Advances and Applications of DSmT for Information Fusion Collected Works Volume 1

Front 
Cover......Page 1
Title Page
......Page 2
Copyright
......Page 3
Contents
......Page 4
Preamble......Page 14
Prefaces......Page 16
Part I Advances on DSmT......Page 20
1.1 Introduction......Page 22
1.2.2 Dempster's rule of combination......Page 24
1.2.3 Alternatives to Dempster's rule of combination......Page 25
1.2.4 The discounting of sources of evidence......Page 29
1.3.1 Notion of free and hybrid DSm models......Page 30
1.3.2 Notion of hyper-power set......Page 32
1.3.3 Generalized belief functions......Page 34
1.3.4 The classic DSm rule of combination......Page 35
1.3.5 The hybrid DSm rule of combination......Page 36
1.3.6 On the re nement of the frames......Page 37
1.3.7 On the combination of sources over di erent frames......Page 39
1.4.1 First example......Page 40
1.4.2 Second example......Page 44
1.4.3 Third example......Page 45
1.4.5 Fifth example......Page 46
1.5 Summary......Page 48
1.6 References......Page 50
2.1 Introduction......Page 56
2.3 Example of the rst hyper-power sets......Page 57
2.4.1 Memory size requirements and complexity......Page 58
2.4.2 Monotone Boolean functions......Page 59
2.4.3 Generation of MBF......Page 61
2.5 Conclusion......Page 64
2.6 References......Page 65
3.1 Introduction to matrix calculus for belief functions......Page 68
3.2.1 Order based on the enumeration of isotone Boolean functions......Page 70
3.2.2 Ordering based on the DSm cardinality......Page 71
3.2.3 Ordering based on the intrinsic informational content......Page 75
3.3 Conclusion......Page 78
3.4 References......Page 79
4.1 Introduction......Page 80
4.3.1 De nition of the free-DSm model......Page 81
4.3.2 Example of a free-DSm model......Page 82
4.4.1 De nition......Page 83
4.4.2 Example 1 : hybrid DSm model with an exclusivity constraint......Page 84
4.4.3 Example 2 : hybrid DSm model with another exclusivity constraint......Page 85
4.4.5 Example 4 : Shafer's model......Page 86
4.4.7 Example 6 : hybrid DSm model with two non-existential constraints......Page 87
4.4.8 Example 7 : hybrid DSm model with a mixed constraint......Page 88
4.5.1 Notations......Page 89
4.5.2 Programming of the......Page 90
4.5.3 The hybrid DSm rule of combination for 2 sources......Page 92
4.5.5 On the associativity of the hybrid DSm rule......Page 93
4.5.6 Property of the hybrid DSm Rule......Page 95
4.5.7 On the programming of the hybrid DSm rule......Page 97
4.5.8 Application of the hybrid DSm rule on previous examples......Page 98
4.5.9 Example with more general basic belief assignments......Page 108
4.5.10 The hybrid DSm rule versus Dempster's rule of combination......Page 111
4.6.1 Example 1......Page 112
4.6.2 Example 2......Page 113
4.6.3 Example 3......Page 114
4......Page 120
4.8 Conclusion......Page 121
4.9 References......Page 122
5.1 Introduction......Page 124
5.2.1 Counter-examples for Bayesian sources......Page 125
5.2.2 Counter-examples for more general sources......Page 127
5.3.1 Zadeh's example......Page 129
5.3.3 Generalization with......Page 133
5.4 Third in nite class of counter examples......Page 134
5.4.2 Example with......Page 135
5.4.4 Even more general......Page 136
5.5.2 Another example with......Page 137
5.5.5 Generalization......Page 138
5.6 Conclusion......Page 139
5.7 References......Page 140
6.1 Introduction......Page 142
6.2.1 General DSm rule of combination......Page 143
6.2.2 Examples......Page 145
6.3 Operations on sets......Page 146
6.4.1 DSm rules of combination......Page 149
6.4.2 Example with the DSm classic rule......Page 151
6.4.3 Example with the hybrid DSm rule......Page 153
6.5 Generalization of DSm rules for sets......Page 154
6.5.2 Some lemmas and a theorem......Page 155
6.5.3 An example with multiple-interval masses......Page 157
6.6 Conclusion......Page 159
6.7 References......Page 160
A Generalized Pignistic Transformation......Page 162
7.1 A short introduction to the DSm cardinality......Page 163
7.2 The Classical Pignistic Transformation (CPT)......Page 164
7.3.2......Page 165
7.4.2 Example for the 3D case......Page 167
7.5 Conclusion......Page 170
7.6 References......Page 171
8.1 Introduction......Page 174
8.2.1 Preliminary: about probability......Page 176
8.2.2 Dempster Shafer Theory......Page 180
8.2.3 Transferable Belief Model......Page 181
8.3 Dezert Smarandache Theory (DSmT)......Page 182
8.3.1 Dezert Smarandache model......Page 183
8.3.2 Fusion rule......Page 185
8.4.1 De nition......Page 186
8.5.1 A possible modal interpretation......Page 187
8.5.2 Deriving a fusion rule......Page 188
8.6.1 Modal logic......Page 190
8.6.2 A multi-modal logic......Page 194
8.6.3 Some multi-modal theorems......Page 195
8.6.4 Sensor fusion......Page 196
8.7 Logical interpretation of the Bayes inference......Page 202
8.7.1 De nitions......Page 203
8.7.2 Properties......Page 205
8.8 Conclusion......Page 208
8.9 References......Page 209
On conjunctive and disjunctive combination rules of evidence......Page 212
9.1 Introduction......Page 213
9.2.1 Source of information and multi-valued mappings......Page 215
9.2.3 Degree of belief......Page 216
9.2.4 The DS combination rule......Page 217
9.3.1 De nition of probability measure over the mapping space......Page 218
9.3.2 Derivation of the DS combination rule......Page 219
9.3.3 New explanations for the problems in DS combination rule......Page 220
9.3.4 Remark about \multi-valued mapping" in Shafer's paper......Page 222
9.4.1 Derivation of combination rule of probabilities......Page 223
9.4.2 Combination rule of probability measures in space......Page 225
9.5 The disjunctive combination rule......Page 227
9.6 Properties of conjunctive and disjunctive combination rules......Page 229
9.6.1 The combination rules of evidence......Page 230
9.6.2 Properties of combination rules of evidence......Page 232
9.6.3 Example......Page 235
9.7 Conclusion......Page 237
9.8 References......Page 238
10.1 Introduction......Page 242
10.2 Con ict in belief combination......Page 243
10.3.1 A system of di erent types of con icts......Page 244
10.3.2 Combination on generalized frames of discernment......Page 246
10.3.3 Reallocation of belief masses of con icts......Page 248
10.3.4 Summary of the idea of the minC combination......Page 249
10.4.1 Comparison of generalized frames of discernment......Page 250
10.4.2 Comparison of principles of combination......Page 251
10.4.3 Two steps of combination......Page 252
10.4.5 The special cases......Page 253
10.5 Examples......Page 254
10.7 References......Page 259
General Fusion Operators from Cox's Postulates......Page 262
11.1 About uncertainty......Page 263
11.1.1 Probabilistic modelling......Page 264
11.1.2 The mathematical theory of evidence......Page 266
11.1.3 Fuzzy logic......Page 267
11.1.4 Con dence measures......Page 269
11.2.2 Machine on con dence......Page 270
11.2.3 Operator......Page 271
11.3 T-norm......Page 272
11.3.2 T-norm description......Page 275
11.4 Conclusions......Page 277
11.5 References......Page 279
Part II Applications of DSmT......Page 282
12.1 Introduction......Page 284
12.2 The Tweety Penguin Triangle Problem......Page 285
12.3.1 The Pearl's analysis......Page 286
12.3.2 The weakness of the Pearl's analysis......Page 288
12.4 The Dempster-Shafer reasoning......Page 293
12.5 The Dezert-Smarandache reasoning......Page 300
12.6 Conclusion......Page 305
12.7 References......Page 306
Estimation of Target Behavior Tendencies using DSmT......Page 308
13.2 Statement of the Problem......Page 309
13.3.1 The fuzzi cation interface......Page 310
13.3.2 The behavior model......Page 311
13.3.4 State updating using DSmT......Page 313
13.5 Simulation study......Page 314
13.6 Comparison between DSm and Fuzzy Logic Approaches......Page 318
13.7 Conclusions......Page 319
13.8 References......Page 320
Generalized Data Association for Multitarget Tracking in Clutter......Page 322
14.2.1 Data Association......Page 323
14.3 The Attribute Contribution to GDA......Page 325
14.3.1 The Input Fuzzi cation Interface......Page 326
14.3.2 Tracks' Updating Procedures......Page 329
14.4 The Generalized Data Association Algorithm......Page 331
14.4.1 Kinematics probability term for generalized data association......Page 333
14.4.2 Attribute probability terms for generalized data association......Page 334
14.5.1 Simulation scenario1: Crossing targets......Page 335
14.5.2 Simulation scenario 2: Closely spaced targets......Page 336
14.6.1 Simulation results: Two crossing targets......Page 337
14.6.2 Simulation results: Four closely spaced targets......Page 338
14.6.3 Simulation results of GDA based on Dempster-Shafer theory......Page 339
14.7 Comparative analysis of the results......Page 340
14.9 References......Page 342
15.1 Introduction......Page 344
15.2.2 Association Problem no. 2......Page 345
15.3.2 The minimum con ict approach......Page 346
15.3.4 Tchamova's approach......Page 347
15.3.5 The entropy approaches......Page 348
15.3.6 Schubert's approach......Page 350
15.4 DSmT approaches for BAP......Page 352
15.5 Monte-Carlo simulations......Page 353
15.6 Conclusion......Page 354
15.7 References......Page 355
Neutrosophic Frameworks for Situation Analysis......Page 356
16.1 Introduction......Page 357
16.2 Situation analysis......Page 358
16.2.1 Situation awareness as a mental state......Page 359
16.2.2 Situation Analysis as a process......Page 360
16.3 Sources of uncertainty in Situation Analysis......Page 361
16.4.1 Allowing statements and reasoning about uncertainty......Page 364
16.4.2 Contextualization......Page 367
16.4.3 Enrichment of the universe of discourse......Page 369
16.4.4 Autoreference......Page 371
16.5.1 Neutrosophy......Page 372
16.5.2 Neutrosophic logic......Page 373
16.5.3 Dezert-Smarandache theory (DSmT)......Page 374
16.6 Possible worlds semantics for neutrosophic frameworks......Page 375
16.6.1 Kripke model......Page 376
16.6.2 Kripke structure for neutrosophic propositions......Page 378
16.6.3 Probability assignments and structures......Page 379
16.6.4 Connection between DSmT and neutrosophic logic in Kripke structures......Page 384
16.8 References......Page 385
Application of DSmT for Land Cover Change Prediction......Page 390
17.1 Introduction......Page 391
17.2.2 Hierarchization of the factors of land cover change......Page 392
17.3.1 Basic belief assignment......Page 394
17.4 Land cover prediction with DSmT......Page 396
17.4.1 Mass belief assignment......Page 397
17.4.2 Results......Page 398
17.6 References......Page 400
Power and Resource Aware Distributed Smart Fusion......Page 402
18.1 Introduction......Page 403
18.2.1 Discovery of missing information......Page 404
18.2.3 Feature discrimination......Page 406
18.2.4 Measures of value of information......Page 408
18.2.5 Fusion using DSmT......Page 409
18.3.1 Simulated network of radar sensors......Page 410
18.3.2 A real network of spatially DSN with disparate sensors......Page 418
18.5 References......Page 427
Biographies of contributors......Page 430