| Preface |
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1 | (20) |
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1 | (5) |
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1.2 Physical Significance for Cantor's Sets |
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6 | (2) |
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1.3 Background of Fuzzy Sets |
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8 | (6) |
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1.4 Definition and Operations of Fuzzy Sets |
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14 | (7) |
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20 | (1) |
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Chapter 2 Fuzzy Relations |
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21 | (45) |
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21 | (7) |
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2.2 Definition of Fuzzy Relations |
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28 | (3) |
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2.3 Projections and Cross-section' Projections of Relations |
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31 | (4) |
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2.4 Projections and Cross-section' Projections of Fuzzy Relations |
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35 | (4) |
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2.5 Cantor's Set Transformations |
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39 | (3) |
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2.6 Fuzzy Set Transformations |
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42 | (3) |
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2.7 Ternary Relations and Their Projections and Cross-section' Projections |
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45 | (5) |
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2.8 Fuzzy Ternary Relations and Its Projections and Cross-section' Projections |
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50 | (4) |
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2.9 Fuzzy Set Transformations Based on Fuzzy Ternary Fuzzy Relations |
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54 | (4) |
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2.10 On Zadeh's Extension Principle |
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58 | (8) |
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65 | (1) |
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66 | (27) |
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3.1 Structure of One-input One-output Fuzzy Systems |
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66 | (11) |
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3.2 Structure of Two-input One-output Fuzzy Systems |
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77 | (11) |
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3.3 Interpolation Mechanism of Fuzzy Systems |
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88 | (5) |
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91 | (2) |
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Chapter 4 Function Approximation Properties of Fuzzy Systems and Its Error Analysis |
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93 | (39) |
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93 | (1) |
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4.2 Structures of Fuzzy Systems |
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93 | (10) |
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4.3 Function Approximation Properties of Fuzzy Systems |
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103 | (7) |
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4.4 The Approximation Remainder Estimation |
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110 | (8) |
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4.5 Error Estimation between Fuzzy Systems sn(x) and fn(x) |
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118 | (12) |
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130 | (2) |
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131 | (1) |
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Chapter 5 Probability Representations of Fuzzy Systems |
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132 | (73) |
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5.1 Background of Birth of Fuzzy Systems |
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132 | (3) |
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5.2 Sketch of Fuzzy Systems |
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135 | (4) |
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5.3 Probability Significance of Fuzzy Systems |
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139 | (10) |
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5.4 Several Typical Probability Distributions |
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149 | (12) |
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5.5 Probability Representations of Double-input and Single-output Fuzzy Systems |
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161 | (7) |
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5.6 The Probability Representations of Multi-input Multi-output Fuzzy Systems |
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168 | (13) |
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5.7 A Conclusion on Uniform Distributions in Fuzzy Systems |
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181 | (2) |
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5.8 Probability Representations of Fuzzy Systems Constructed by Triple I Method |
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183 | (18) |
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201 | (4) |
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202 | (3) |
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Chapter 6 Fuzzy System Representations of Stochastic Systems |
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205 | (63) |
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205 | (1) |
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6.2 Sketch of Fuzzy Systems |
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205 | (3) |
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6.3 Fuzzy Reasoning Meaning of Stochastic Systems |
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208 | (14) |
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6.4 Fuzzy Reasoning Representations of Double-inputs Single-output Continuous Stochastic Systems |
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222 | (15) |
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6.5 Fuzzy Reasoning Representations of Discrete Stochastic Systems |
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237 | (6) |
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6.6 Reducibility in the Transformations between Fuzzy Systems and Stochastic Systems |
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243 | (6) |
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6.7 Uncertainty Systems with One Dimension Random Variables and their Representations |
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249 | (14) |
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6.8 Unification on Uncertainty Systems |
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263 | (1) |
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264 | (4) |
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266 | (2) |
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Chapter 7 The Normal Numbers of Fuzzy Systems and Their Classes |
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268 | (81) |
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268 | (5) |
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273 | (5) |
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7.3 R -- Fuzzy Implication Operations |
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278 | (1) |
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7.4 Fuzzy Systems Based on 1-Sets |
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279 | (11) |
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7.5 Normal Numbers of Fuzzy Systems |
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290 | (9) |
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7.6 Bernstein Fuzzy Systems |
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299 | (13) |
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7.7 Fitted Type Fuzzy Systems |
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312 | (4) |
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7.8 Hermite Fuzzy Systems and Collocation Factor Fuzzy Systems |
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316 | (17) |
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7.9 Normal Numbers of Hermite Fuzzy Systems |
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333 | (5) |
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338 | (6) |
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344 | (5) |
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346 | (3) |
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Chapter 8 Unified Theory of Classic Mechanics and Quantum Mechanics |
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349 | (68) |
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349 | (1) |
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8.2 Quantum Mechanics Representation of Classic Mechanics |
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350 | (37) |
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8.3 Duality of Mass Point Motion |
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387 | (8) |
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8.4 An Important Mathematical Conclusion Generated by Theorem 8.2.1 |
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395 | (3) |
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8.5 Approximation Theory Significance of Theorem 8.2.1 |
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398 | (15) |
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413 | (4) |
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415 | (2) |
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Chapter 9 Unification of Riemann Integral and Lebesgue Integral |
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417 | (31) |
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417 | (1) |
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418 | (7) |
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425 | (8) |
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9.4 Unification of Riemann Integral and Lebesgue Integral |
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433 | (3) |
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9.5 Riemann Integral of Continuous Functions |
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436 | (9) |
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445 | (3) |
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446 | (2) |
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Chapter 10 Fuzzy Systems with a Kind of Self-adaption |
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448 | (37) |
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10.1 Fuzzy Inference Relations with Self-adaption |
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448 | (7) |
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10.2 Fuzzy Systems with Self-adaption |
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455 | (7) |
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10.3 Approximation Properties of Fuzzy Systems with Self-adaption |
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462 | (13) |
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475 | (7) |
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482 | (3) |
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482 | (3) |
| Index |
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485 | |
Lisainfo e-raamatute kohta