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Wolkenhauser O. — Data Engineering: Fuzzy Mathematics in Systems Theory and Data Analysis
Wolkenhauser O. — Data Engineering: Fuzzy Mathematics in Systems Theory and Data Analysis



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Название: Data Engineering: Fuzzy Mathematics in Systems Theory and Data Analysis

Автор: Wolkenhauser O.

Аннотация:

System scientists wielding the tools of fuzzy math have a central role to play in modeling increasingly complex engineering and operations research problems of an interdisciplinary nature, according to the author. To cope with real world uncertainties and provide a philosophical and practical guide to system modeling, system identification, and decision-making, several methodologies are presented from probability theory, possibility theory, and fuzzy mathematics. Appends material on sets, relations, and mapping; measuring forecast accuracy; clustering; measuring spaces and integrals; unbiasedness of estimators; statistical reasoning; and frequency analysis. Wolkenhauer is affiliated with the U. of Manchester Institute of Science and Technology


Язык: en

Рубрика: Математика/Вероятность/Статистика и приложения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 287

Добавлена в каталог: 15.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Additivity      241
Aggregation, intersection      221
Aggregation, union      221
Algebra      241
Algebra, $\sigma-$      130 241
Algebra, $\sigma-$, Borel      241
Algebra, boolean      106 154 198 201
Algebra, Borel      130
Algebra, complete Heyting      107
Algebra, conditional event      108 154
Algebra, De Morgan      106
Algorithm, agglomerative      239
Algorithm, clustering      86—87
Algorithm, clustering, fuzzy      81
Algorithm, Expectation Maximization      52 74 78 125 217—218
Algorithm, fuzzy-c-means      90 95 101—102 110 120 122 124—125 218
Algorithm, Gustafson — Kessel      99 111 122 218
Algorithm, hard-c-means      94 125 218
Algorithm, linkage      239
Algorithm, merging      144
Algorithm, single-linkage      86
Antecedent      108 113 227
Approximation, basis function      77—79 222
Approximation, non-parametric      174
Approximation, universal      78 161 213
Autocovariance      57
Automaton      17 21
Average, ensemble      81
Average, time      81
Basis function expansion      116 173
Belief      132
Calculus, predicate      155
Calculus, propositional      108 154—155 197 227
Causality      3 227
Central tendency      32 214
Centroid      87
Certainty      152 224
Chaining effect      108
Class, equivalence      5—7 9—10 24 84 93 108 235
Class, power      132
Classification      73 99
Classification, intrinsic partitional      86
Classifier      87 99 102
Classifier, Bayesian      77 104
Classifier, fuzzy      77 104 173 175—176
Classifier, fuzzy, rule-based      173
Classifier, probabilistic      176
Classifier, rule-based      179
Classifier, statistical      77 173 176
Cluster      83—84 96 108 110 123
Cluster center      101 104 122 177 219
Cluster orientation      110 218
Cluster shape      110 218
Cluster volume      111
Cluster, ellipsoidal      96
Cluster, fuzzy      106 115 206
Cluster, hyperellipsoidal      88 111
Cluster, hyperspherical      88
Cluster, spherical      110
Clustering      73 84—85
Clustering criterion      87
Clustering, fuzzy      82—83 86 94 99 108—109 124 166 173
Clustering, fuzzy-c-means      101 218
Clustering, hard      83 89 94 119 123
Clustering, hard-c-means      88 218
Clustering, hierarchical      86 106 108 239
Clustering, partitional      86 108 218
Clustering, product space      82 109
Clustering, single linkage      240
Codomain      70 235
Coefficient, correlation      33 46 59
Coefficient, correlation, multiple      142 239
Coefficient, Fourier      50
Coefficient, Fourier, complex      249
Coefficient, weighting      110
Commutative diagram      12 131
complexity      xx
Composite (product)      235
composition      23
Composition, max-min      159
Composition, max-product      159
Compositional rule of inference      116 158 163 202 219
Confidence interval      45 247
Conjunction      94 113
Connective      106
Connective, logical      197
Consequent      108 113 227
Context of a state      136
Control, adaptive      182
Control, fuzzy      181—182
Control, nonlinear      195
Control, optimal      182
Control, PID      182
Control, robust      182
Controller, fuzzy      181
Controller, PI      182
Controller, PI, fuzzy      182—183
Correlation      215
Covariance      33 56—58 215
Coverage function      133
Covering      232
Curse of dimensionality      81
Cybernetics      181
Data engineering      229
Data Mining      228
Data, complete      79
Data, experimental      17 19
Data, incomplete      79 125
Data, mixed      124
Data, normalized      103—104
Data, relational      239
Data, sampled      35 38 135
Data, time-series      53 83
Data, training      51 73
Data, training, identically distributed      72
Data, training, independent      72
Data, training, labelled      100
Data, unlabeled      101 103—104 124—125 173
Decision making      3 136 138 151 222 228 247
Decision surface      101 104
Deduction      74 225
Defuzzification      221
Defuzzification, center-average      187
Defuzzification, linear      185 187
Defuzzification, nonlinear      188
Defuzzifier      166
Defuzzifier, center of gravity      166
Defuzzifier, center-average      167—170
Degree of confidence      137 179
Degree of consistency      245
Degree of feasibility      35 137 245
Degree of frequency      245
Degree of fulfillment      113 116 179 219
Degree of indistinguishability      108 149
Degree of likelihood      245
Degree of membership      89 91 157 198 219 222
Degree of possibility      35
Dendrogram      86 239
density      50 53
Density contour plot      104
Density, conditional      72
Density, joint      81
Density, marginal      58
Density, probability      3 32 72 136 174
Determinism      16
Deviation, mean absolute      238
Discrimination      99
dispersion      32—33 58
distribution      50
Distribution, conditional      60 62
Distribution, Gaussian      125
Distribution, individual      54
Distribution, joint      54
Distribution, marginal      54 201
Distribution, normal      51
Distribution, possibility      35 82 129 135 138 207 228 245
Distribution, possibility, conditional      137 220
Distribution, probability      32—33 35 207
Distribution, probability, infinite-dimensional      55
Distribution, probability, joint      55 81
Distribution, probability, time-invariant      56
Domain      70 235
Domain, frequency      50 248
Domain, time      50 248
Dynamics      12
Eigenstructure      98 110
Eigenvalue      26 110
Eigenvector      26 98 110
Empirical risk minimization      73
Encoding      3 5 17 24
Ensemble      54
Entailment      226—227
Equation of state      11
Equation, characteristic      26 98
Equation, normal      3940
Equation, output      25
Equation, state      25
Equilibrium      56
Equilibrium, statistical      81
Ergodicity      81
Error, estimation      60 64—65
Error, filtering, minimum      62
Error, forecast      238
Error, mean absolute percent      238
Error, mean square      238
Error, mean square, root      238
Error, prediction      39 48
Error, quadratic      47
Error, quadratic, mean      48
Error, quadratic, minimal mean      47
error, random      41
Error, squared      37
Estimate, empirical      75
Estimate, least-squares      39—40 61
Estimate, linear      62
Estimate, maximum likelihood      50 52 77 216
Estimate, multivariate kernel density      77
Estimate, optimal      65 73
Estimate, parameter      31 44
Estimate, pooled      100
Estimate, state      64
Estimate, statistical      60
Estimation, density      69 72—73 75 77—79 81 217
Estimation, density, Kernel      69
Estimation, density, mixture      217—218
Estimation, kernel density      217
Estimation, least-squares      63
Estimation, maximum likelihood      50 125
Estimator      33
Estimator, kernel      76—77
Estimator, kernel density      104
Estimator, kernel, Gaussian      76
Estimator, kernel, multi-variate      76
Estimator, kernel, naive      76
Estimator, kernel, Parzen’s      75 174 212
Estimator, unbiased      33
Event, certain      241
Event, crisp      35
Event, fuzzy      34—35 244
Event, impossible      241
Event, observable      4 6
Expectation      34 61
Expectation operator      31—32 34 57 131 214
Expectation, conditional      38 61—62
Extension Principle      75 203—204 219
Extensional hull      93 105—106 220
Extensionality      93
Factors, linked      6
Factors, partially linked      6
Factors, unlinked      6
Feasibility      155
Field      241
Filter, Kalman — Bucy      43 62 67
Filter, optimal      62 64
Finite-state machine      17—18
Firing level      184
Forecasting      139 142 206
Forecasting, qualitative      138 141
Fourier series      31 43 49—50 216 249
Fourier series, complex      249
Frequency domain      50
Function      235
Function, approximating      74 77—78
Function, autocorrelation      57
Function, autocovariance      56
Function, basis      69 77 117 217
Function, characteristic      134
Function, composite      12
Function, cost      87
Function, cost, least-squares      46
Function, coverage      129 135
Function, cumulative distribution      73 75
Function, density      80 217
Function, density, approximating      80
Function, deterministic      37 41
Function, distance      149
Function, distribution, cumulative      148
Function, distribution, generalized      130
Function, fuzzy set-membership      92 159 221
Function, fuzzy set-membership, piecewise-linear      182
Function, fuzzy set-membership, trapezoidal      198
Function, fuzzy set-membership, triangular      198
Function, indicator      75 175—176
Function, kernel      76 174
Function, kernel, multi-dimensional      174
Function, likelihood      50—51 77 79 125 216—217
Function, linear      37 63
Function, logical      3
Function, loss      37 60 63 73 77 215 217
Function, membership      35 106 152 157 166 175 198 204
Function, membership, antecedent      114
Function, membership, class      102
Function, membership, multi-variate      113 162
Function, membership, triangular      169
Function, nonlinear      82
Function, objective      36 85 87—89 124 126 218
Function, objective, fuzzy      89 126
Function, orthogonal      43 49
Function, parametric      115
Function, periodic      49
Function, predictor      39
Function, probability density      54 69 73 75 241
Function, probability density, class-conditional      174
Function, probability density, joint      72
Function, probability distribution      35 52 58 125
Function, probability distribution, conditional      60
Function, quadratic      39
Function, regression      37 126
Function, Riemann integrable      243
Function, sample      54
Function, set-distance      239
Function, time      3 226
Function, trigonometric      78
Function, vector-valued      13
Functional, c-means      90
Functional, fuzzy-c-means      90
Functional, maximum likelihood empirical risk      217
Functional, risk      37 73 77 215
Fuzzy mathematics      75 152
Fuzzy proposition      157
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