Uncertain rule-based fuzzy logic systems introduction and new directions
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Upper Saddle River, NJ
Prentice Hall
2001
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| 245 | 1 | 0 | |a Uncertain rule-based fuzzy logic systems |b introduction and new directions |c Jerry M. Mendel |
| 264 | 1 | |a Upper Saddle River, NJ |b Prentice Hall |c 2001 | |
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| adam_text | UNCERTAIN RULE-BASED FUZZY LOGIC SYSTEMS: INTRODUCTION AND NEW
DIRECTIONS JERRY M. MENDEL UNIVERSITY OF SOUTHERN CALIFORNIA LOS
ANGELES, CA PH PTR PRENTICE HALL PTR UPPER SADDLE RIVER, NJ 07458
WWW.PHPTR.COM ISBN 0-13-040*^-3 CONTENTS PREFACE * XV *I PART 1:
PRELIMINARIES * 1 INTRODUCTION 3 1.1 RULE-BASEDFLSS 6 1.2 A NEW
DIRECTION FOR FLSS 8 1.3 NEW CONCEPTS AND THEIR HISTORICAL BACKGROUND 9
1.4 FUNDAMENTAL DESIGN REQUIREMENT 11 1.5 THE FLOW OF UNCERTAINTIES H
1.6 EXISTING LITERATURE ON TYPE-2 FUZZY SETS 12 1.7 COVERAGE 1.8
APPLICABILITY OUTSIDE OF RULE-BASED FLSS 18 1.9 COMPUTATION 18
SUPPLEMENTARY MATERIAL: SHORT PRIMERS ON FUZZY SETS AND FUZZY LOGIC 1.10
PRIMER ON FUZZY SETS 19 1.10.1 CRISP SETS 19 1.10.2 FROM CRISP SETS TO
FUZZY SETS 20 1.10.3 LINGUISTIC VARIABLES 22 1.10.4 MEMBERSHIP FUNCTIONS
23 1.10.5 SOME TERMINOLOGY 25 1.10.6 SET THEORETIC OPERATIONS FOR CRISP
SETS 26 1.10.7 SET THEORETIC OPERATIONS FOR FUZZY SETS 27 1.10.8 CRISP
RELATIONS AND COMPOSITIONS ON THE SAME PRODUCT SPACE 31 1.10.9 FUZZY
RELATIONS AND COMPOSITIONS ON THE SAME PRODUCT SPACE 33 1.10.10 CRISP
RELATIONS AND COMPOSITIONS ON DIFFERENT PRODUCT SPACES 36 1.10.11 FUZZY
RELATIONS AND COMPOSITIONS ON DIFFERENT PRODUCT SPACES 3 9 1.10.12
HEDGES 42 VI CONTENTS 1.10.13 EXTENSION PRINCIPLE 44 1.11 PRIMER ON FL
48 1.11.1 CRISPLOGIC 48 1.11.2 FROM CRISP LOGIC TO FL 53 1.12 REMARKS 59
EXERCISES 59 * 2 SOURCES OF UNCERTAINTY 66 2.1 UNCERTAINTIES IN A FLS 66
2.2.1 UNCERTAINTY: GENERAL DISCUSSIONS 66 2.2.2 UNCERTAINTY: IN A FLS 68
2.2 WORDS MEAN DIFFERENT THINGS TO DIFFERENT PEOPLE 70 EXERCISES 78 * 3
MEMBERSHIP FUNCTIONS AND UNCERTAINTY 79 3.1 INTRODUCTION 79 3.2 TYPE-1
MEMBERSHIP FUNCTIONS 79 3.3 TYPE-2 MEMBERSHIP FUNCTIONS 80 3.3.1 THE
CONCEPT OF A TYPE-2 FUZZY SET 81 3.3.2 DEFINITION OF A TYPE-2 FIIZZY SET
AND ASSOCIATED CONCEPTS 81 3.3.3 MORE EXAMPLES OF TYPE-2 FUZZY SETS AND
FOUS 91 3.3.4 UPPER AND LOWER MEMBERSHIP FUNCTIONS 93 3.3.5 EMBEDDED
TYPE-2 AND TYPE-1 SETS 98 3.3.6 TYPE-1 FUZZY SETS REPRESENTED AS TYPE-2
FUZZY SETS 102 3.3.7 ZERO AND ONE MEMBERSHIPS IN A TYPE-2 FUZZY SET 102
3.4 RETURNING TO LINGUISTIC LABELS 102 3.5 MULTIVARIABLE MEMBERSHIP
FUNCTIONS 105 3.5.1 TYPE-1 MEMBERSHIP FUNCTIONS 105 3.5.2 TYPE-2
MEMBERSHIP FUNCTIONS 107 3.6 COMPUTATION 107 EXERCISES 108 TABLE OF
CONTENTS VII * 4 CASESTUDIES 110 4.1 INTRODUCTION 110 4.2 FORECASTING OF
TIME-SERIES 110 4.2.1 EXTRACTING RULES FROM THE DATA 112 4.2.2
MACKEY-GLASS CHAOTIC TIME-SERIES 115 4.3 KNOWLEDGE MINING USING SURVEYS
118 4.3.1 METHODOLOGY FOR KNOWLEDGE MINING 119 4.3.2 SURVEY RESULTS 121
4.3.3 METHODOLOGY FOR DESIGNING A FLA 122 4.3.4 HOWTOUSEAFLA 124
EXERCISES 126 PART 2: TYPE-1 FUZZY LOGIC SYSTEMS * 5 SINGLETON TYPE-1
FUZZY LOGIC SYSTEMS: NO UNCERTAINTIES 131 5.1 INTRODUCTION 131 5.2 RULES
132 5.3 FUZZY INFERENCE ENGINE 135 5.4 FUZZIFICATION AND ITS EFFECT ON
INFERENCE 138 5.4.1 FUZZIFIER 139 5.4.2 FUZZY INFERENCE ENGINE 139 5.5
DEFUZZIFICATION 142 5.5.1 CENTROID DEFUZZIFIER 143 5.5.2 CENTER-OF-SUMS
DEFUZZIFIER 143 5.5.3 HEIGHT DEFUZZIFIER 145 5.5.4 MODIFIED HEIGHT
DEFUZZIFIER 147 5.5.5 CENTER-OF-SETS DEFUZZIFIER 147 5.5.6 AN
INTERESTING FACT 148 5.6 POSSIBILITIES 149 VIII CONTENTS 5.7 FUZZY BASIS
FUNCTIONS 151 5.8 FLSS ARE UNIVERSAL APPROXIMATORS 156 5.9 DESIGNING
FLSS 157 5.9.1 ONE-PASS METHODS 160 5.9.2 LEAST-SQUARES METHOD 162 5.9.3
BACK-PROPAGATION (STEEPEST DESCENT) METHOD 164 5.9.4 SVD-QR METHOD 166
5.9.5 ITERATIVE DESIGN METHOD 168 5.10 CASE STUDY: FORECASTING OF
TIME-SERIES 169 5.10.1 ONE-PASS DESIGN 171 5.10.2 BACK-PROPAGATION
DESIGN 171 5.10.3 A CHANGE IN THE MEASUREMENTS 173 5.11 CASE STUDY:
KNOWLEDGE MINING USING SURVEYS 17 6 5.11.1 A VERAGING THE RESPONSES 178
5.11.2 PRESERVING ALL THE RESPONSES 183 5.12 A FINAL REMARK 183 5.13
COMPUTATION 184 EXERCISES 184 * 6 NON-SINGLETON TYPE-1 FUZZY LOGIC
SYSTEMS M 6.1 INTRODUCTION 186 6.2 FUZZIFICATION AND ITS EFFECT ON
INFERENCE 187 6.2.1 FUZZIFIER 187 6.2.2 FUZZY INFERENCE ENGINE 188 6.3
POSSIBILITIES 193 6.4 FBFS 193 6.5 NON-SINGLETON FLSS ARE UNIVERSAL
APPROXIMATORS 195 6.6 DESIGNING NON-SINGLETON FLSS 197 6.6.1 ONE-PASS
METHODS 200 6.6.2 LEAST-SQUARES METHOD 200 6.6.3 BACK-PROPAGATION
(STEEPEST DESCENT) METHOD 200 6.6.4 SVD-QR METHOD 202 6.6.5 ITERATIVE
DESIGN METHOD 203 6.7 CASE STUDY: FORECASTING OF TIME-SERIES 203 6.7.1
ONE-PASS DESIGN 204 6.7.2 BACK-PROPAGATION DESIGN 205 6.8 A FINAL REMARK
209 TABLE OF CONTENTS IX 6.9 COMPUTATION 209 EXERCISES 209 PART 3:
TYPE-2 FUZZY SETS * 7 OPERATIONS ON AND PROPERTIES OF TYPE-2 FUZZY SETS
213 7.1 7.2 7.3 7.4 7.5 7.6 7.7 INTRODUCTION EXTENSION PRINCIPLE
OPERATIONS ON GENERAL TYPE-2 FUZZY SETS 7.3.1 S ET THEORETIC OPERATIONS
217 7.3.2 ALGEBRAIC OPERATIONS ON FUZZY NUMBERS 223 OPERATIONS ON
INTERVAL TYPE-2 FUZZY SETS 7.4.1 SET THEORETIC OPERATIONS 224 7.4.2
ALGEBRAIC OPERATIONS ON INTERVAL FUZZY NUMBERS 227 SUMMARY OF OPERATIONS
PROPERTIES OF TYPE-2 FUZZY SETS 7.6.1 TYPE-1 FUZZY SETS 230 7.6.2 TYPE-2
FUZZY SETS 230 COMPUTATION EXERCISES 213 214 216 224 229 230 231 231 * 8
TYPE-2 RELATIONS AND COMPOSITIONS 235 8.1 INTRODUCTION 235 8.2 RELATIONS
IN GENERAL 235 8.3 RELATIONS AND COMPOSITIONS ON THE SAME PRODUCT SPACE
238 8.4 RELATIONS AND COMPOSITIONS ON DIFFERENT PRODUCT SPACES 241 8.5
COMPOSITION OF A SET WITH A RELATION 243 8.6 CARTESIAN PRODUCT OF FUZZY
SETS 244 X CONTENTS .7 IMPLICATIONS 246 EXERCISES 247 * 9 CENTROID OF A
TYPE-2 FUZZY SET: TYPE-REDUCTION 248 9.1 INTRODUCTION 248 9.2 GENERAL
RESULTS FOR THE CENTROID 248 9.3 GENERALIZED CENTROID FOR INTERVAL
TYPE-2 FUZZY SETS 256 9.4 CENTROID OF AN INTERVAL TYPE-2 FUZZY SET 260
9.5 TYPE-REDUCTION: GENERAL RESULTS 265 9.5.1 CENTROID TYPE-REDUCTION
265 9.5.2 CENTER-OF-SUMS TYPE-REDUCTION 267 9.5.3 HEIGHT TYPE-REDUCTION
268 9.5.4 MODIFIED HEIGHT TYPE-REDUCTION 270 9.5.5 CENTER-OF-SETS
TYPE-REDUCTION 270 9.5.6 COMPUTATIONAL COMPLEXITY OF TYPE-REDUCTION 272
9.5.7 CONCLUDING EXAMPLE 273 9.6 TYPE-REDUCTION: INTERVAL SETS 277 9.6.1
CENTROID TYPE-REDUCTION 277 9.6.2 CENTER-OF-SUMS TYPE-REDUCTION 278
9.6.3 HEIGHT TYPE-REDUCTION 278 9.6.4 MODIFIED HEIGHT TYPE-REDUCTION 278
9.6.5 CENTER-OF-SETS TYPE-REDUCTION 278 9.6.6 CONCLUDING EXAMPLE 279 9.7
CONCLUDING REMARK 279 9.8 COMPUTATION 280 EXERCISES 281 PART 4: TYPE-2
FUZZY LOGIC SYSTEMS TABLE OF CONTENTS XI * 10 SINGLETON TYPE-2 FUZZY
LOGIC SYSTEMS 287 10.1 INTRODUCTION 287 10.2 RULES 288 10.3 FUZZY
INFERENCE ENGINE 289 10.4 FUZZIFICATION AND ITS EFFECT ON INFERENCE 291
10.4.1 FUZZIFIER 291 10.4.2 FUZZY INFERENCE ENGINE 292 10.5
TYPE-REDUCTION 293 10.6 DEFUZZIFICATION 297 10.7 POSSIBILITIES 298 10.8
FBFS: THE LACK THEREOF 300 10.9 INTERVAL TYPE-2 FLSS 302 10.9.1 UPPER
AND LOWER MEMBERSHIP FUNCTIONS FOR INTERVAL TYPE-2 FLSS 302 10.9.2 FUZZY
INFERENCE ENGINE REVISITED 304 10.9.3 TYPE-REDUCTION AND DEFUZZIFICATION
REVISITED 308 10.9.4 FBFS REVISITED 318 10.10 DESIGNING INTERVAL
SINGLETON TYPE-2 FLSS 321 10.10.1 ONE-PASS METHOD 323 10.10.2
LEAST-SQUARES METHOD 325 10.10.3 BACK-PROPAGATION (STEEPEST DESCENT)
METHOD 326 10.10.4 SVD-QR METHOD 332 10.10.5 ITERATIVE DESIGN METHOD 333
10.11 CASE STUDY: FORECASTING OF TIME-SERIES 334 10.12 CASE STUDY:
KNOWLEDGE MINING USING SURVEYS 338 10.13 COMPUTATION 350 EXERCISES 350 *
11 TYPE-1 NON-SINGLETON TYPE-2 FUZZY LOGIC SYSTEMS 353 11.1 INTR O DUCTI
ON 353 11.2 FUZZIFICATION AND ITS EFFECT ON INFERENCE 354 11.2.1
FUZZIFIER 354 11.2.2 FUZZY INFERENCE ENGINE 355 11.3 INTERVAL TYPE-1
NON-SINGLETON TYPE-2 FLSS 356 XII CONTENTS 11.4 DESIGNING INTERVAL
TYPE-1 NON-SINGLETON TYPE-2 FLSS 369 11.4.1 ONE-PASS METHOD 372 11.4.2
LEAST-SQUARES METHOD 372 11.4.3 BACK-PROPAGATION (STEEPEST DESCENT)
METHOD 373 11.4.4 SVD-QR METHOD 376 11.4.5 ITERATIVE DESIGN METHOD 376
11.5 CASE STUDY: FORECASTING OF TIME-SERIES 376 11.6 FINAL RERAARK 380
11.7 COMPUTATION 380 EXERCISES 380 * 12 TYPE-2 NON-SINGLETON TYPE-2
FUZZY LOGIC SYSTEMS 382 12.1 INTRODUCTION 382 12.2 FUZZIFICATION AND ITS
EFFECT ON INFERENCE 383 12.2.1 FUZZIFIER 383 12.2.2 FUZZY INFERENCE
ENGINE 383 12.3 INTERVAL TYPE-2 NON-SINGLETON TYPE-2 FLSS 385 12.4
DESIGNING INTERVAL TYPE-2 NON-SINGLETON TYPE-2 FLSS 401 12.4.1 ONE-PASS
METHOD 405 12.4.2 LEAST-SQUARES METHOD 405 12.4.3 BACK-PROPAGATION
(STEEPEST DESCENT) METHOD 406 12.4.4 SVD-QR METHOD 408 12.4.5 ITERATIVE
DESIGN METHOD 408 12.5 CASE STUDY: FORECASTING OF TIME-SERIES 409 12.5.1
SIX-EPOCH BACK-PROPAGATION DESIGN 409 12.5.2 ONE-EPOCH COMBINED
BACK-PROPAGATION AND SVD-QR DESIGN 413 12.5.3 SIX-EPOCH ITERATIVE
COMBINED BACK-PROPAGATION AND SVD-QR DESIGN 415 12.6 COMPUTATION 417
EXERCISES 420 * 13 TSK FUZZY LOGIC SYSTEMS 421 13.1 INTRODUCTION 421
13.2 TYPE-1 TSK FLSS 422 13.2.1 FIRST-ORDER TYPE-1 TSK FLS 422 TABLE OF
CONTENTS XIII 13.2.2 A CONNECTION BETWEEN TYPE-1 TSK AND MAMDANI FLSS
423 13.2.3 TSK FLSS ARE UNIVERSAL APPROXIMATORS 424 13.2.4 DESIGNING
TYPE-1 TSK FLSS 424 13.3 TYPE-2 TSK FLSS 429 13.3.1 FIRST-ORDER TYPE-2
TSK FLS 429 13.3.2 INTERVAL TYPE-2 TSK FLSS 430 13.3.3 UNNORMALIZED
INTERVAL TYPE-2 TSK FLSS 434 13.3.4 FURTHER COMPARISONS OF TSK AND
MAMDANI FLSS 435 13.3.5 DESIGNING INTERVAL TYPE-2 TSK FLSS USING A
BACK-PROPAGATION (STEEPEST DESCENT) METHOD 437 13.4 EXAMPLE: FORECASTING
OF COMPRESSED VIDEO TRAFFIC 441 13.4.1 INTRODUCTION TO MPEG VIDEO
TRAFFIC 442 13.4.2 FORECASTING I FRAME SIZES: GENERAL INFORMATION 444
13.4.3 FORECASTINGLFRAME SIZES: USINGTHE SAMENUMBER OF RULES 447 13.4.4
FORECASTING I FRAME SIZES: USING THE SAME NUMBER OF DESIGN PARAMETERS
448 13.4.5 CONCLUSION 451 13.5 FINAL REMARK 451 13.6 COMPUTATION 451
EXERCISES 452 * 14 E PILOGUE 454 14.1 INTRODUCTION 454 14.2 TYPE-2
VERSUS TYPE-1 FLSS 456 14.3 APPROPRIATE APPLICATIONS FOR A TYPE-2 FLS
457 14.4 RULE-BASED CLASSIFICATION OF VIDEO TRAFFIC 458 14.4.1 SELECTED
FEATURES 459 14.4.2 FOUS FOR THE FEATURES 461 14.4.3 RULES 461 14.4.4
FOUS FOR THE MEASUREMENTS 462 14.4.5 DESIGN PARAMETERS IN A FL RBC 462
14.4.6 COMPUTATIONAL FORMULAS FOR TYPE-1 FL RBCS 463 14.4.7
COMPUTATIONAL FORMULAS FOR TYPE-2 FL RBCS 464 14.4.8 OPTIMIZATION OFRULE
DESIGN-PARAMETERS 466 14.4.9 TESTING THE FL RBCS 467 14.4.10 RESULTS AND
CONCLUSIONS 468 14.5 EQUALIZATION OF TIME-VARYING NON-LINEAR DIGITAL
COMMUNICATION CHANNELS 469 14.5.1 PRELIMINARIES FOR CHANNEL EQUALIZATION
470 14.5.2 WHY A TYPE-2 FAF IS NEEDED 475 14.5.3 DESIGNING THE FAFS 476
XIV CONTENTS 14.5.4 SIMULATIONS AND CONCLUSIONS 476 14.6 OVERCOMING CCI
AND ISI FOR DIGITAL COMMUNICATION CHANNELS 480 14.6.1 COMMUNICATION
SYSTEM WITH ISI AND CCI 481 14.6.2 DESIGNING THE FAFS 485 14.6.3
SIMULATIONS AND CONCLUSIONS 486 14.7 CONNECTION ADMISSION CONTROL FOR
ATM NETWORKS 489 14.7.1 SURVEY-BASED CAC USING A TYPE-2 FLS: OVERVIEW
491 14.7.2 EXTRACTING THE KNOWLEDGE FOR CAC 491 14.7.3 CHOOSING
MEMBERSHIP FUNCTIONS FOR THE LINGUISTIC LABEIS 492 14.7.4 SURVEY
PROCESSING 492 14.7.5 CAC DECISION BOUNDARIES AND CONCLUSIONS 495 14.8
POTENTIAL APPLICATION AREAS FOR A TYPE-2 FLS 497 14.8.1 PERCEPTUAL
COMPUTING 498 14.8.2 FL CONTROL 499 14.8.3 DIAGNOSTIC MEDICINE 499
14.8.4 FINANCIAL APPLICATIONS 499 14.8.5 PERCEPTUAL DESIGNS OFMULTIMEDIA
SYSTEMS 500 EXERCISES 500 * A JOIN, MEET, AND NEGATION OP- ERATIONS FOR
NON-LNTERVAL TYPE-2 FUZZY SETS 502 A.L INTRODUCTION 502 A.2 JOIN UNDER
MINIMUM OR PRODUCT T-NORMS 503 A.3 MEET UNDER MINIMUM T-NORM 504 A.4
MEET UNDER PRODUCT T-NORM 509 A.5 NEGATION 512 A.6 COMPUTATION 514
EXERCISES 515 * B PROPERTIES OF TYPE-1 AND TYPE-2 FUZZY SETS 517 B.L
INTRODUCTION 517 TABLE OF CONTENTS XV B.2 TYPE-1 FUZZY SETS 517 B.3
TYPE-2 FUZZY SETS 520 EXERCISES 525 * C C OMPUTATION 526 C.L TYPE-1 FLSS
526 C.2 GENERAL TYPE-2 FLSS 527 C.3 INTERVAL TYPE-2 FLSS 528 R I
EFERENCES 530 NDEX 547
|
| any_adam_object | 1 |
| author | Mendel, Jerry M. 1938- |
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| author_facet | Mendel, Jerry M. 1938- |
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| id | DE-604.BV023786323 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T21:36:47Z |
| institution | BVB |
| isbn | 0130409693 |
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| physical | XX, 555 S. graph. Darst. |
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| record_format | marc |
| spellingShingle | Mendel, Jerry M. 1938- Uncertain rule-based fuzzy logic systems introduction and new directions Fuzzy-Logik (DE-588)4341284-1 gnd |
| subject_GND | (DE-588)4341284-1 |
| title | Uncertain rule-based fuzzy logic systems introduction and new directions |
| title_auth | Uncertain rule-based fuzzy logic systems introduction and new directions |
| title_exact_search | Uncertain rule-based fuzzy logic systems introduction and new directions |
| title_full | Uncertain rule-based fuzzy logic systems introduction and new directions Jerry M. Mendel |
| title_fullStr | Uncertain rule-based fuzzy logic systems introduction and new directions Jerry M. Mendel |
| title_full_unstemmed | Uncertain rule-based fuzzy logic systems introduction and new directions Jerry M. Mendel |
| title_short | Uncertain rule-based fuzzy logic systems |
| title_sort | uncertain rule based fuzzy logic systems introduction and new directions |
| title_sub | introduction and new directions |
| topic | Fuzzy-Logik (DE-588)4341284-1 gnd |
| topic_facet | Fuzzy-Logik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017428531&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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