introduction 275
Preliminaries 275
.-Convergence of Filters 277
Relationships Among .-Convergence of Filters, .-Convergence of Nets and .-Convergence of Ideals 279
Some Applications of .-Convergence of Filters 281
References 282
On the Perturbation of Fuzzy Matrix Equations with $.$-T Composition 284
Preliminaries 284
Fuzzy Solution-Invariant Matrix 286
Fuzzy Perturbation Issues 289
References 294
Normal Distribution Fuzzy Sets 295
Introduction 295
Normal Distribution Fuzzy Sets 296
Some Properties of Union, Complementation and Intersection 299
The Relationship Among Fuzzy Sets, Intuitionistic Fuzzy Sets and Normal Distribution Fuzzy Sets 300
Conclusion 303
References 303
Probabilistic Fuzzy Hypernear-Rings 305
Introduction 305
Preliminaries 306
Probabilistic Fuzzy Hypernear-Rings 307
Conclusions 309
References 310
Isomorphic Fuzzy Sets and Fuzzy Approximation Space 311
Introduction 311
Isomorphism and Homomorphism of Fuzzy Sets 312
Fuzzy Sets and Approximation Spaces 314
Fuzzy Relations and Fuzzy Approximation Spaces 316
Conclusion 320
References 321
Part III Soft Computing 322
Particle Swarm Optimization Algorithm Design for Fuzzy Neural Network 323
Introduction 323
Fuzzy Neural Network Architecture 323
Particle Swarm Optimization with Division of Work 324
Pruning Algorithm 326
Numerical Simulations 327
Conclusion 327
References 328
A Method of Intuitionistic Fuzzy Reasoning Based on Inclusion Degree and Similarity Measure 329
Introduction 329
Inclusion Degree Based on Fuzzy Implication Operators 330
Similarity Measure Between IFSs Based on Inclusion Degree 331
Intuitionistic Fuzzy Reasoning Based on Similarity Measure 333
Single Rule Case of IFMP 333
Multi-rules Case of IFMP 334
Numerical Example 334
Conclusion 335
References 336
A Discrete Particle Swarm Optimization Algorithm for the Multiobjective Permutation Flowshop Sequencing Problem 337
Introduction 337
The Discrete Particle Swarm Optimization Algorithm for the MPFSP 338
Discrete PSO for the Single Objective PFSP 339
The Proposed DPSO for the MPFSP 339
Experimental Results 341
The 5 Small Problems with the Objectives of Minimizing the Makespan and the Total Tardiness 341
The 20 Problems of Taillard with the Objectives of Minimizing the Makespan and the Total Flowtime 343
Conclusions 344
References 345
An Optimization Method for Fuzzy c-Means Algorithm Based on Grid and Density 346
Introduction 346
Grid and Density 346
Initialization Method for Fuzzy c-Means Algorithm Based on Grid and Density 347
Extract Approximate Clustering Center Algorithm Based on Grid and Density 347
Initialization 348
Experiments 348
Conclusions 349
References 350
Obstacle Recognition and Collision Avoidance of a Fish Robot Based on Fuzzy Neural Networks 351
Distance Scanning System for Fish Robots 351
Distance Scanning System for Fish Robots 352
Obstacle Recognition System 355
Scanning Obstacles 355
Recognition of Shapes and Estimation of Approaching Angles 356
Experiments 357
Conclusions 358
References 358
Generalization of Soft Set Theory: From Crisp to Fuzzy Case 359
Introduction 359
Theory of Fuzzy Soft Set 360
Soft Set Theory 360
Fuzzy Soft Set Theory 361
Operators on Fuzzy Soft Set 363
Fuzzy Logic Operators 363
Operators on Fuzzy Soft Set 363
Application of Fuzzy Soft Set 365
Conclusion 367
References 367
A New QPSO Based BP Neural Network for Face Detection 369
Introduction 369
Quantum Particle Swarm Optimization 370
PSO Algorithm 370
QPSO Algorithm 370
Improved BPNN Learning Algorithm Based on QPSO 371
Face Detection Based on the Improved Learning Algorithm 373
Preprocessing 373
Designing the Network 373
Training 373
Detection 374
Experiment Results 374
Conclusion 376
References 377
ECC-Based Fuzzy Clustering Algorithm 378
Introduction 378
The Hierarchical Model of ECC 379
ECC-Based Vector Space Model 380
ECC-Based Fuzzy Clustering Algorithm 382
Validation 383
Experimental Results and Analysis 384
Conclusion 386
References 386
A New Algorithm for Attribute Reduction Based on Discernibility Matrix 387
Introduction 387
Basic Concepts 388
Decision Tables and Pawlak Reduction 388
Discernibility Matrices 389
Algorithms 391
Algorithm Principle 391
Algorithm Describing 392
Complexity Analysis of the Algorithm 393
Experimental Analysis 393
Conclusions 394
References 394
Optimal Computing Budget Allocation Based Compound Genetic Algorithm for Large Scale Job Shop Scheduling 396
Introduction 396
Job Shop Scheduling Problem Formulation 397
Heuristic and Search Techniques for Job Shop Scheduling Problem 398
Genetic Algorithm for Job Shop Scheduling 399
The Encoding Representation and Fitness Value 399
The Selection, Crossover and Mutation Operator 400
Genetic Algorithm Scheme Designing 401
Optimal Computing Budget Allocation Algorithm for GA Parameters Selection 402
Problem Statement 402
The Method for Algorithm Comparison and Selection 403
Optimal Computing Budget Allocation in Algorithm Comparison 404
Optimal-Computing-Budget-Allocation Based Compound Genetic Algorithm 406
Computational Experiments and Analysis 407
Conclusions 409
References 409
Part IV Fuzzy Engineering 411
Multi-Immune-Agent Based Power Quality Monitoring Method for Electrified Railway 412
Introduction 412
Immune Agent Model 413
Immune Supervision Networks Model 413
Architecture and Algorithm of Immune Agent 414
Cooperative Multi-Immune-Agent Based Power Quality Monitoring Systems 415
Immune-Terminal Parameter 416
Control Algorithm 418
Control Decision Algorithm 419
Resolving Conflicts 420
Experiment Evaluation 420
Evaluation 421
Solution to Conflicts 422
Conclusions 422
References 422
BF Hot Metal Silicon Content Prediction Using Unsupervised Fuzzy Clustering 424
Introduction 424
General Scheme and Principle of the Methods 425
Established Temporal Patterns 426
Fuzzy Clustering by State Recognition 426
Fit a Prediction Model to Each Fuzzy Cluster 427
Predicting by a Combination of the Models 427
Simulation of Predictive Algorithm 427
Conclusions and Discussion 430
Refences 430
Speech Emotion Pattern Recognition Agent in Mobile Communication Environment Using Fuzzy-SVM 432
Introduction 432
Proposed System 433
Emotional Feature Extractions and Optimization 435
Pre-processing 435
Emotional Feature Extraction 436
SFS Feature Optimization 436
MA (Moving Average) Filter to Minimize Noise Effect 437
Experimental Results 438
Speech Database and Experimental Setup 438
SFS Feature Optimization Experiment 439
Classification Results for Five Emotional States 439
Classification Results with Two Emotional States 441
Conclusion 442
References 442
Efficient Wavelet Based Blind Source Separation Algorithm for Dependent Sources 444
Introduction 444
BSS Model and Indeterminacies 445
CWT Based BSS Algorithm for Dependent Sources 446
Problem Statement and Why Use WT 446
How to Use CWT and the Basic Algorithm 448
CWT Based General BSS Algorithm 449
$m$=2 Mixtures and $n$ Source Signals 449
General Case: $n$ Mixtures and $n$ Source Signals 450
Procedure of the BSS Algorithm 451
Simulation Results 452
Conclusion 453
References 454
An Incentive Mechanism for Peer-to-Peer File Sharing 455
Introduction 455
Relation Work 456
Incentive Mechanism 456
Experiments 459
Conclusions and Future Work 460
References 460
Application of the BP Neural Network in the Checking and Controlling Emission of Vehicle Engines 461
Introduction 461
Model of the BP Neural Network 461
Construction of the BP Neural Network 462
Equation of the BP Neural Network 462
Process of the Neural Network Leaning 463
Application of the BP Neural Network in Checking and Controlling Emission 463
Result 466
References 466
Oil and Gas Pipeline Limited Charge Optimum Maintenance Decision-Making Analysis Based on Fuzzy-Gray-Element Theory and Fuzzy Analytical Hierarchy Process 468
Foreword 468
Theoretical Basis of Fuzzy-Gray-Element 469
Concept of Fuzzy-Gray-Element 469
Correlation Analysis 469
Fuzzy Hierarchy Analysis Method Assurance the Maintenance Measure Weight 470
The Analytic Hierarchy Process Brief Introduction 470
Maintenance Measure Support Layer Model Establishment 470
Establishment Triangle Fuzzy Number Complementary Judgment Matrix 471
Calculation Triangle Fuzzy Number Weight Vector of Maintenance Factor 471
Calculation Weight of Maintenance Factor 472
The Fuzzy-Grey-Element Correlative Decision-Making Model 472
The Establishment of the Maintenance Project Decision Model 472
Determination of Optimum Project Based on Fuzzy-Gray-Element Theory 474
Conclusion 475
References 476
The Fuzzy Seepage Theory Based on Fuzzy Structuring Element Method 477
Introduction 477
Fuzzy Structuring Element and Fuzzy Value Function 478
Fuzzy Structuring Element 478
Analysis Expression of Fuzzy Value Function 479
Establish of Fuzzy Seepage Model 480
Classical Landfill Gas Seepage Model 480
Fuzzy Qualified Differential Equation 481
Fuzzy Seepage Equation 481
Fuzzy Solution of Fuzzy Seepage Model 482
Analysis Solution of One-Dimension Ideal Seepage Model 482
Expressible Problem of Fuzzy Differential Equation Solution 483
Analysis Expression of Fuzzy Seepage Model 483
Conclusions 484
References 484
Ecological Safety Comprehensive Evaluation on Mineral-Resource Enterprises Based on AHP 485
Introduction 485
Method of Ecological Safety Evaluation for MRE 486
Meaning of Ecological Safety Evaluation for MRE 486
Index System of Ecological Safety Evaluation 486
Method of Evaluating the Ecological Safety of MRE 487
Example for the Applying of Comprehensive Evaluation on Ecological Safety of MRE 490
Conclusion 493
References 493
A Note on the Optimal Makespan of a Parallel Machine Scheduling Problem 494
Introduction 494
Level Algorithm 495
The Errors in Proofs for the Optimal Makespan 496
The Error in the Proof of $C_{/textmd{max}}/leq l_{/textmd{max}}+c$ in /cite{Tang} 497
The Errors in the Proof of Cmax = lmax + c in [7] 498
A New Algorithm and the Proof for the OptimalMakespan of $P|p_j=1,intree|C_{/textmd{max}}$ 501
Conclusion 506
References 506
Part V Fuzzy Operation Research and Management 507
Advances in Fuzzy Geometric Programming 508
Introduction 508
Fuzzy Geometric Programming 509
Present Situation of Fuzzy Geometric Programming 510
Future Development of Fuzzy Geometric Programming 511
References 512
A Method for Estimating Criteria Weights from Intuitionistic Preference Relations 514
Introduction 514
Preliminaries 515
Consistent Intuitionistic Preference Relation 516
A Method for Estimating Criteria Weights 517
Conclusions 521
References 521
The Area Compensation Method About Fuzzy Order and Its Application 524
Introduction 524
Basic Concept 525
Ranking Fuzzy Numbers 526
Approach to the Fuzzy Linear Programming with Fuzzy Variables 528
Extensions for the Area Compensation Ranking Method 531
Conclusion 532
References 533
A Method for the Priority Vector of Fuzzy Reciprocal Matrix 534
Introduction 534
Some Properties of Fuzzy Consistent Matrix 535
Algorithm 539
Numerical Examples 542
Conclusion 543
References 543
The Theory of Fuzzy Logic Programming 545
Introduction 545
Syntax and Semantics of Fuzzy Horn Clause Logic 545
Fuzzy Proof Theory 550
Fuzzy Procedural Interpretation 552
Conclusions 553
References 553
Multiobjective Matrix Game with Vague Payoffs 554
Introduction 554
Definition and Order Function of Vague Set 555
Model of Multiobjective Two-Person Zero-Sum Matrix Game Based on Vague Set 556
Solutions of Multiobjective Two-Person Zero-Sum Matrix Game Based on Vague Set 557
Conclusion 561
References 561
Fuzzy Geometric Object Modelling 562
Introduction 562
Modelling Fuzzy Geometric Objects Using Smooth Unit Step Function and Implicit Functions 564
Method 1: Fuzzification of a Solid Geometric Object 565
Method 2: Fuzzification of the Boundary of a Geometric Object 566
Method 3: Adding a Fuzzy Boundary to an Ordinary Solid Geometric Object 567
Modelling Fuzzy Geometric Objects Using Geometric Meshes and Parametrically Defined Geometric Shapes 568
Fuzzy Geometric Objects Blending 568
Shape Preserving Fuzzy Geometric Blending 569
References 572
A Fuzzy Portfolio Selection Methodology Under Investing Constraints 575
Introduction 575
Possibilistic Mean and Variance 576
A Fuzzy Portfolio Selection Model Under Investing Constraints 578
Numerical Example 581
Conclusions 582
References 583
The Interaction Among Players in Fuzzy Games 584
Introduction 584
Interaction for Crisp Cooperative Games 585
Interaction Among Players in Games with Fuzzy Coalitions 586
Fuzzy Coalitions and $LP$-Derivative 586
Mutual Independence Among Levels Based on $s$ 588
Interaction Among Levels of $LP(|LP|/geq 2)$ with Respect to Players of $M$ 589
The Interaction Among Players of $P(|P|/geq 2)$ 590
Conclusion 593
References 593
Novel Method for Fuzzy Hybrid Multiple Attribute Decision Making 594
Introduction 594
The Description for the Problem of Fuzzy Hybrid Multiple Attribute Decision Making 595
The Principle and Method of the Decision Making 595
Processing Data for Indexes 595
The New Method Based on the Grey Relational Degree 597
The Basic Steps of the New Decision Making Method 599
An Application Example 600
Conclusions 601
References 602
Auto-weighted Horizontal Collaboration Fuzzy Clustering 603
Introduction 603
Prelimimary 604
Fuzzy C-Means (FCM) 604
Horizontal Collaboration Fuzzy C-Means 604
The Determining of Weights in HC-FCM 606
Measure of Partition Similarity 606
Encouragement Approach 607
Penalty Approach 609
Conclusions 610
References 611
A Web-Based Fuzzy Decision Support System for Spare Parts Inventory Control 612
Introduction 612
The Framework for SPICDSS 613
The General Integrated Framework 613
The Criticality Class Evaluation Methodology 613
The Web-based Replenishment DSS (WRDSS) 616
The Development of SPICDSS and Application 618
Prototype System 618
Application Analysis 619
Conclusions 619
References 619
Fuzzy Ranking for Influence Factor of Injury Surveillance Quality in Hospital 621
Introduction[5][6] 621
Factors from the Filling Staff Include 622
Factors from the Injury Patients Include 622
Factors from the Staff of Collecting and Checking Include 622
Factors from the Supervising and Guidance Include 623
Factors from the Process of Inputting Include 623
Factors from the Group of Surveillance Work Include 623
Factors from the Quality Control and Managing Include 623
Some Basic Concepts[1][2] 623
0.50-0.90 Scale[3] 624
Ranking Based on the Fuzzy Complementary Judgement Matrix[4] 625
Conclusion 628
References 629
Decision-Making Rules Based on Belief Interval with D-S Evidence Theory 630
Introduction 630
Decision Rule Based on the Belief Interval 631
The Decision Rule on $Bel$ 632
The Decision Rule on $Pl$ 632
The Colligation Rule 632
Unitary Operator 633
Example[5] 635
Conclusion 638
References 638
An Optimization Model for Stimulation of Oilfield at the Stage of High Water Content 639
Introduction 639
Source of Data for Professional System 640
Method of Optimization for the Adjustment of Oilfield Development 640
Evaluation of Development Status of Oilfield 640
Method for Predicting the Pressure of Single-Phase Flow 640
Prediction of Residual Oil Saturation 641
Optimization of Adjustment Project by Fuzzy Theory 641
The First Step 642
The Second Step 642
The Third Step 643
Method of Integral Optimization 644
Diagram for the Idea of the Integral Optimization of Adjustment of Water Flooding Oilfield 644
Applications of the Optimization Model 644
Working out of Development Plan 644
Application Effect of the Model 645
Conclusions 646
References 646
New Research of Coefficient-Fuzzy Linear Programming 648
Introduction 648
Membership Function of FLP 649
Solution Method 651
Optimal Solution of FLP 651
Algorithm 652
Numerical Example 652
Conclusion 653
References 653
Part VI Artificial Intelligence 655
Robust Fuzzy Control for Uncertain Nonlinear Systems with Regional Pole and Variance Constraints 656
Introduction 656
Problem Description and Preliminaries 657
Main Results 661
Solving Procedures 664
Conclusions 664
References 665
The Existence of Fuzzy Optimal Control for the Semilinear Fuzzy Integrodifferential Equations with Nonlocal Conditions 666
Introduction 666
Preliminaries 667
Fuzzy Optimal Control 670
References 674
A PSO-Based Approach to Rule Learning in Network Intrusion Detection 675
Introduction 675
Standard Particle Swarm Optimization 676
PSO for Rule Learning 677
Coding Scheme 677
Fitness Function 678
Inertia Weight 678
Algorithm Description 679
Experiment Results 679
Conclusions 681
References 682
Similarity Mass and Approximate Reasoning 683
Introduction 683
The Construction of $Q$-Formula Mass and $Q$-Logic 684
Type V Simple Approximate Reasoning Based on $Q$-Logic $C_Q $ 684
Type V Multiple Approximate Reasoning Based on $Q$-Logic $C_Q$ 686
Type V Completeness and Type V Perfection of Knowledge Base K in $Q$-Logic $C_Q$ 688
Conclusion 692
References 692
Intelligent Knowledge Query Answering System Based on Short Message 694
Introduction 694
System Framework 695
Short Message Processing Module 695
Hardware Condition 695
Correlative AT Command and PDU Data Format Analyses 695
Processing Flow of Short Message 697
Knowledge Query Module 697
Query Mode of Users 697
Knowledge Organization 697
Query Sentences Classification 698
Examples of Parsing Query Sentence 698
Drawing Answer 700
Conclusion 701
References 701
Comparison Study on Different Core Attributes 702
Introduction 702
Preliminary 703
Core Attributes of Simplified Discernibility Matrix Based on Hu's Discernibility Matrix 704
Core Attributes of Simplified Discernibility Matrix Based on Positive Region 705
Core Attributes of Simplified Discernibility Matrix Based on Information Entropy 706
Comparison Study on Three Kinds of Core Attributes 710
Conclusion 711
References 712
Controllability for the Impulsive Semilinear Fuzzy Integrodifferential Equations 713
Introduction 713
Existence and Uniqueness of Fuzzy Solution 714
Controllability 717
Example 720
References 722
Remodeling for Fuzzy PID Controller Based on Neural Networks 723
Introduction 723
Fuzzy PID Controller 724
Remodeling for an Equivalent NN of Fuzzy PID Controller 728
Control Simulation 730
Conclusion 734
References 734
Monitoring for Healthy Sleep Based on Computational Intelligence Information Fusion 735
Introduction 735
Scheme of Monitoring Sleep Fidget 736
Information Fusion Strategy Based on NN 737
Experimental System for Input/Output Data Acquisition 739
NN Model of Monitoring Sleep Fidget 741
Precision Verification of Sleep Fidget Model 745
Conclusions 747
References 747
Minimization of Mizumoto Automata 748
Introduction 748
Mizumoto Automata and Their Equivalent Canonical Form 749
Minimization of NA 750
References 751
Transformation of Linguistic Truth Values During the Sensor Evaluation 753
Introduction 753
Basic Concepts and Hypotheses 754
Transformation Models 755
Point to Point Model 755
Fuzzy to Point Model 756
Point to Fuzzy Set Model 756
Fuzzy Set to Fuzzy Set Model 756
Example 757
Conclusions 758
References 759
Guaranteed Cost Control for a Class of Fuzzy Descriptor Systems with Time-Varying Delay 760
Introduction 760
Preliminaries and Problem Formulation 761
Main Results 762
Example 767
Conclusions 767
References 768
The Research and Simulation on the Walking Trajectory of the Hexapod Walking Bio-robot 769
Foreword 769
The Brief Introduction About the Integral Structure of the Bionic Hexapod Walking Robot 769
The Gait Theory Analyses on the Bionic Hexapod Walking Robot 770
The Trajectory Choices of Bionic Hexapod Walking Robot 771
The Moving Trajectory Simulation of the Bionic Hexapod Walking Robot 772
The Creation of Bionic Hexapod Walking Robot’s Feet-Tip Trajectory Curve 772
The Virtual Prototype Model Construction of Bionic Hexapod Walking Robot[7] 772
Bionic Hexapod Walking Robot’s Kinematic Inverse Solution 774
End 776
References 776
Research of Group Decision Consensus Degree Based on Extended Intuitionistic Fuzzy Set 777
Introduction 777
The Definition of Extended IFS 777
The Definition of Distance of Extended IFS 778
Example Analysis 780
Conclusions 781
References 781
Part VII Rough Sets and Its Application 782
A Novel Approach to Roughness Measure in Fuzzy Rough Sets 783
Introduction 783
Preliminaries 784
The Novel Approach to Roughness Measure in Fuzzy Rough Sets 785
An Example 787
Conclusions 788
References 788
Rough Communication of Dynamic Concept 789
Introduction 789
Two Direction S-Rough Sets and a - Generation of Two Direction Assistant Sets 790
Rough Communication of Dynamic Concept 791
Example 792
Conclusions 793
References 794
Some Entropy for Rough Fuzzy Sets 796
Introduction 796
Rough Fuzzy Sets 797
The Expression of Rough Fuzzy Sets 797
The Cardinalities of RFSs 798
Entropy for RFSs 799
Conclusions 805
References 805
A Fuzzy Measure Based on Variable Precision Rough Sets 806
Introduction 806
Basic Notions Related to Rough Sets 807
Pawlak Rough Sets 807
Information Systems 807
Variable Precision Rough Sets 808
A Fuzzy Measure Based on VPRS 809
Basic Notions of Fuzzy Sets 809
A Fuzzy Measure Based on VPRS 810
Conclusion 813
References 814
Rough Sets of System 816
Introduction 816
Rough Sets of System 817
Discussion About the Rough Sets of System 819
Some Properties of Rough Sets of System 820
Some Examples of Rough Sets of System 821
Rough Sets on the Real Line 821
Rough Sets of the Additive Group of Integers 822
Conclusions 823
References 823
Synthesis of Concepts Based on Rough Set Theory 824
Introduction 824
Rough Sets 825
Synthesis of Concepts Based on Rough Set Theory 825
Reduction Based on the Ideas of Synthesis of Concepts 828
Conclusion and Further Research 831
References 831
.-Tolerance Relation-Based RS Model in IFOIS 833
Introduction 833
Basic Theories 834
Incomplete Information System 834
Fuzzy Objective Information System 835
.-Tolerance Relation 836
Rough Set Model in Incomplete and Fuzzy Objective Information System 837
The Concept of Incomplete and Fuzzy Objective Information System [19] 837
Rough Set Model 838
Precision Reduction in Incomplete and Fuzzy Objective Information System 840
Basic Theory of Precision Reduction 840
Precision Reduction Algorithm 842
Conclusion 842
References 843
Granular Ranking Algorithm Based on Rough Sets 845
Introduction 845
The Granular Ranking Algorithm 846
The Thought of Algorithm Designing 846
The Framework of Algorithm 848
The Description of Granular Ranking Algorithm 848
The Complexity of Algorithm 850
Experiment 850
Dataset 850
Hit Rate 851
The Result of Experiment 851
Conclusion 852
References 853
Remote Sensing Image Classification Algorithm Based on Rough Set Theory 854
Introduction 854
Principles of Rough Sets 855
Remote Sensing Image Classification Model Based on Rough Set Theory 856
Results of Experiment and Analysis 857
Conclusion 858
References 859
Topological Relations Between Vague Objects in Discrete Space Based on Rough Model 860
Introduction 860
Rough Model 861
The Definition of Region and Boundary of Raster Space 861
Definition of Rough Model 863
Study of Topological Relations Between Vague Objects Based on Rough Model and RCC-D-8 865
The Constraints of Lower and Upper Approximate Regions 865
Study of Topological Relations 867
Conclusions 867
References 868
Part VIII Application in Fuzzy Mathematics and Systems 870
A Least Squares Fuzzy SVM Approach to Credit Risk Assessment 871
Introduction 871
Methodology Formulation 872
SVM (By Vapnik [25]) 872
FSVM (By Lin and Wang [24]) 874
Least Squares FSVM 875
Experiment Analysis 877
Conclusions 879
References 879
Similarity Measures on Interval-Valued Fuzzy Sets and Application to Pattern Recognitions 881
Introduction 881
Degree of Similarity Between IVFSs and Similarity Measures 882
Applications of the Similarity Measures to Pattern Recognitions 887
References 889
Updating of Attribute Reduction for the Case of Deleting 890
Introduction 890
Preliminaries 891
Improvement of Discernibility Matrix and Updating of a Core 892
Updating Principle of Attribute Reduction 894
Updating Algorithm of Attribute Reduction Based on Discernibility Matrix 895
Conclusions 898
References 898
The Research of the Exposition Economy Model 900
Introduction 900
Investment Multiplier of Exposition 900
The Value of Development Potential of a City’s Exposition Economy 902
The Pull Model of Exposition Economy on National Economy 903
The Theoretical Analysis of the Model 904
Conclusion 906
References 907
A Region-Based Image Segmentation Method with Kernel FCM 908
Introduction 908
Region Segmentation Process 909
Integrated Feature Extraction 909
Extracting Texture Features 909
Extracting Other Features 911
Region-Based Color Image Segmentation 911
The Number of the Optimal Clusters 912
Label and Segment Image 913
Experiment Results 915
Conclusion and Future Work 916
References 916
An Efficient Threshold Multi-group-Secret Sharing Scheme 917
Introduction 917
The Proposed Scheme 918
System Parameters 918
Secret Distribution 918
Secret Reconstruction 920
Numerical Example 921
Analyses and Discussions 922
Security Analysis 922
Performance Analysis 923
Conclusions 924
References 924
A Morphological Approach for Granulometry with Application to Image Denoising 925
Introduction 925
Fuzzy Logical Operators 926
Operations of Fuzzy Sets 926
Convex Fuzzy Sets 929
Granulometry 931
Experiment Results 933
Conclusion 934
References 935
A Hybrid Decision Tree Model Based on Credibility Theory 936
Introduction 936
Credibility Theory 937
Hybrid Decision Trees Model 938
Fuzzification of Numerical Numbers 938
Hybrid Decision Trees Model 940
Experimental Results and Discussion 941
Experimental Results 941
Discussion 943
Conclusion 944
References 944
A Region-Based Image Retrieval Method with Fuzzy Feature 946
Introduction 946
Image Segmentation 947
Region Fuzzy Feature Extraction 948
Similarities Between Images Computation 950
Experiment Results and Analysis 951
Conclusions and Further Work 953
References 954
Association Rule Mining of Kansei Knowledge Using Rough Set 955
Introduction 955
Frameworks 956
Rough Set Theory 956
Review and Background 956
Definition 957
Reduction and Core Computing 958
Association Rule Mining Based on Rough Set 959
Association Rule Definition 959
Association Rule Algorithm Using Rough Set 960
Case Study 960
Product Knowledge Representation System Construction 960
Attributes Reduction 961
Strong Rule Extracting 962
Conclusion and Future Works 963
References 963
A Survey of Fuzzy Decision Tree Classifier Methodology 965
Introduction 965
Preliminaries 966
Potentials and Problems with Fuzzy Decision Tree Classifiers 967
Special Issues of a Fuzzy Decision Tree Classifier 968
Attribute Selection Criteria in Fuzzy Decision Trees 969
Inference for Decision Assignment 970
Stopping Criteria 971
Summary and Conclusions 972
References 973
The Optimization for Location for Large Commodity’s Regional Distribution Center 975
Problem Statement 975
The Model Hypothesis and Data Processing 976
The Theory and the Algorithm of Optimization Model for Location 977
The Calculation Result and Processing 983
Conclusion 984
References 985
Fuzzy Evaluation of Different Irrigation and Fertilization on Growth of Greenhouse Tomato 986
Introduction 986
Materials and Methods 987
Experimental Materials 987
Experimental Design 987
Experimental Method 987
Sampling Collection and Analysis 989
Result and Analysis 989
Confirm of Model Fuzzy Synthetic Evaluation 989
The Solve of Fuzzy Synthetic Evaluation Model 990
The Result of Fuzzy Synthesis Evaluation Model 991
Conclusion 992
References 992
The Solution of Linear Programming with LR-Fuzzy Numbers in Objective Function 994
Introduction 994
Preliminaries 995
Fuzzy Linear Programming Problem and Fuzzy Max Order 996
Possibility and Necessity Maximization Problems 1000
Numerical Examples 1003
References 1004
On Relationships of Filters in Lattice Implication Algebra 1006
Introduction 1006
Preliminaries 1007
$FL$-Filter of Lattice Implication Algebra 1008
On FL-Filter and NF-Filter of Lattice Implication Algebra 1010
Conclusions 1013
References 1013
Study on Adaptive Fuzzy Control System Based on Gradient Descent Learning Algorithm 1015
Introduction 1015
How to Design a General Fuzzy Control System 1016
Adaptive Fuzzy Control Algorithm 1017
System Structure 1017
Adaptive Control Algorithm 1017
Fuzzy Control Rules 1019
Simulation Results and Discussions 1021
Step Response 1021
Ramp Response 1023
Acceleration Response 1023
Sine Response 1023
Discussions 1024
Stability Discussion 1025
Conclusions 1025
References 1026
Uncertainty Measure of Fuzzy Rough Set 1027
Introduction 1027
Prelimilary 1027
Rough Entropy of Fuzzy Rough Set 1029
Information Entropy and Rough Entropy of Fuzzy Knowledge R 1029
Rough Entropy of Fuzzy Rough Set 1030
Conclusions 1032
References 1032
Author Index 1034