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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
Relation, fuzzy, transitive      149
Relation, inclusion      154
Relation, linkage      10 19
Relation, non-reflexive      108
Relation, non-transitive      124
Relation, similarity      92—93 104—106 124 149 219—220
Relation, single-valued      235
Relation, transitive      148—149 151
Representation theorem      199
Residual      38 41 63
Risk, empirical      74 216
Risk, estimated      73
Risk, expected      81
Robustness      182
Rule consequents      113
Scatter diagram      45
Semi-group      107
SEQUENCE      232
Sequence, normalized sample covariance      57
Sequence, sample autocorrelation      57
Sequence, sample autocovariance      57
Sequence, uncorrelated      57
Set      231
Set, countable      232
Set, crisp      93 201 244
Set, denumerable      232
Set, factor      87
Set, finite      232
Set, fully overlapping      211
Set, fuzzy      35 82 93 105 112 135 156—157 162 166 175 198—200 206 211 219 228
Set, fuzzy, antecedent      118 121 185 222
Set, fuzzy, discrete      115
Set, fuzzy, extensional      93 105
Set, fuzzy, multi-dimensional      113—114
Set, fuzzy, normalized      167
Set, fuzzy, piecewise-linear (triangular)      183
Set, fuzzy, triangular      211
Set, fuzzy, two-dimensional      113
Set, fuzzy, unimodal      113
Set, fuzzy, univariate      113
Set, image      235
Set, index      232
Set, infinite      232
Set, infinite, countably      232
Set, level      199
Set, partially ordered      107
Set, partially ordered (poset)      147
Set, power      201
Set, quotient      5—6 9—10 87 108 150 235
Set, random      129 132
Set, state      6
Similarity      107
Singleton      116 165
Space, antecedent      113—114
Space, cluster      85
Space, event      34
Space, hard partitioning      87
Space, hypermeasurable      133
Space, measurable      241
Space, measure      241
Space, measure, fuzzy      245
Space, metric      148
Space, metric, bounded      149
Space, metric, probabilistic      148—149
Space, orthogonal      63
Space, partition      90 218
Space, partition, fuzzy      89 218
Space, phase      10
Space, probabilistic      94 124
Space, probability      34 133 241—242
Space, product      141
Space, regressor      36
Space, sample      34
Space, state      5 10 15
Stability      182
Standard deviation      33 45 59 125
State      1 3—5 17—18 20 25
State, abstract      4—5 10 16 69 136 220
State-transition      18
State-vector      14 24
Statement, compound      157
Statement, conditional      154 166
Statement, conditional, independent      162
Statement, conditional, strongly coupled      162
Statement, implicative      154
Statement, logical      166
Static approximation problem      139
Stationarity      56—57 81
Stationarity, second order      56
Stationarity, strict      81
Stationarity, weak      56
Statistics, point-valued      134
Statistics, set-valued      134
Symmetry      93
System, abstract      107
System, anticipatory      17
System, autoregressive, nonlinear      140
System, deterministic      20 56
System, distributed      21
System, dynamic      1 15 21 62 98 108 135
System, dynamic, continuous-time      25
System, dynamic, discrete-time      26
System, dynamical      15
System, dynamical, discrete-event      18
System, dynamical, discrete-time      18 24
System, fuzzy      84 106 109 138 161 163 166 168 173 202 213 222
System, piecewise-linear      195
System, polytopic      116
System, propositional logical      106 108
System, rule-based      82 106 112 116 129 168 198 206 228
System, sampled-data      249
System, spatial      21
System, stochastic      56
Test of significance      246—247
Theory, category      202
Theory, estimation      247
Theory, evidence      132
Theory, Markov decision      18
Theory, measure      243
Theory, possibility      32 75
Theory, probability      32
Theory, sampling      247
Theory, statistical decision      174 247
Theory, statistical learning      73—75 216—217
Theory, systems      1 214
Time domain      50
Time-series      53
Time-series, Mackey — Glass      120
Trajectory      16 22 192
Transform, Fourier      50 250
Transform, integral      50
Transform, Laplace      30 50 251
Transformation      15 235
Transformation, bijective      35
Transformation, integral      248
Transition map      13
Transitivity      93 107 124 145—146 149—152 219
Truth value      106—107 153—154 156—157 206
Unbiasedness      245
Uncertainty      74 84 138 148—149 152 156 197 213 247
Uncorrelatedness      66
Universe of discourse      157 183 199
Unlinked, totally      7—8
Variability      214
Variable, antecedent      113
Variable, consequent      113
Variable, endogenous      71
Variable, exogenous      71
Variable, fuzzy      113 157
Variable, random      15 32 54 57 59 131 241
Variable, random, binomially distributed      75
Variable, random, identically distributed      41 81
Variable, random, independent      41 81
Variable, random, t-dependent      54
Variable, random, uncorrelated      55
Variable, regressor      85 113
Variable, state      10 19—20 25
Variance      33 54 56 58—59 75 97 245
Variance, sample      33 38
Variance, within-cluster      88 218
Variance, within-cluster-overall      218
White noise      55 62
1 2 3
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