Index. ,a-possibility efficient solution, programming, 275
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1 Index,a-possibility efficient solution, programming, 275 aggregation, 31 of fuzzy number, 55 operator, 37, 45 agreement-discordance principle, 61 agricultural economics, 205 Arrow's impossibility theorem, 105 asset replacement problem, 433 assignment problem, 206, 262 Barlow-Wu class, 394 Bayes' principle, 335 bottom-up consideration, 400 branch-and-bound, 291, 294 cash flow, 424 centered fuzzy number, 197 choice, 69 function, 71, 75 Choquet integral, 43 clustering, 95 compromise solution, 202 computational complexity, 300 concordance-discordance principle, 61 consensus, 127 consequence crisp, 18 ill-known, 22 core, 160 a-approached, 172 last, 172 peripheral, 167 covering relation, 78 CPM,264 criterion comprehensive, 34 function, 19 degree of consensus, 127 a/q1/q2/i/b-consensus, 129 of Q1/Q2/I/B-consensus, 128 s/q1/q2/i/b-consensus, 130 dependence analysis, 399, 411 discrete fuzzy optimization, 249 dominance (see also Pareto principle), 71 dynamic programming, 282, 296, 432 dynamic system, 285 deterministic, 287, 292 fuzzy, 290, 293 stochastic, 288, 293 economic decision analysis, 421 life of an asset, 423, 428 economics, 139 ELECTRE, 21, 61, 88 equilibrium, 143 Nash, 145, 147 error probability, 397 expected fuzzy criterion, 296
2 450 DECISION ANALYSIS, OPERATIONS RESEARCH AND STATISTICS utility, 336 value of a fuzzy random variable, 319 exponential possibility regression, 362 extended addition, 197 failure probability, 397, 408 fault tree analysis, 405 favor, 50 filtering, 95 fixed point theorem, 141,145 flexible manufacturing, 303 programming, 181 FLIP, 201 flood control, 303 FULPAL,204 fuzzy consensus winner, 123 cr/q-consensus winner, 124 minimax consensus winner, 126 Q-consensus winner, 124 s/q-consensus winner, 125 fuzzy constraint, 181, 189,283 fuzzy control, 302 fuzzy core, 114 cr-core, 114 cr/q-core, 115 Q-core, 115 s/q-core, 116 fuzzy criterion, 296 fuzzy data, 186,312,320 fuzzy decision, 181, 216, 221, 252, 284 convex, 222 min-type, 285 product, 222 fuzzy dynamic programming, 281, 287,295 applications, 301 fuzzy event, 289 fuzzy goal, 181,216,283 induced, 285 fuzzy information, 324 sample, 326 system, 325 fuzzy integral, 42 fuzzy linear programming (FLP), 179 applications, 205 fuzzy measure, 42 fuzzy multiobjective linear programming, 191, 201 nonlinear programming, 234 fuzzy nonlinear programming, 215 fuzzy number, 180,234 fuzzy objective, 181, 191,295 fuzzy probability, 313, 318, 402 fuzzy programming, 182 fuzzy random sample, 327 variable, 313, 316, 382 fuzzy regression, 349, 360 fuzzy resource allocation, 301 fuzzy system state, 394 fuzzy-valued statistics, 315, 320 game cooperative, 140, 159 noncooperative, 145 ordinal, 153 theory, 137 Gibbard and Satterthwaite's theorem, 106 goal programming, 181, 227 graph, 251 graph-theoretic approach, 294 graphical interface, 202 grinding model, 358 group decision making, 103, 105 human reliability, 400 subjectivity, 396, 443 identification of operators, 51 incomparability, 6 indifference, 6, 20 inspection and replacement, 438 interaction, 48 index, 49 interactive procedure, 199,225,229 interval regression, 354
3 INDEX 451 inventory problem, 302 iterative approach, 294 kernel, 86 knapsack problem, 274 kriging, 383 L-R-type fuzzy number, 186 Lagrange function, 238, 244 multiplier, 232, 243 least squares regression, 353, 369 likelihood function, 328 ratio, 333 linear programming (LP), 179 linguistic term, 398, 406 linguistic quantifier, 107 fuzzy, 108 maintenance decision, 441 option, 442 majority, 107 fuzzy, 108, 123, 127 soft, 107 manufacturing and production, 206 marketing, 206 Markov chain, 288 mathematical programming, 179, 215,281 maximal flow, 251 meaningfulness, 33 membership function, 182, 216, 234, 283 concave, 183 exponential, 219 hyperbolic, 219 hyperbolic inverse, 221 linear, 183,219 piecewise linear, 221 s-shape, 183 strictly monotone, 217 metric distance, 371 minicost flow, 253 minimax problem, 229, 236, 242 augmented, 230, 237, 242 minimax set, 118 a-minimax set, 118 a/q-minimax set, 120 Q-minimax set, 120 s/q-minimax set, 121 multicriteria decision aid, 16, 31 multiobjective linear fractional programming, 201 nonlinear programming, 217 optimization problem, 183,201 multistage decision making (control), 281 under fuzziness, 285 multistate structure function, 395 system, 394 natural language expression, 406 necessity regression model, 357 network, 251 plannig, 264 nonlinear programming, 215 regression, 352 operator, 37 averaging, 38 compensative, 38 compensatory, 40 conjunctive, 38 disjunctive, 38 mean, 39 median, 39 non-compensative, 39 order statistic, 39 OWA,41 symmetric sum, 39 weighted, 40 optimal stationary strategy, 294, 295 optimistic index, 190 ordered weighted averaging (OWA), 41, 108, 110 outranking, 5
4 452 DECISION ANALYSIS, OPERATIONS RESEARCH AND STATISTICS overhaul option, 442 parametric programming, 185 Pareto principle (see also dominance), 56, 128 Cl- Pareto-optimal, 195 G-Cl- Pareto-optimal solution, 195 local Cl-Pareto optimal solution, 235 local M-Cl-Pareto optimal solution, 241 local M-Pareto optimal solution, 225 local Pareto optimal solution, 225 M-Pareto optimal solution, 224 pay-off function, 140 personnel management, 206 PERT, 266 pessimistic index, 190 policy iteration algorithm, 295 POSFUST, 395 possibilistic programming, 182 regression, 352, 353, 357 possibility theory, 23 preference, 3,31,70, 165,180 aggregation, 31 individual, 106, 112, 127 modeling,3 relation, 5, 8, 106 strict, 20, 71, 257 structure, 5,7, 10 weak, 20 probability, 325 PROBIST,395 production planning, 206 PROFUST,395 PROMETHEE, 21,64 pseudo-criterion, 20 psychological stress, 397 random experiment, 312 ranking, 69, 91 recurrence equation, 288, 291 redundant system, 398 reference fuzzy state, 291 membership level, 229, 236, 242 reliability, 391 replacement analysis, 421 cycle, 431 policy, 437 research and development, 302 scheduling, 206, 267, 302 scoring, 76 semi-criterion, 19 sensitivity theorem, 238, 244 set covering, 273 Shapley value, 49 shortest route, 255 social choice, 104, 105 choice (welfare) function, 105 decision function, 106 fuzzy preference relation, 106, 123 soft constraint, 180, 182 sorting, 69, 91 state transition equation, 285 statistics, 311 subjective measure of reliability, 409, 412 Sugeno integral, 43 system reliability analyzer, 415 reliability evaluation, 400 state, 393 technological change, 432 termination set of states, 294 termination time fixed and specified, 287 fuzzy, 291 implicitly specified, 294 infinite, 294 optimal, 292 top-down consideration, 400
5 INDEX 453 trade-off information, 232, 244 rates, 239, 244 transitive closure, 83 transportation problem, 258 system, 206, 302 utility function, 140, 170, 337 variance of a fuzzy random variable, 319 vertex method, 426 veto, 50 water resources planning, 205, 303 Yager's parametrized t-norm, 197 Zadeh's extension principle, 189, 233, 318
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