Quantitative Logic and Soft Computing (eBook)

Title 1
Foreword 5
Preface 7
Organization 9
Contents 11
Keynote Speakers 11
Learning Structure of Human Behavior Patterns in a Smart Home System 18
Introduction 18
Understanding of Human Behavior Patterns in a Smart Home Environment 21
Activity Recognition and Its Applications 21
Understanding of Irregular Behavior Patterns 22
Life-Long and Non-supervised Learning of Human Behavior Patterns in a Smart Home Environment 22
Life-Long Learning of Human Behavior Patterns 23
Non-supervised Learning of Human Behavior Patterns 24
Remarks on a Future Smart Home System for the Aged and the Disabled 25
Conclusion 27
References 28
Modeling the Degree of Truthfulness 33
Introduction 34
Linguistic Logic 38
Representations for Linguistic Truth Value 39
MIN and MAX Operators of Linguistic Truth Values 40
Natural Operators for Linguistic Logic 41
Linguistic Truth Relation by a Linguistic Implication 46
Linguistic Logic Propositions 46
Linguistic Implication 48
Linguistic Truth Relation 50
Linguistic Approximated Reasoning [LAR] 51
Concluding Remarks 53
References 54
A Nonlinear Integral Which Generalizes Both the Choquet and the Sugeno Integral 55
Motivation 55
Universal Integrals 57
A Construction Method 60
Restriction to the Unit Interval 62
References 65
On Virtues of Many-Valued (Fuzzy) Type Theories 69
Introduction 69
TruthValues for FTT 70
Virtues of Fuzzy Type Theory 72
Virtue 1: FTT has a Simple and Highly Uniform Syntax 72
Virtue 2: Semantics of FTT Is Based on a Small Collection of Well-Established Ideas 75
Virtue 3: FTT Is a Highly Expressive Logic 77
Virtue 4: There Are Practical Extensions of FTT That Can be Effectively Implemented 79
Conclusion 83
References 83
Semilinear Space, Galois Connections and Fuzzy Relation Equations 86
Introduction 86
Idempotent Semilinear Spaces 87
Galois Connections in Semilinear Spaces 89
Systems of Fuzzy Relation Equations and Their Semilinear Analogs 89
Systems of Equations in Semilinear Spaces $/mathcal{L}^m_{/vee}$ and $/mathcal{L}^n_{/wedge}$ 90
System of Equations in Semilinear Space $/mathcal{L}^m_{/vee}$ 90
Solvability in Terms of Galois Connection 91
References 93
Quantitative Logic: A Quantitative Approach to Many-Valued Logics 95
Introduction 95
Truth Degrees of Formulas 97
Truth Degrees of Propositions in Classical Logic 97
Truth Degrees of Propositions in $n$-Valued Logics 98
Truth Degrees of Propositions in Fuzzy Propositional Logic 99
Recent Developments 99
Similarity Degrees between Propositions 101
Entailment Degrees of Propositions from Theories 102
References 104
D-Completions of Net Convergence Structures 106
Introduction 106
Universal K-Fications in Topological Categories 107
Net Convergence Spaces 109
Niceness Conditions 115
Iterated-Limit Spaces 118
$d$-Spaces 119
Conclusion 122
References 123
Quantitative Logic 11
Modal $R_{0}$-algebra-valued Modal Logic System M$/mathcal {L}$$^{/ast}$ 124
Introduction 124
Preliminaries 125
Modal $R_{0}$-Algebras 126
The M$R_{0}-Algebra-Valued Modal Logic System M$/mathcal {L}$$^{/ast}$ 127
Semantics of System M$/mathcal {L}$$^{/ast}$ 127
Syntactics of System M$/mathcal {L}$$^{/ast}$ 129
Completeness of System M$/mathcal {L}$$^{/ast}$ 130
Conclusions 132
References 133
Deduction Theorem for Symmetric Cirquent Calculus 134
Introduction 134
Definition 135
Deduction Theorem 135
Conclusion 138
References 138
Equilateral Polygons in Classical Logic Metric Space 140
Introduction 140
Basic Concepts 141
Equilateral Polygons on the Classical Logic Metric Space 143
The Characters of the Equidistant Transform on the Space of $([F(S)],/rho)$ 146
Conclusion 146
References 147
Reflexive Transformation in $L^*$-Logic Metric Space 148
Introduction 148
Preliminaries 149
Reflexive Transformation 150
Truth Degree, Similarity Degree and Ppseudo-Distance of $L^*$ under the Reflexive Transformation $/varphi$ 151
Approximate Reasoning of $L^*$ under the Reflexive Transformation $/varphi$ 152
Reflexive Transformation $/varphi^*$ on $L^*-$Lindenbaum Algebra and Its Properties 154
Conclusion 156
References 156
A Quantitative Analysis of Rough Logic 158
Introduction 158
Pre-rough Algebra and Pre-rough Logic PRL 160
Rough(Upper, Lower) Truth Degrees of Rough Formulas 162
Concluding Remarks 168
References 168
Applying Association Rules to e-Reduction of Finite Theory in Two-Valued Propositional Logic 170
Introduction 170
$/varepsilon$-Reduction of Theory 171
Judgment of $/varepsilon$-Reduction of Theory $/Gamma $ and Some Properties 174
Methods to Explore the $/varepsilon$-Reduction 175
Conclusion 177
References 178
A Family $I_{L/Pi GN(q,p)}$ of Implication Operators and Triple I Methods Based on It 179
Introduction 179
Preliminaries 180
Family $T_{L/Pi GN(q,p)}$ of t-Norms and Its Residual Family $I_{L/Pi GN(q,p)}$ of Implication Operators 181
Triple I Method on FMP (FMT) Based on the Family ${I_{(q,p)}}- L/Pi GN$ of Implication Operators 185
Conclusion and Expectation 186
References 187
The Properties of Normal R_0 Algebras 188
Introduction 188
Preliminaries 189
The Existence of Normal R0 Algebras and Their Properties 190
The Filters of Normal $R0$ Algebras 194
Conclusion 195
References 195
A Splitting Algorithm Based on Soft Constraints for the Computation of Truth Degree in Quantitative Logic 197
Introduction 197
Preliminaries 200
The Concept of Ttruth Degree of Formulas (Wang [4-5]) 200
Soft Constraint Satisfaction Problems (SCSPs) 201
A Splitting Algorithm for Computing the Truth Degree of Formulas in Quantitative Logic 202
Characterizations of “Truth Degree” with Concepts from Constraint Theory 202
A Splitting Algorithm for Computing the Truth Degree of Formulas in Quantitative Logic 203
Conclusion 206
References 207
Some Remarks on a Few Approximate Reasoning Patterns 209
Introduction 209
Preliminaries 210
Approximate Reasoning in Randomized Quantified Logic 212
Conclusion 215
References 215
The Interval-Valued Truth Degree Theory of the Modal Formulas 217
Introduction 217
Preliminaries 218
The Interval-Valued Truth Degree 220
The Standard Model 220
The Interval-Valued Truth Degree 222
The Harmonious Theorem 223
References 224
T-Seminorms and Implications on a Complete Lattice 225
Introduction 225
Adjoint Mappings on a Complete Lattice 226
T-Seminorms and Their Residual Implications 228
T-Seminorms Induced by Implications on a Complete Lattice 231
Conclusion 234
References 235
Reversibility of Triple I Method Based on /L ukasiewicz and Goguen Implication 236
Introduction 236
Preliminaries 237
Reversibility of Triple I Method 238
Conclusion 240
References 241
Random Truth Theory of Proposition Logic and Its Application 242
Introduction 242
Random Function Derived from Logic Formulas 243
Random Truth Degree of Logic Formulas 244
Similarity Degree and Pseudo-metric among Formulas 249
Approximation Reasoning Based on Truth Degrees 250
Conclusion 252
References 253
Soft Set Based Approximate Reasoning: A Quantitative Logic Approach 254
Introduction 254
Preliminaries 255
The Degree of the Truth of Formulas (By Wang and Zhou [6]) 255
Approximate Reasoning Based on Soft Sets 258
Formulas over a Soft Set 258
Valuation and Semantic Interpretation of Formulas 258
Evaluate the Soundness of Formulas 259
Decision Rules 260
Rule Evaluation 262
An Illustrative Example 263
Conclusion 264
References 264
Left(Right)-Continuity of t-Norms on the Metric Lattice 265
Introduction 265
Preliminaries 266
A Necessary and Sufficient Condition for t-Norms on L Being Left(right)-Continuous 267
Conclusion 269
References 269
Predicate Formal System $/forall/mathcal {UL}_{h/in(0,1]}^{/triangle }$ and Its Completeness 270
Introduction 270
Predicate Formal System $/forall/mathcal {UL}^{/triangle }_{h/in (0,1]}$ 271
Completeness of $/forall/mathcal {UL}^{/triangle }_{h/in (0,1]}$ 275
Some Extension Logics of $/forall/mathcal {UL}^{/triangle }_{h/in (0,1]}$ 277
Conclusion 278
References 279
The Degree of the Quasi-similarity and the Pseudo-metric between Predicate Formulae 280
Introduction 280
Preliminaries 281
Basic Concepts and Symbols in the Present Paper 281
The Degree of the Quasi-truth of Formulae 282
The Degree of the Quasi-similarity between Formulae 284
The Relative Degree of the Similarity between Formulae 284
The Degree of the Quasi-similarity between Formulae 285
The Pseudo-metric on the Set $F$ of Formulae 289
Conclusion 290
References 290
Conditional Truth Degree of a Logic Theory in Two-Valued Propositional Logic System and Its Application 291
Introduction 291
Preliminaries 292
Conditional Truth Degrees of Theories 293
Relations of $/sigma$-Truth Degrees, as well as $/sigma$-ConsistencyDegrees and $/sigma$-Divergency Degrees of Logic Theories 295
Conclusion 301
References 301
$PIMP$-Filters of $R_{0}$-Algebras 303
Introduction 303
Preliminaries 303
$PIMP$-Filters 304
References 308
Quantitative Logic Theory in G/"{o}del System 309
Introduction 309
Preliminaries 309
Truth Degree of Formulas in G/"{o}del Logic System 310
Resemblance Degree between Formulas in G/"{o}delLogic System 312
Pseudo-metric between Formulas in G/"{o}del LogicSystem 313
References 314
Finite Topological Models of Modal Logic Systems S4 and S5 316
Introduction 316
Preliminaries 317
Finite Models of Systems S4 and S5 318
Finite Topological Models of System S4 and S5 321
References 324
Researches on (n) Truth Degrees in Modal Logic 325
Introduction 325
Preliminaries 326
The $(n)$ Truth Degree of a Modal Formula 329
Metric Spaces of $(n)$ Modal Logic 331
References 334
Lattice-Valued Truth Degree in /L ukasiewicz Propositional Fuzzy Logic 335
Introduction 335
Preliminaries 336
Lattice-Valued Truth Degree 337
Conclusion 340
References 340
Fuzzy Sets and Systems 13
Decomposition Theorems and Representation Theorems on the IVIFS 342
Introduction 342
Preliminary 343
Decomposition Theorems 346
Representation Theorems 349
References 351
Approximation of Fuzzy Neural Networks to Fuzzy-Valued Measurable Function 353
Introduction 353
Preliminaries 353
Approximation in Fuzzy Mean by Regular Fuzzy Neural Networks 354
References 359
Fuzzy Divergences Based on Tsallis Relative Entropy 361
Introduction 361
Entropy and Distance Measure 362
Fuzzy Divergence Based on Tsallis Relative Entropy 363
The Novel Tsallis Fuzzy Divergences 363
The Properties of the Tsallis Fuzzy Divergences 364
Conclusion 370
References 370
Strong-II $N_{/beta}$-Compactness in $L$-Topological Spaces 371
Introduction 371
Preliminaries 371
Strong-II $N_{/beta}$-Compactness 372
Relations between Strong-II $N_{/beta}$-Compactness and Other Compactness 374
References 375
Some Notes on K-Harmonic Means Clustering Algorithm 377
Introduction 377
FCM and KHM$_p$ 378
FCM 378
KHM and KHM$_P$ 379
The Relationship between General FCM(GFCMP) and KHM$_p$ and the Analysis on Robustness Property of GFCM$_P$ 379
General FCM: GFCM$_P$ 379
The Reformulation of GFCM$_P$ 380
Analysis on the Robust Property of GFCMP for Different Value of Parameter $p$ 381
Numerical Experiments and Analysis 383
Conclusion 385
References 385
On Fuzzy Prime Filters of Lattice H Implication Algebras 387
Introduction 387
Preliminaries 388
Fuzzy Prime Filters of LHIA 389
Conclusion 394
References 394
Numerical Characteristics of Intuitionistic Fuzzy Sets 396
Introduction 396
Preliminaries 397
The Relationship among Four Numerical Characteristics 399
Conclusion 404
References 405
The Study of Time Division Scheduling Mechanisms for Zigbee Cluster-Tree Wireless Sensor Networks 406
Introduction 406
Problem Discription 406
Beacon Frame Scheduling Mechanisms for the Time Division Approach 408
Superframe Duration Scheduling algorithm for the Time Division Approach 408
Superframe Duration Scheduling with Coordinator Grouping 409
Implementation Introduction 411
Conclusion 412
References 412
Discovery of S-Rough Decision Law and Its Relation Metric 413
Introduction 413
Two Direction S-Rough Decision 414
Decision Law Generation and F -Decision Law Relation Metric 415
Relation Metric and the Discovery of F -Rough Decision Laws 419
The Application of $F$ -Rough Decision Law 421
Conclusions 423
References 424
On $/odot$-Ideals and Lattices of $/odot$-Ideals in Regular Residuated Lattices 425
Introduction 425
Basic Notions and Related Results 426
/large The $/odot$-Operation and $/odot$-Ideals in Residuated Lattices 427
/large Generated $/odot$-Ideals by a Nonempty Subset 430
/large The $/odot$-Ideal Lattice of a Regular Residuated Lattice 432
References 433
A Fuzzy System with Its Applications Based on MISS 435
Introduction 435
Data Structures of Fuzzy MISS 436
Logical Tree Data Structures 436
Logical Linear Table Data Structures 436
The Technical Architecture of the System 437
The Technical Architecture and Implemented Functions of the System 437
The Constructions of the System 438
The Security of Fuzzy MISS 441
The Implementing Scheme of Fuzzy MISS 442
Client Connects Server 442
Server Returns to Client 443
The Data Stream between Inquiry Client and Server 443
Conclusion 444
References 445
Particle Swarm Optimization of T-S Fuzzy Model 446
Introduction 446
T-SModel 447
Pruning Algorithm 447
PSO 447
Description of the Algorithm 448
The Execution of the Algorithm 449
Numerical Simulations 449
Conclusion 450
References 450
Inverse Limits of Category CL 452
Definitions and Preliminaries 452
The Closed-Set-Latticefies of Join-Semilattice 453
Inverse Limits of Category CL 454
References 457
Relative Density Weights Based Fuzzy C-Means Clustering Algorithms 458
Introduction 458
Fuzzy C-Means (FCM) Algorithms 459
Relative Density Weights Based Fuzzy C-Means Clustering Algorithms 460
Clusters-Independent Relative Density Weights Based Fuzzy C-Means (CIRDWFCM) Clustering Algorithm 461
Clusters-Dependent Relative Density Weights Based Fuzzy C-Means (CIRDWFCM) Clustering Algorithm 462
Experimental Results and Analysis 463
Experimental Data Descriptions 463
Clustering Results Evaluation 464
Experimental Results and Analysis 464
Conclusions 465
References 465
A Generalization of the Lowen Functor $/omega_L$ 466
Introduction 466
Preliminaries 467
$/prec$-Lower Semicontinuous Functions 468
$/omega_L=/omega_L^/ll$ for Distributive Continuous Lattices 469
References 470
Remote Sensing Image Classification Based on Fuzzy Entropy Triple I Algorithm 471
Introduction 471
Minimum Distance Discrimination Method 472
Traditional Bayes Criterion 473
Fuzzy Entropy Triple I Algorithm 474
The Basic Idea of Fuzzy Reasoning 474
Fuzzy Entropy Triple I Algorithm 475
Experimental Results 477
Conclusion 480
References 480
Formalized Solutions for Reverse Triple-I under Theory of Truth Degree 481
Introduction 481
Preliminaries 482
n-Valued Logic Systems: ${ /L_n}$ and ${L_n}^*$ 482
About the Theory of Truth Degree 482
Formalized Solutions for Problems of Reverse Triple I 483
Conclusion 487
References 488
Properties of $L$-Extremally Disconnected Spaces 489
Introduction and Preliminaries 489
Some Properties of a-open, Pre-open and Semi-pre-open Sets 490
$L$-Extremally Disconnected Spaces 492
References 496
Fuzzy Cluster Analysis of Regional City Multi-level Logistics Distribution Center Location Plan 497
Introduction 497
Fuzzy Clustering Analysis Preparation 498
Fuzzy Clustering Analysis Procedure 501
Planning Instance 503
Conclusion 505
References 506
The Establishment and Reliability Analysis of the Majorized Model of a Kind of Fuzzy Multidimensional Synthetical Decision 507
Introduction 507
Research on BFMSD 508
Application Examples 511
Conclusion 515
References 515
$/omega/theta$-Countability in an $L/omega$-Space 516
Introduction 516
Preliminary Concepts and Notations 516
The Second $/omega/theta$-Countable Space 518
TheFirst $/omega/theta$-Countable Space 520
Conclusion 523
References 523
Using Two-Level Fuzzy Pattern Recognition in the Classification of Convex Quadrilateral 524
Introduction 524
Some Auxiliary Definitions and Basic Formulas 525
The Two-Level FPR for Convex Quadrilateral 525
Electing the Characteristics of the Objects 526
Constructing the Membership Function of the First-Level FPR [5-6] 526
Judgments of the First-Level FPR [7-9] 527
Constructing the Membership Function of the Two-Level FPR 527
Judgments of the Two-Level FPR 528
The Algorithms 528
The Analysis of Numerical Experiments and Results 529
Conclusion 530
References 530
Moore-Smith $/omega/theta$-Convergence Theory in $/omega$-Molecular Lattices 532
Introduction 532
Preliminaries 532
$/omega/theta$-Convergence of Molecular Nets on $/omege$-MLs 534
$/omega/theta$-Convergence of Ideals on $/omega$-MLs 536
The Relationships between $/omega/theta$-Convergence of Molecular Nets and Ideals 538
Some Applications of $/omega/theta$-Convergence Theory in $/omega$-MLs 539
Conclusion 540
References 540
Some Properties about $L/omega$-Quotient Spaces and $L/omega$-Product Spaces 541
Introduction 541
Some Properties of $/omega$-Sets 542
Quotient Space and Its Properties 545
Product Space and Its Properties 546
References 547
Self-adaptive Fuzzy PID Controller for Airborne Three-Axis Pan-Tilt 549
Introduction 549
Design and Realization of Fuzzy PID Controller 550
Three Axis Self-Stabilization Pan-tilt 550
Traditional PID Control 550
Traditional Fuzzy Control 551
Structure and Adjusting Principle of Fuzzy PID Controller 552
Establishment of Membership Function and Fuzzy Control Rules 553
System Simulation and Analysis 554
Conclusion 555
References 555
$/omega$-Convergence Theory of Filters in $/omega$-Molecular Lattices 556
Introduction 556
$/omega$-Convergence of Filters 557
Some Applications of $/omega$-Convergence of Filters 561
References 562
Soft Computing 15
The Structures and Constructions of Power Group 564
Introduction 564
Definitions and Constructions of Power Group 565
Relationship between Power Groups and Common Groups 567
Characterization of Power Groups by Common Groups 569
Structures of Power Groups 571
Conclusion 573
References 573
P-Sets and Applications of Internal-Outer Data Circle 575
Introduction 575
P-Sets and Its Set Pair Structure 576
Internal-Outer Data Circle and Dynamic Data Restore 579
Data Identification of System State and Its Application 582
Discussion 584
References 584
Convergent Properties of Arbitrary Order Neural Networks 586
Introduction 586
Preliminaries 587
MainResults 588
References 593
Analyzing and Predicting Interannual Variability in Nearshore Topographic Field on Large Scales by EOF and ANN 595
Introduction 595
Data and Methods 597
Spatial Pattern of Eigenvectors 599
Fitting and Predicting Topographic Field 600
Summary and Conclusion 603
References 603
$f$-Model Generated by $P$-Set 605
Introduction 605
$P$-Set and Its Structure 606
$f$-Model and Generation of $f-t$ Order Unilateral Dynamic Model 607
Application in Information System Prediction 610
Conclusion 611
References 611
Mining Fuzzy Association Rules by Using Nonlinear Particle Swarm Optimization 613
Introduction 613
Preliminaries: The 2-Tuples Fuzzy Association Rule 614
The Definition of Fuzzy Association Rule 614
The 2-Tuples Linguistic Representation 615
NPSO-Based Method to Obtain the Membership Functions 616
Nonlinear Particle Swarm Optimization (NPSO) 616
MFs Codification 616
Fitness Evaluation 618
Algorithm 618
Experiment Results 618
Parameter Settings 619
Results and Discussions 619
Conclusion 621
References 621
On $(/bar/in,/bar/in/vee /bar q)$-Fuzzy Filters of Residuated Lattices 623
Introduction 623
Preliminaries 624
$(/bar/in,/bar/in/vee /bar q)$-Fuzzy Filters of Residuated Lattices 624
$(/bar/in,/bar/in/vee /bar q)$-Fuzzy Regular Filters 627
Relations among Some Generalized Fuzzy Filters 630
References 632
On the Interpolation by Entire Function of the Exponential Type 633
Introduction 633
Interpolation Problem and Its Main Conclusion 634
References 640
A Multi-objective Algorithm Based on Discrete PSO for VLSI Partitioning Problem 642
Introduction 642
Problem Description 643
Proposed Algorithm 644
Encoding Scheme 644
Crossover and Mutation 644
DPSO Algorithm 645
Local Search 646
Multi-objective Approach 647
Algorithm Description 648
Experimental Results 648
Conclusion 650
References 651
Generation and Recovery of Compressed Data and Redundant Data 652
Introduction 652
Prerequisites 653
The Generation-Recovery of $F$ -Compressed Data and $F$ -Redundant Data 654
Measures of F -Compressed Data and $F$ -Redundant Data 659
Application of $F$ -Compressed Data and $F$ -Redundant Datain Communication System 660
Discussion 661
References 661
On the Decomposition of Distribution Function by Using Hausdorff Calculus 663
Introduction 663
Basic Concepts 664
Main Results 665
An Example 668
References 671
A New Artificial Glowworm Swarm Optimization Algorithm Based on Chaos Method 672
Introduction 672
The Basic GSO 673
Chaos Method 675
GSO with Chaotic Local Search (CLS-GSO) 676
Simulation Experiments 678
Conclusion 681
References 681
Another Metric Model for Trustworthiness of Softwares Based on Partition 683
Introduction 683
Criteria for Trustworthiness 684
A Metric Model for Trustworthiness of Softwares Based on Partition 686
A Small Simulation 691
Conclusion 692
References 693
Multi-random Relation and Its Applications 694
Introduction 694
Extension to Multi-random Relation Algebra 695
Usual Relation 695
Multi-random Relation Algebra 696
Applications 699
Conclusion 700
References 701
An Algorithm of Context Rules Generation Based on Virtual Environment 702
Introduction 702
Problems and Solutions 703
Preliminaries 704
Automatic Generation of Context Rules 705
Context Decision Tree Based on Modified ID3 706
Example Analysis for Generation of Context Rules 708
Experiment and Analysis 710
Conclusion 712
References 712
A Classification Method of Grassland and Trees in Remote Sensing Image 714
Introduction 714
Bilateral Filter 715
Color Edge Detection 716
Region Filling 717
Experimental Results and Analysis 718
Conclusion 720
References 720
$P$-Set and Its $(f, ^¯ f)$-Heredity 722
Introduction 722
$P$-Set and Its Structure [1, 2] 724
The $f$ -Heredity and Its Measurement of Interior $P$-Set 725
The $^¯ f$-Heredity of Exterior $P$-Set and Its Measurement 727
Conclusion 729
References 730
Notes on Two-Sided Quantales 731
Introduction and Preliminaries 731
TheQuantale $Idl(L)$ 733
Free Two-Sided Quantales 735
The Coproduct of Commutative Two-Sided Quantales 737
References 739
Counting the Solutions of a System of Equations over Finite Field is NP-Hard 740
Introduction 740
MainResults 742
Conclusion 743
References 744
The Stability of BAM Networks with Delayed Self-feedback and Impulses 745
Introduction 745
Preliminaried 746
Existence and Uniqueness of Equilibrium 748
Exponential Stability of Equilibrium 749
An Illustrative Example 752
References 753
The Selection and Rational Evaluation of Surface Mining Technology System 754
Introduction 754
Classifiable System of Surface Mining Technology and Its Influencing Factors 755
Rational Evaluation System of Surface Mining Technology 756
Conclusion 760
References 761
The Blow-Up of Discrete Solution for NLS Equation with Potential 762
Introduction 762
Fully Discrete Spectral Method 763
Conservation Laws and Sufficient Conditions for Blow-Up of Approximate Solution 764
Conclusion 771
References 771
$P$-Sets and $F$ -Data Selection-Discovery 773
Introduction 773
The Structure and Characteristic of $P$-sets 774
$F$ -Data and $F$ -Data Selection Theorem 777
Application of $F$ -Data Selection 779
Discussion 781
References 781
AI-VCR Addition Computing without Overflowing 782
Forewords 782
Numbers Computation of VCN & FCN
AI-VCR, VCO, CN, PM, CP and PC 785
AI-VCR Addition Computing with VCO 786
Discussion of AI-VCR Addition Computing with VCO 788
Conclusion 789
References 790
A New Face Recognition Algorithm Based on DCT and LBP 792
Introduction 792
Face Representation 793
DCT 794
LBP 795
Feature Level Fusion 796
Experiment 797
Conclusions 798
References 798
An Building Edge Detection Method Using Fuzzy SVM 800
Introduction 800
Construct Edge Point Feature 801
SVM 802
Fuzzy SVM 803
Experiments and Results 805
Image Edge Detection Steps Base on FSVM 805
Simulation and Results 805
Conclusion 807
References 807
Author Index 808