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Index

k-success rule, 25, 237

ADALINE,61 Adaptive Resonance Theory, 225 AI,290 allele, 31 alpha cut, 91 AND fuzzy neuron, 206 ANFIS, 216, 228 antecedent, 109 approximate reasoning, 107 arithmetic, 100 arms race, 37 artificial intelligence, 26, 290 asexual reproduction, 4 asset cl ass , 44 associative memory, 220

fuzzy, 220 neural, 220

asynchronous parallel algorithm, 264

automatically defined functions, 22

backpropagation algorithm, 62 ball-and-beam problem, 241 belief measure, 114 belief theory, 112 biology, 1 bloating, 21 breast cancer diagnosis, 189 breeder genetic algorithm, 246 breeding, 30 bucket brigade algorithm, 170 building blocks hypothesis, 14

Cartesian product, 96 fuzzy,97

center of area, 111 center of gravity, 111, 170 center of sums, 111 centroid method, 111 character recognition, 67 characteristic function, 88, 90 classification, 120 classifier system, 167

fuzzy, 167 classifier systems, 15 cluster analysis, 81 clustering, 120, 225 co-evolution, 21, 37, 243 competition, 239 competitive, 37 complement, 86, 95 complexity, 15 confidence, 190 conjunction, 105, 170 consequent, 109 control, 34, 163, 175 control theory, 117 controller

adaptive fuzzy logic, 177 fuzzy logic, 163 fuzzy-rule-based, 235

convergence, 15, 26, 27, 29 premature, 29 rate of, 15, 26

convex membership function, 91 cooperative, 38, 291

Index

324

core, 91 cost function, 11 credit assignment, 17, 167, 170 crossover, 4, 20

rate, 4, 237

Darwin, Charles, 1 data mining, 162 De Morgan's laws, 88, 94 deception, 14

remedies to, 14 decision support system, 119 decision theory, 28 decision tree, 178

fuzzy, 178 decoders, 35 defining length, 12 defuzzification, 110, 170 delta rule, 225 demes, 258 Dempster-Shafer theory of

evidence, 115 dependent variable, 81 difference, 86 differential competitive learning,

222, 223 digital

signal processor, 284 brains, 145

disjoint sets, 86 disjunction, 105, 170 distributed

architectures, 251 evolutionary algorithms, 254,

258 memory, 253 architectures, 250 neural network models, 276

diversity, 236 downside risk, 39

ecology, 291 economy, 291 efficient frontier , 40 elitist, 31 embryo, 248 encoding

direct, 130 grammar, 135 indirect, 134 rule ID, 166

engineering design, 32

epistasis, 31 error

propagation, 103 ERUDIT,115 evidence theory, 112 evolution

of neural architectures, 129 of adaptive robots, 147 of learning rules, 138 of neural machines, 140 of trading models, 272

evolution strategies, 1, 22, 32, 237 evolutionary

circuit design, 142 robotics, 147

evolutionary algorithm adaptive, 234, 235 human supervision of, 234 parameters, 237 real-coded, 245 small-sized, 177

evolutionary algorithms, 1, 254 and fuzzy logic, 233 distributed, 255 human supervision of, 233 parallel, 255

evolutionary design of fuzzy systems, 161

evolutionary neural networks, 123 evolutionary programming, 1, 26 evolvable hardware, 141 excluded middle, 88, 95 exhaustive search, 28 expert knowledge, 161, 163 expert system, 119

fuzzy, 119 exploitation, 28, 245

-oriented genetic operators, 238

exploration, 28, 234, 245 explotation, 234 extension principle, 98

FAM,220 fault tolerance, 79 feasible set, 11 feasible solution, 11 feature maps, 75, 134 feature space, 121 financial markets, 69, 269 financial markets prediction, 69,

269

fine-grained evolutionary algorithm, 260

finite states automata, 26 fitness, 11, 23, 26, 28-30, 35

fuzzy, 233, 243 noisy, 177, 239, 244 relative, 37

fitness of a schema, 12 fitness proportionate selection, 3,

28-30 fittest

survival of the, 3 Flynn's taxonomy, 251 FogeI, David B., 27 FogeI, Lawrence J., 1 frequency of exchange, 259 function approximation, 218 function set, 19 future prospects, 291 fuzzification of neural networks, 202 fuzzy arithmetic, 100 Fuzzy ART, 225, 230 Fuzzy ARTMAP, 227 fuzzy associative memory, 220 fuzzy behavior, 243 fuzzy c-means, 120 fuzzy classifier system, 167 fuzzy control, 117, 219, 234

of evolution, 234 fuzzy controller, 161, 167

synthesis and optimization, 171

fuzzy decision tree, 178 fuzzy filter, 186 fuzzy government, 233, 235 fuzzy IF-THEN rule, 162 fuzzy indexing, 182 fuzzy logic, 83, 161

and evolutionary algorithms, 233

and probability, 84 in the narrow sense, 103

fuzzy modeling, 190 fuzzy number, 99, 101, 162

L-R,102 triangular, 102

fuzzy numbers triangular, 224

fuzzy query, 182, 184 fuzzy relation, 109, 223 fuzzy representation, 248

fuzzy rule, 109 fuzzy set, 90

genotypes representing, 247 fuzzy set theory, 83, 85 fuzzy subset, 95 fuzzy system, 162 fuzzy-rule-based system, 109, 118,

163, 175

generalization, 65, 271 genetic algorithms, 1, 2

cell ular, 260 genetic programming, 1, 18, 34,

134, 184, 239, 243 GENOCOP, 181 genotype, 11, 22, 26, 35, 36 gradient descent, 28 greedy algorithms, 36 grid models, 258

hardware devices, 292 health care, 119 Hebb matrix

fuzzy,221 Hebb's rule, 71 Hebb, Donald 0., 71 height method, 110 heuristics, 35 Holland, John H., 1, 28 host-parasite, 37 hybrid,291 hybrid evolutionary algorithms, 35

ID3, 178 ignorance, 115 image compression, 186 implication, 105 imprecision, 83, 119, 244

propagation, 103 independent variable, 81 individual, 3 inference, 109

engine, 119 information retrieval, 182 input data selection, 139 interpretability, 190 intersection, 86, 94 inverted pendulum, 243 investment horizon, 44 island model, 258

Jaccard score, 183

Index

325

Index

326

k-armed bandit, 28 knowledge base, 119 Kohonen learning algorithm, 76 Koza, John R., 1

Lamarekian mutation, 36 learning, 81

ANFIS, 218 eompetitive, 73 differential eompetitive, 222,

223 Hcbbian, 71 in fuzzy networks, 209 Kohonen,76 neural, 58 parameters, 215 pereeptron, 59 reinforeement, 129 struetural, 214 supervised, 59, 81, 209, 227 unsupervised, 71, 81 usupervised, 225

least mean square, 61 linear ranking selcction, 29-31 linguistic deseription, 223 linguistie integrity, 192 linguistie valuc, 108, 119, 162, 237 linguistie variable, 108, 162, 179,

223 LMS, 61 load balaneing, 258 loeal

mating, 261 tournamcnt sclcetion, 29, 30

loeal and global minima, 64 logie proeessors, 208 Lukasiewiez, Jan, 104, 106

Mackey-Glass equation, 215 Malsburg, von der, 76 Mamdani fuzzy system, 109, 213 Mamdani model, 110 Mamdani, E. H., 106 many-valued logic, 104 master proeess, 256 maximum membership prineiple,

110 MAXONE problem, 5 mean-max method, 111 measurable spaee, 112 measure, 112 medical seienee, 119

membership function, 90, 162, 163 messy genetie algorithms, 14 meta-GA,242 metaeomputing, 254 mcxiean hat, 76 middle of maxima, 111 migration, 258 migration frequeney, 267 migration rate, 267 migration topology, 259 MI MD arehiteeture, 253 minimum deseription length, 21 model estimation, 81 modeling

fuzzy, 190 modules, 22 modus ponens, 108 moleeular devices, 292 Monte Carlo methods, 28 Muehlenbein, Heinz, 30 multi-set, 12 multilayered fuzzy neural networks,

208 mutation, 2, 4, 20, 23, 27, 30, 35

Lamarckian, 36 rate, 4, 237 soft modal, 246

nanoteehnology, 292 natural language, 84, 105 neeessity measure, 113 NEFPROX, 211 negation, 105 neighborhood, 261 neural maehines, 282 neural nets and statisties, 80 neural networks

applieations, 66 fuzzy, 202 learning in fuzzy networks, 209

neuro-fuzzy systems, 201 neuroeom puters

analog, 286 digital, 283 optieal, 287

non-linear foreeasting, 70 non-linear regression, 81 non-standard parallel models, 265 non-stationary optimization

problem, 177 normal memberhip function, 91

numerical analysis, 103

Oja's algorithm, 72 ontogeny, 247 opportunity set, 44 optimization problem, 11 OR fuzzy neuron, 205 OR/ AND fuzzy neuron, 207 order of a schema, 12 orgy, 24 orthogonal fuzzy sets, 97 Orthoplanner, 119 overfitting, 65, 271

parallel architectures, 251 evolutionary algorithms, 254 neural network models, 276 architectures, 250 evolutionary algorithm, 256

parallelism coarse-grain, 265 geometrie, 277

parameter setting, 234 Pareto-optimal, 40 parse tree, 19 pattern recognition, 121 payoff, 170 PCA networks, 72 penalty functions, 35 perceptron

learning algorithm, 59 permutation problem, 127 phenotype, 11, 22, 26, 36 phylogeny, 247 PID controller, 11 7 pie problem, 32, 41 plausibility measure, 115 population, 11

size, 237 small-sized, 248

portfolio optimisation, 39 portfolio theory, 39 possibility distribution, 113 possibility measure, 113 possibility theory, 112 pray-predator, 37 precision, 182, 185 predicate, 104 premature convergence, 29,

233-235, 237 principal component analysis, 72

probability theory, 112 and fuzziness, 84

program induction, 19, 22 proposition, 103

query, 182 fuzzy, 182

radial basis function networks, 219 random topology, 259 real-coded evolutionary algorithms,

245 recall, 182, 185 Rechenberg, Ingo, 1, 25 recombination, 2, 4, 24, 27, 30, 35,

245 soft modal, 246 using templates, 247

reconfigurable circuits, 284 regression, 32

non-linear, 81 symbolic, 239

relation, 96 equivalence, 98 fuzzy, 96, 223

relative fitness, 37 relevance, 182 repair algorithms, 35 representation

fuzzy, 248 representation theorem, 91, 100 reproduction, 4

asexual, 4 sexual, 4

response to selection, 30 restricted language, 19 risk aversion, 40 roulette wheel, 6, 9 Russel's Paradox, 85

s-norm: see triangular co-norm, 93 schema, 12

fitness of a, 12 order of a, 12 theorem, 12-14

Schlierkamp-Voosen, Dirk, 30 Schwefel, Hans-Paul, 26 selection, 2, 3, 25, 28, 30

fitness proportionate, 3, 28-30 linear ranking, 29-31, 238 local tournament, 29, 30 pressure, 237

Index

327

Index

328

random tournament, 239 response to, 30 truncation, 29, 30

selective differential, 30 pressure, 28, 29, 238

self-adaptation, 23-26 self-organizing maps, 75, 223, 225 semivariance, 40

target, 40 Sendai subway, 117 series prediction, 34 set, 85 set theory, 85 sexual reproduction, 4 shared memory, 253 SIMD architecture, 251 similarity measure, 98, 236 simulation, 178 SISD architecture, 251 size penalty, 21 small-population evolutionary

algorithm, 177 soft modal recombination and

mutation, 246 SOM,75 spatial structure, 258 speedup, 264 statistics

and neural nets, 80 genotypic, 236 of an evolutionary algorithm,

236 phenotypic, 236

steady-state, 31 stochastic

optimization, 1 selection operator, 244

stopping condition, 239 subtree, 20, 22 Sugeno fuzzy system, 110, 216 Sugeno model, 110 superindividual, 29 support, 91 survival of the fittest, 3 sustainable development, 291 syllogism, 107 symbolic regression, 34, 239 synchronous parallel algorithm, 264

t-conorm: see triangular co-norm, 94

t-norm: see triangular norm, 93 template, 247 terminal set, 19 termination condition, 4 time series prediction, 218 time-variant systems, 177 tolerance

for imprecision, 84 trading models, 269 traveling salesman problem, 32 tree, 19

representation, 20 size, 21

triangular co-norm, 94, 105, 245, 246

triangular norm, 94, 105, 245 truncation selection, 29, 30 truth

function, 105 partial, 83 value, 103, 105

TSK fuzzy model, 164, 166 TSK model, 110

uncertainty, 83, 112 union, 86, 94 universe of discourse, 86

variable dependent, 81 independent, 81

vector quantization, 75, 222 vigilance, 227 visualization, 241 Voigt, Hans-Michael, 246

W.A.R.P., 162, 171 weight evolution, 124 Werbos, Paul J., 62 Widrow-Hoff rule, 61

Zadeh, Lotfi, 83 Zeno's paradox, 89