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| Авторизация |
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| Wolkenhauser O. — Data Engineering: Fuzzy Mathematics in Systems Theory and Data Analysis |
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| Предметный указатель |
Additivity 241
Aggregation, intersection 221
Aggregation, union 221
Algebra 241
Algebra,  130 241
Algebra, , 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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