Fuzzy logic and probability applications: bridging the gap
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Format: | Buch |
Sprache: | English |
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Philadelphia, PA
Soc. for Industrial and Applied Mathematics
2002
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Schriftenreihe: | ASA-SIAM series on statistics and applied probability
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Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | XXIII, 409 S. graph. Darst. |
ISBN: | 0898715253 |
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Datensatz im Suchindex
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adam_text | FUZZY LOGIC AND PROBABILITY APPLICATIONS BRIDGING THE GAP EDITED BY
TIMOTHY J. ROSS UNIVERSITY OF NEW MEXICO ALBUQUERQUE, NEW MEXICO JANE M.
BOOKER LOS ALAMOS NATIONAL LABORATORY LOS ALAMOS, NEW MEXICO W. JERRY
PARKINSON LOS ALAMOS NATIONAL LABORATORY LOS ALAMOS, NEW MEXICO 5IAJTL
ASA SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS AMERICAN STATISTICAL
ASSOCIATION PHILADELPHIA, PENNSYLVANIA ALEXANDRIA, VIRGINIA CONTENTS
FOREWORD XV LOTFTA. ZADEH FOREWORD ^ XIX PATRICK SUPPES PREFACE XXI
ACKNOWLEDGMENTS XXIII PART I. FUNDAMENTALS 1 1 JANE M. BOOKER 1.1
CHAPTERS 1-6 1 1.2 SUGGESTED READING 2 REFERENCES 2 1 INTRODUCTION 3
TIMOTHY J. ROSS, JANE M. BOOKER, AND W. JERRY PARKINSON 1.1 SOME HISTORY
AND INITIAL THOUGHTS 3 1.2 THE GREAT DEBATE _. 6 1.2.1 THE DEBATE
LITERATURE 6 1.2.2 THE ISSUES AND CONTROVERSY Y 7 1.3 FUZZY LOGIC AND
PROBABILITY: THE BEST OF BOTH WORLDS 20 1.4 ORGANIZATION OF THE BOOK 22
REFERENCES 24 2 FUZZY SET THEORY, FUZZY LOGIC, AND FUZZY SYSTEMS 29
TIMOTHY J. ROSS AND W. JERRY PARKINSON 2.1 INTRODUCTION 29 2.1.1 . FUZZY
SETS 31 2.1.2 FUZZY SET OPERATIONS 32 2.2 FUZZY RELATIONS 34 2.2.1
OPERATIONS ON FUZZY RELATIONS 34 2.2.2 FUZZY CARTESIAN PRODUCT AND
COMPOSITION 35 2.3 FUZZY AND CLASSICAL LOGIC 36 2.3.1 CLASSICAL LOGIC 36
2.3.2 FUZZY LOGIC 41 2.3.3 APPROXIMATE REASONING 43 VII VIII CONTENTS
2.3.4 FUZZY SYSTEMS 43 2.3.5 AN EXAMPLE NUMERICAL SIMULATION 46 2.3.6
SUMMARY 52 REFERENCES 53 3 PROBABILITY THEORY 55 NOZER D. SINGPURWALLA,
JANE M. BOOKER, AND THOMAS R. BEMENT 3.1 THE CALCULUS OF PROBABILITY 55
3.2 POPULAR VIEWS OF PROBABILITY 57 3.2.1 THE INTERPRETATION OF
PROBABILITY 57 3.2.2 THE CLASSICAL THEORY OF PROBABILITY 57 3.2.3 THE A
PRIORI THEORY OF PROBABILITY 58 3.2.4 THE RELATIVE FREQUENCY THEORY 58
3.2.5 THE PERSONALISTIC OR SUBJECTIVE THEORY 60 3.2.6 CHOOSING AN
INTERPRETATION OF PROBABILITY 61 3.2.7 THE USE OF EXPERT TESTIMONIES IN
PERSONALISTIC/SUBJECTIVE PROBABILITY 62 3.3 CONCEPTS FOR PROBABILITY
THEORY 63 3.3.1 CONCEPTS OF A RANDOM VARIABLE AND SAMPLE SPACE 63 3.3.2
PROBABILITY DISTRIBUTION FUNCTIONS 64 3.3.3 CONDITIONAL PROBABILITY AND
DEPENDENCE 66 3.3.4 COMPARING DISTRIBUTIONS 66 3.3.5 REPRESENTING DATA,
INFORMATION, AND UNCERTAINTIES AS DISTRIBUTIONS 67 3.4 INFORMATION,
DATA, AND KNOWLEDGE 68 REFERENCES 69 4 BAYESIAN METHODS 73 KIMBERLY F.
SELLERS AND JANE M. BOOKER 4.1 INTRODUCTION 73 4.2 PROBABILITY THEORY OF
BAYESIAN METHODS 76 4.2.1 THE INCORPORATION OF ACTUAL INFORMATION
(EXPANSION OF H) 11 4.2.2 THE LIKELIHOOD PRINCIPLE Y. 78 4.2.3
DISTRIBUTION FUNCTION FORMULATION OF BAYES THEOREM ... 78 4.3 ISSUES
WITH BAYES THEORY 79 4.3.1 CRITICISMS AND INTERPRETATIONS OF
BAYES THEOREM 79 4.3.2 USES AND INTERPRETATIONS 80 4.4 BAYESIAN
UPDATING: IMPLEMENTATION OF BAYES THEOREM IN PRACTICAL AP- PLICATIONS
81 4.4.1 BINOMIAL/BETA EXAMPLE 81 4.4.2 ,EXPONENTIAL/GAMMA EXAMPLE 82
4.4.3 NORMAL/NORMAL EXAMPLE 82 4.5 BAYESIAN NETWORKS 83 4.6 RELATIONSHIP
WITH FUZZY SETS 85 REFERENCES 85 5 CONSIDERATIONS FOR USING FUZZY SET
THEORY AND PROBABILITY THEORY 87 TIMOTHY J. ROSS, KIMBERLY F. SELLERS,
AND JANE M. BOOKER 5.1 VAGUENESS, IMPRECISION, AND CHANCE: FUZZINESS
VERSUS PROBABILITY . . . 87 CONTENTS IX 5.1.1 A HISTORICAL PERSPECTIVE
ON VAGUENESS 88 5.1.2 IMPRECISION 89 5.2 CHANCE VERSUS VAGUENESS 89 5.3
MANY-VALUED LOGIC 90 5.4 AXIOMATIC STRUCTURE OF PROBABILITY AND FUZZY
LOGICS 91 5.4.1 RELATIONSHIP BETWEEN VAGUENESS AND MEMBERSHIP FUNCTIONS
94 5.4.2 RELATIONSHIP BETWEEN FUZZY SET THEORY AND BAYESIAN ANALYSIS 95
5.5 EARLY WORKS COMPARING FUZZY SET THEORY AND PROBABILITY THEORY ....
95 5.6 TREATMENT OF UNCERTAINTY AND IMPRECISION: TREATING MEMBERSHIP
FUNCTIONS AS LIKELIHOODS 97 5.7 AMBIGUITY VERSUS CHANCE: POSSIBILITY
VERSUS PROBABILITY 98 5.8 CONCLUSIONS ~ 102 REFERENCES 103 6 GUIDELINES
FOR ELICITING EXPERT JUDGMENT AS PROBABILITIES OR FUZZY LOGIC 105 MARY
A. MEYER, KENNETH B. BUTTERFIELD, WILLIAM S. MURRAY, RONALD E. SMITH,
AND JANE M. BOOKER 6.1 INTRODUCTION 105 6.2 METHOD 106 6.2.1
ILLUSTRATION 106 6.2.2 SUMMARY TABLE OF PHASES AND STEPS 108 6.2.3
PHASES AND STEPS FOR EXPERT ELICITATION 108 6.3 SUMMARY 121 REFERENCES
122 PART II. APPLICATIONS 125 TIMOTHY J. ROSS II.L CHAPTERS 7-15 125 7
IMAGE ENHANCEMENT: PROBABILITY VERSUS FUZZY EXPERT SYSTEMS 127 ALY
EL-OSERY AND MO JAMSHIDI 7.1 INTRODUCTION 127 7.2 BACKGROUND .?. 128
7.2.1 DIGITAL IMAGE-PROCESSING ELEMENTS 128 7.2.2 IMAGE FORMATS 128
7.2.3 SPATIAL DOMAIN 132 7.2.4 PROBABILITY DENSITY FUNCTION 132 7.3
HISTOGRAM EQUALIZATION 133 7.4 EXPERT SYSTEMS AND IMAGE ENHANCEMENT 137
7.4.1 SOI DETECTION 138 7.4.2 FUZZY EXPERT SYSTEM DEVELOPMENT 139
7.4.3 EXAMPLE 139 7.5 FINAL REMARKS 143 REFERENCES 143 8 ENGINEERING
PROCESS CONTROL 145 W. JERRY PARKINSON AND RONALD E. SMITH 8.1
INTRODUCTION 145 CONTENTS 8.2 BACKGROUND 146 8.2.1 BASIC PID CONTROL 148
8.2.2 BASIC FUZZY LOGIC CONTROL 150 8.2.3 BASIC PROBABILISTIC CONTROL
152 8.3 SISO CONTROL SYSTEMS 156 8.3.1 A SYSTEM MODEL AND A PID
CONTROLLER 160 8.4 MULTI-INPUT-MULTI-OUTPUT CONTROL SYSTEMS 167 8.5 THE
THREE-TANK MIMO PROBLEM 174 8.5.1 THE FUZZY AND PROBABILISTIC CONTROL
SYSTEMS 174 8.5.2 THE PI CONTROLLER 178 8.5.3 SETPOINT TRACKING:
COMPARISON BETWEEN THE CONTROLLERS . . 179 8.5.4 DISTURBANCE REJECTION:
THE FUZZY AND PROBABILISTIC CONTROLLERS 181 8.5.5 DISTURBANCE REJECTION:
COMPARISON BETWEEN THE CONTROLLERS 186 8.6 CONCLUSIONS 188 REFERENCES
190 9 STRUCTURAL SAFETY ANALYSIS: A COMBINED FUZZY AND PROBABILITY
APPROACH 193 TIMOTHY J. ROSS AND JONATHAN L. LUCERO 9.1 INTRODUCTION 193
9.2 AN EXAMPLE 194 9.3 TYPICAL UNCERTAINTIES 194 9.4 CURRENT TREATMENT
OF UNCERTAINTIES 196 9.4.1 RESPONSE SURFACE METHOD 197 9.5 PROBLEMS WITH
CURRENT METHODS 200 9.6 THE FUZZY SET ALTERNATIVE 201 9.7 EXAMPLES 203
9.7.1 DETERMINISTIC/RANDOM UNCERTAINTIES 204 9.7.2 MODELING
UNCERTAINTIES 204 9.7.3 INTERPRETATION OF DAMAGE 211 9.8 SUMMARY _ 216
REFERENCES -.* 217 10 AIRCRAFT INTEGRITY AND RELIABILITY - F 219 CARLOS
FERREGUT, ROBERTO A. OSEGUEDA, YOHANS MENDOZA, VLADIK KREINOVICH, AND
TIMOTHY J. ROSS 10.1 CASE STUDY: AIRCRAFT STRUCTURAL INTEGRITY:
FORMULATION OF THE PROBLEM . 219 10.1.1 AEROSPACE TESTING: WHY 219
10.1.2 AEROSPACE TESTING: HOW 219 10.1.3 AEROSPACE INTEGRITY TESTING IS
VERY TIME-CONSUMING AND EXPENSIVE 220 10.2 SOLVING THE PROBLEM 220
10.2.1 OUR MAIN IDEA 220 10.2.2 STEPS NECESSARY FOR IMPLEMENTING THE
MAIN IDEA 220 10.2.3 WE DO NOT HAVE SUFFICIENT STATISTICAL DATA, SO WE
MUST USE EXPERT ESTIMATES 221 10.2.4 SOFT COMPUTING 221 10.2.5 THE
CHOICES OF TRANSFORMATION AND COMBINATION FUNCTIONS ARE VERY IMPORTANT
221 CONTENTS XI 10.2.6 HOW CAN WE SOLVE THE CORRESPONDING OPTIMIZATION /
PROBLEM? 222 10.3 HOW TO DETERMINE PROBABILITIES FROM OBSERVED VALUES OF
EXCESS ENERGY: OPTIMAL WAY (USE OF SIMULATED ANNEALING) 222 10.3.1 AN
EXPRESSION FOR PROBABILITIES 222 10.3.2 BEST IN WHAT SENSE? 223 10.3.3
AN OPTIMALITY CRITERION CAN BE NONNUMERIC 223 10.3.4 THE OPTIMALITY
CRITERION MUST BE FINAL 224 10.3.5 THE CRITERION MUST NOT CHANGE IF WE
CHANGE THE MEASURING UNIT FOR ENERGY 224 10.3.6 DEFINITIONS AND THE MAIN
RESULT 225 10.4 HOW TO DETERMINE THE PROBABILITY OF DETECTION: OPTIMAL
WAY (USE OF NEURAL NETWORKS) 226 10.4.1 THE POD FUNCTION MUST BE SMOOTH
AND MONOTONIC .... 226 10.4.2 WE MUST CHOOSE A FAMILY OF FUNCTIONS, NOT
A SINGLE FUNCTION 227 10.4.3 DEFINITION AND THE MAIN RESULT 227 10.5 HOW
TO COMBINE PROBABILITIES (USE OF FUZZY TECHNIQUES) 228 10.5.1
TRADITIONAL PROBABILISTIC APPROACH: MAXIMUM ENTROPY . . 228 10.5.2
TRADITIONAL APPROACH IS NOT ALWAYS SUFFICIENT 228 10.5.3 MAIN IDEA:
DESCRIBE GENERAL COMBINATION OPERATIONS . . . 229 10.5.4 THE NOTIONS OF
R-NORMS AND /-CONORMS 230 10.6 PRELIMINARY RESULTS 231 10.7 ALTERNATIVE
APPROACH TO FUSING PROBABILITIES: FUZZY RULES 231 10.7.1 MAIN PROBLEMS
WITH THE ABOVE APPROACH 231 10.7.2 THE USE OF FUZZY RULES 231 10.7.3
EXPERT RULES FOR FAULT DETECTION 232 10.7.4 THE PROBLEM WITH THIS RULE
BASE AND HOW WE SOLVE IT ... 233 10.7.5 EXPERIMENTAL RESULTS 234 10.8
APPLICATIONS TO AIRCRAFT RELIABILITY 235 10.8.1 RELIABILITY: GENERAL
PROBLEM 235 10.8.2 TRADITIONAL APPROACH TO RELIABILITY 235 10.8.3
TRADITIONAL APPROACH IS NOT ALWAYS SUFFICIENT: A PROBLEM . 235 10.8.4
PROPOSED APPROACH TO FUSING PROBABILITIES: MAIN IDEA . . 236 10.8.5
RESULTING SOLUTION 237 10.9 CLOSING THOUGHTS 237 APPENDIX: PROOFS 237
PROOF OF THEOREM 10.1 237 PROOF OF THEOREM 10.2 238 REFERENCES 240 11
AUTO RELIABILITY PROJECT 243 JANE M. BOOKER AND THOMAS R. BEMENT 11.1
DESCRIPTION OF THE RELIABILITY PROBLEM 243 11.2 IMPLEMENTING THE
PROBABILITY APPROACH 246 11.2.1 LOGIC AND RELIABILITY MODELS 246 11.2.2
EXPERT ELICITATION 247 11.2.3 UPDATING METHODS 249 11.2.4 CALCULATING
RELIABILITIES 250 XII CONTENTS 11.2.5 RESULTS 252 11.2.6 DOCUMENTATION
253 11.3 AUTO PERFORMANCE USING FUZZY APPROACH 253 11.3.1 ASPECTS OF THE
FUZZY AND PROBABILITY APPROACHES 253 11.3.2 A FUZZY/PROBABILITY HYBRID
APPROACH 254 11.3.3 A FUZZY AUTOMOTIVE EXAMPLE 256 11.4 COMMENTS ON
APPROACHES FOR SYSTEM PERFORMANCE/RELIABILITY 259 REFERENCES 260 12
CONTROL CHARTS FOR STATISTICAL PROCESS CONTROL 263 W. JERRY PARKINSON
AND TIMOTHY J. ROSS 12.1 INTRODUCTION 263 12.2 BACKGROUND 264 12.2.1
EXAMPLE 1: MEASURED VARIABLE CONTROL CHART 265 12.2.2 EXAMPLE 2:
SPECIAL-CAUSE EVENTS 269 12.2.3 EXAMPLE 3: TRADITIONAL SPC 272 12.3
FUZZY TECHNIQUES FOR MEASUREMENT DATA: A CASE STUDY 275 12.3.1
BACKGROUND 275 12.3.2 THE FUZZY SYSTEM 276 12.3.3 PLANT SIMULATION 278
12.3.4 EXAMPLE 4: ESTABLISHING FUZZY MEMBERSHIP VALUES .... 281 12.3.5
EXAMPLE 5: FUZZY CONTROL 284 12.3.6 EXAMPLE 6: A CAMPAIGN 286 12.4 SPC
TECHNIQUES FOR MEASUREMENT DATA REQUIRING CORRELATION AND USING
REGRESSION 288 12.4.1 EXAMPLE 7: REGRESSION ON EXAMPLE 4 290 12.4.2
EXAMPLE 8: REGRESSION ON EXAMPLE 5 291 12.4.3 EXAMPLE 9: REGRESSION ON
EXAMPLE 6 293 12.4.4 COMMENTS ON REGRESSION 294 12.5 SPC TECHNIQUES FOR
ATTRIBUTE DATA 294 12.5.1 EXAMPLE 10: LOG-CABIN REVISITED 294 12.5.2
EXAMPLE 11: THE LOG CABIN WITH A SPECIAL-CAUSE PROBLEM 296 12.6 FUZZY
TECHNIQUES FOR ATTRIBUTE DATA ^ 296 12.6.1 EXAMPLE 12: FUZZY ATTRIBUTE
DATA 299 12.6.2 THE FUZZY SYSTEM USED TO DOWNGRADE PARTS 300 12.7
STATISTICAL TECHNIQUES FOR MULTINOMIAL ATTRIBUTE DATA 312 12.8
DISCUSSION AND CONCLUSIONS 322 REFERENCES 323 13 FAULT TREE LOGIC MODELS
325 JONATHAN L. LUCERO AND TIMOTHY J. ROSS 13.1 INTRODUCTION 325 13.2
OBJECTIVE 325 13.3 CHAPTER OVERVIEW 327 13.4 PART A: GENERAL METHODOLOGY
327 13.4.1 FAULT TREES 327 13.4.2 GENERAL LOGIC METHODOLOGY 328 13.4.3
MATHEMATICAL OPERATORS 331 13.4.4 EXAMPLES 335 CONTENTS XIII 13.4.5
SUMMARY 338 13.5 PART B: GENERAL METHODOLOGY EXTENDED WITH FUZZY LOGIC
341 13.5.1 MEMBERSHIP FUNCTIONS 341 13.5.2 DEPENDENCE 341 13.5.3 SUMMARY
344 13.6 CONCLUSIONS 345 REFERENCES 345 14 UNCERTAINTY DISTRIBUTIONS
USING FUZZY LOGIC 347 RONALD E. SMITH, W. JERRY PARKINSON, AND THOMAS R.
BEMENT 14.1 INTRODUCTION 347 14.2 EXAMPLE 1: THE USE OF FUZZY EXPERTISE
TO DEVELOP UNCERTAINTY DISTRIBUTIONS FOR CUTTING TOOL WEAR 349 14.2.1
DEMONSTRATION OF THE TECHNIQUE 350 14.3 EXAMPLE 2: DEVELOPMENT OF
UNCERTAINTY DISTRIBUTIONS USING FUZZY AND PROBABILISTIC TECHNIQUES 352
14.3.1 DESCRIPTION AND ILLUSTRATION OF THE FUZZY SETUP OF THE METHOD 353
14.3.2 FUZZY DEVELOPMENT OF UNCERTAINTY DISTRIBUTIONS 356 14.3.3
PROBABILISTIC CHARACTERIZATION OF THE DEVELOPMENT OF UNCERTAINTY
DISTRIBUTIONS 359 14.3.4 EXTENDED EXAMPLE 361 14.3.5 CONCLUDING REMARKS
362 14.4 SUMMARY 363 REFERENCES 364 15 SIGNAL VALIDATION USING BAYESIAN
BELIEF NETWORKS AND FUZZY LOGIC 365 HRISHIKESH ARADHYE AND A. SHARIF
HEGER 15.1 INTRODUCTION 365 15.2 BAYESIAN BELIEF NETWORKS 367 15.2.1
BBNSFORSFDIA 373 15.2.2 CONSTRUCTION OF NODES, LINKS, AND ASSOCIATED
FUNCTIONS . . 373 15.2.3 A SINGLE-VARIABLE, SINGLE-SENSOR SYSTEM 374
15.2.4 INCORPORATION OF REDUNDANCIES IN THE NETWORK STRUCTURE . . 375
15.3 FUZZY LOGIC 381 15.3.1 USING FUZZY LOGIC FOR FAULT DETECTION 382
15.4 SUMMARY 389 REFERENCES 390 INDEX 393
|
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record_format | marc |
series2 | ASA-SIAM series on statistics and applied probability |
spelling | Fuzzy logic and probability applications bridging the gap ed. by Timothy J. Ross ... Philadelphia, PA Soc. for Industrial and Applied Mathematics 2002 XXIII, 409 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier ASA-SIAM series on statistics and applied probability Anwendung (DE-588)4196864-5 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Wahrscheinlichkeit (DE-588)4137007-7 gnd rswk-swf Fuzzy-Logik (DE-588)4341284-1 gnd rswk-swf Fuzzy-Logik (DE-588)4341284-1 s Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Anwendung (DE-588)4196864-5 s DE-604 Wahrscheinlichkeit (DE-588)4137007-7 s 1\p DE-604 Ross, Timothy J. (DE-588)1203408064 edt HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017434576&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Fuzzy logic and probability applications bridging the gap Anwendung (DE-588)4196864-5 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd Fuzzy-Logik (DE-588)4341284-1 gnd |
subject_GND | (DE-588)4196864-5 (DE-588)4064324-4 (DE-588)4137007-7 (DE-588)4341284-1 |
title | Fuzzy logic and probability applications bridging the gap |
title_auth | Fuzzy logic and probability applications bridging the gap |
title_exact_search | Fuzzy logic and probability applications bridging the gap |
title_full | Fuzzy logic and probability applications bridging the gap ed. by Timothy J. Ross ... |
title_fullStr | Fuzzy logic and probability applications bridging the gap ed. by Timothy J. Ross ... |
title_full_unstemmed | Fuzzy logic and probability applications bridging the gap ed. by Timothy J. Ross ... |
title_short | Fuzzy logic and probability applications |
title_sort | fuzzy logic and probability applications bridging the gap |
title_sub | bridging the gap |
topic | Anwendung (DE-588)4196864-5 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd Fuzzy-Logik (DE-588)4341284-1 gnd |
topic_facet | Anwendung Wahrscheinlichkeitsrechnung Wahrscheinlichkeit Fuzzy-Logik |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017434576&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT rosstimothyj fuzzylogicandprobabilityapplicationsbridgingthegap |