Table of Contents
1 Prepare Knowledge 1
1.1 Fuzzy Sets 1
1.2 Operations in Fuzzy Sets 5
1.3 α-Cut and Convex Fuzzy Sets 9
1.4 Fuzzy Relativity and Operator 12
1.5 Fuzzy Functions 18
1.6 Three Mainstream Theorems in Fuzzy Mathematics 21
1.7 Five-Type Fuzzy Numbers 27
2 Regression and Self-regression Models with Fuzzy Coefficients 33
2.1 Regression Model with Fuzzy Coefficients 33
2.2 Self-regression Models with (·, c)-Fuzzy Coefficients 39
2.3 Exponential Model with Fuzzy Parameters 44
2.4 Regression and Self-regression Models with Flat Fuzzy Coefficients 50
2.5 Linear Regression with Triangular Fuzzy Numbers 57
3 Regression and Self-regression Models with Fuzzy Variables 63
3.1 Regression Model with T - Fuzzy Variables 63
3.2 Self-regression Model with T - Fuzzy Variables 71
3.3 Regression Model with (·, c) Fuzzy Variables 76
3.4 Self-regression with (·, c) Fuzzy Variables 78
3.5 Nonlinear Regression with T-fuzzy Data to be Linearized 85
3.6 Regression and Self-regression Models with Flat Fuzzy Variables 91
4 Fuzzy Input-Output Model 95
4.1 Fuzzy Input-Output Mathematical Model 95
4.2 Input-Output Model with T-Fuzzy Data 98
4.3 Input-Output Model with Triangular Fuzzy Data 108
5 Fuzzy Cluster Analysis and Fuzzy Recognition 117
5.1 Fuzzy Cluster Analysis 117
5.2 Fuzzy Recognition 127
6 Fuzzy Linear Programming 139
6.1 Fuzzy Linear Programming and Its Algorithm 139
6.2 Expansion on Optimal Solution of Fuzzy Linear Programming 146
6.3 Discussion of Optimal Solution to Fuzzy Constraints Linear Programming 154
6.4 Relation between Fuzzy Linear Programming and Its Dual One 159
6.5 Antinomy in Fuzzy Linear Programming 165
6.6 Fuzzy Linear Programming Based on Fuzzy Numbers Distance 171
6.7 Linear Programming with L-R Coefficients 177
6.8 Linear Programming Model with T-Fuzzy Variables 182
6.9 Multi-Objective Linear Programming with T-Fuzzy Variables 187
7 Fuzzy Geometric Programming 193
7.1 Introduction of Fuzzy Geometric Programming 193
7.2 Lagrange Problem in Fuzzy Geometric Programming 201
7.3 Antinomy in Fuzzy Geometric Programming 206
7.4 Geometric Programming with Fuzzy Coefficients 214
7.5 Geometric Programming with (α, c) Coefficients 218
7.6 Geometric Programming with L-R Coefficients 224
7.7 Geometric Programming with Flat Coefficients 229
7.8 Geometric Programming with Fuzzy Variables 235
7.9 Dual Method of Geometric Programming with Fuzzy Variables 240
7.10 Multi-Objective Geometric Programming with T-Fuzzy Variables 248
8 Fuzzy Relative Equation and Its Optimizing 255
8.1 (<$>, <$>) Fuzzy Relative Equation 255
8.2 (<$>, ·) Fuzzy Relative Equation 261
8.3 Algorithm Application and Comparing in (<$>, ·) Relative Equations 266
8.4 Lattice Linear Programming with (<$>, ·) Operator 273
8.5 Fuzzy Relation Geometric Programming with (<$>, <$>) Operator 280
8.6 Fuzzy Relation Geometric Programming with (<$>, ·) Operator 286
9 Interval and Fuzzy Differential Equations 293
9.1 Interval Ordinary Differential Equations 293
9.2 Fuzzy-Valued Ordinary Differential Equations 299
9.3 Ordinary Differential Equations with Fuzzy Variables 306
9.4 Fuzzy Duoma Debted Model 309
9.5 Model for Fuzzy Solow Growth in Economics 315
9.6 Application of Fuzzy Economic Model 320
10 Interval and Fuzzy Functional and Their Variation 327
10.1 Interval Functional and Its Variation 327
10.2 Fuzzy-Valued Functional and Its Variation 332
10.3 Convex Interval and Fuzzy Function and Functional 338
10.4 Convex Fuzzy-Valued Function and Functional 345
10.5 Variation of Condition Extremum on Interval and Fuzzy-Valued Functional 350
10.6 Variation of Condition Extremum on Functional with Fuzzy Function 356
References 363
Index 373
