Index

Note: Page numbers with “f’ denote figures; “t” tables.

A
A∗ algorithm, 280–293
Absolutely quotient space approachable, 300, 302
AND node, 149, 152
AND/OR graph, 3–5, 153f, 160, 295–296
Arcwise connected, 208, 351–353
Arcwise connectivity, 209
ASM method, 255, 371–373
Assembly planning, 194, 195
linear assembly planning, 194, 197
monotonic assembly planning, 195
sequential assembly planning, 194
Attribute function, 5, 62, 117–127
Attribute synthetic principle, 117–119
B
Belief function, 141
Belief theory, 132
C
Characteristic network, 213, 221–230, 235, 236f, 238f, 241–242, 246
Closure operation, 315–320, 355–362
Closure space, 316, 355–360
Collision-free paths planning, 210–216, 224, 231–237
Complete semi-order lattice, 14
Complexity function, 48–49
Compressed decomposition, 196–198
Configuration obstacle, 205, 205f
Configuration space, 205–206
Connected, l-connected, 72, 73f
Connected decomposition, 221, 222f, 233f, 241
Connected directed graph, 195, 196f
Connected graph, 196f
Connected set, 72, 73f
Cut relation, 81, 86
Cyclic compressed decomposition, 198
D
D-S combination rule, 143, 146
Dimension reduction, 216–230
Disassembly directed graph, 196
E
Empirically distributed function, 272
Envelope constraint, 179
Equivalence class, 7
Equivalence relation, 334
Evaluation function, 252–253, 294
F
Falsity preserving property, 326, 331
Fuzzy equivalence relation, 77–88, 189
Fuzzy isomorphism, 88, 95
Fuzzy isomorphism discrimination principle, 91, 93, 101
Fuzzy knowledge base, 84
Fuzzy quotient space, 84–86
ɛ-similarity, 88
G
General Harr wavelet, 304
Goal evaluation function, 252–253
Granular computing, 324–326
Granular world, 325
Granularity, 40f, 133–135
Granulation, 8–13, 325
Graph search, 294–296
H
Heuristic search, 250, 267
Hierarchical structure, 6f, 83, 86–87, 296–297
Homomorphism principle, 63, 140, 154, 155f
Homomorphism transform, 160
Homotopic equivalence, 214f, 231, 233
I
Isomorphism of fuzzy subsets, 95
ɛ-similarity discrimination, 100
Isomorphism principle, 96
Isosceles distance, 81
L
Lane, 231, 232f
Lower quotient operation, 164–166
M
MAX1 test, 272
MAX2 test, 273
Maximal homotopically equivalent set, 214, 224
Mechanical assembly planning, 194
Membership function, 77, 88, 101f
Minimal open set, 19–20
Motion planning, 24
geometrical method of motion planning, 205–207
topologic method of motion planning, 207–216
Multi-joint arm, 237–239, 238f
N
Nature projection, 18, 117, 141, 209, 316–319, 322
Network inference model, 135–146
O
Order preserving, 25, 29–30, 42, 110, 117, 318, 318f, 323, 324f
Outer (inner) quotient constraint, 177, 178f, 180
P
Partition, 9, 11, 49, 52–53, 227f, 237f
Possible disassembly direction, 198
Probabilistic model of complexity estimation, 54–62, 256
Projection, 107f, 123, 138–140, 152–155, 180
Q
Qualitative reasoning, 132, 170–171, 181–187
Quasi quotient operation, 303
(Quasi) Semi-order space, 25–26, 33, 38, 42–43, 110–113, 113f, 115, 317–318
Quasi semi-order structure, 317, 323
Quasi–equivalence, 317
Quotient attribute, 7, 105, 323, 326
Quotient closure operation, 318
Quotient constraint, 177–178, 178f, 186
Quotient mapping, 311–312, 323, 325–326
Quotient operation, 161–176, 326
Quotient semi-order, 41–42, 110–112, 117
Quotient set, 13, 15, 32, 138, 153f, 317–319, 324
Quotient space, 7–8, 13, 66–67, 326
Quotient space approachable, 300, 302
Quotient space approximation, 300–311
Quotient structure, 22–23, 32, 79, 160–181
Quotient topology, 16, 18–19, 322–323
R
Reasoning function, 137–138, 151–152
Reasoning rule, 136, 138, 150–152, 159, 188
Right-order topology, 25, 33, 41–42
Rotation Mapping, 212, 239
Rotation Mapping Graph (RMG), 212
S
SA algorithm, 258–259, 279, 292–293
SA(MAX) algorithm, 275, 277–278
SAA algorithm, 262–264
Second generation wavelet, 303–304, 311
Semi-continuous, 217–219, 222
Semi-continuous mapping
Semi-order, 110
Semi-order base, 110–111, 111f
Semi-order closed, 28, 37–39
Semi-order closure, 28, 34, 41
Semi-order lattice, 10–11, 13–14, 85, 108, 162
Sequential statistic, 271
Shaded area, 232, 232f
SPA1 algorithm, 259–260
SPA2 algorithm, 261–262
Spatial planning, 193, 299–300
Statistical heuristic search, 250–259, 267–268, 280–293, 296
Structural definition of fuzzy sets, 90–102
Successive approximation, 174–175
Successive refinement, 173–174, 185
Successive SA algorithm, 293
Synthesis of constraint, 180
Synthesis of domain, 108–109, 126
Synthesis of structure, 109
T
Tolerance relation, 303, 320–322, 324f, 325–326
Tolerant relations, 299
Topologic base, 113
Topologic neighboring, 214, 228, 242, 245–246
Topologic space, 12, 16, 22–23, 25–26
Truth preserving property, 224
U
Upper quotient operation, 162–164, 167–168, 171
V
Visibility graph method, 206, 207f
W
Wald sequential probability ratio test, 61, 254, 284
WSA method, 284, 287–288, 292–293, 294t
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