Advances and Applications of DSmT for Information Fusion

Florentin Smarandache, Jean Dezert9781931233828, 1931233829

This book presents the recent theoretical advances and applications of the Dezert-Smarandache Theory (DSmT) of plausible and paradoxical reasoning for information fusion. DSmT proposes a new mathematical framework to deal with the combination of uncertain, imprecise and highly conflicting sources of information expressed in terms of generalized basic belief functions. DSmT works beyond the limits of the Dempster-Shafer Theory and proposes a new general rule of combination which does not require a normalization step and works with any models (free DSm, hybrid DSm and Shafer’s model) whatever the degree of conflict between sources is. The DSmT is well adapted for static and dynamic fusion problematics and allows to work on any finite frames (discrete, continuous and/or hybrid). Therefore it can combine belief functions even if the refinement of the frame of discernment is inaccessible because of the vague, relative, and imprecise intrinsic nature of its elements. Part 1 of this book presents in details the last investigations on DSmT but also some related theoretical works with other approaches for information fusion. Part 2 of the book presents interesting applications of DSmT for solving both academic fusion problems and real-world fusion problems.
Collected works are by S. Corgne, F. Dambreville, M. Daniel, D. De Brucq, J. Dezert, M. Farooq, L. Hubert-Moy, A.-L. Jousselme, S. Kadambe, M. Khoshnevisan, P. D. Konstantinova, P. Maupin, G. Mercier, T. A. Semerdjiev, F. Smarandache, H. Sun, A. P. Tchamova.
The book has been launched in June at the Fusion 2004 Conference in Stockholm, Sweden.
A second volume about new applications and developments of DSmT (Dezert-Smarandache Theory of plausible, uncertain, and paradoxist information) will be published next year. Anybody is invited to contribute papers or chapters for this second collective book. Deadline: Fall 2005.
Contributed papers should be sent to Dr. Jean Dezert ([email protected], [email protected], ONERA – French National Establishment for Aerospace Research, BP 72 F-92322, Chatillon Cedex, France) and Prof. Florentin Smarandache ([email protected], University of New Mexico, 200 College Road, Gallup, NM 87301, USA).

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Table of contents :
Preamble……Page 13
Prefaces……Page 15
I Advances on DSmT……Page 19
Introduction……Page 21
Dempster’s rule of combination……Page 23
Alternatives to Dempster’s rule of combination……Page 24
The discounting of sources of evidence……Page 28
Notion of free and hybrid DSm models……Page 29
Notion of hyper-power set D……Page 31
Generalized belief functions……Page 33
The classic DSm rule of combination……Page 34
The hybrid DSm rule of combination……Page 35
On the refinement of the frames……Page 36
On the combination of sources over different frames……Page 38
First example……Page 39
Second example……Page 43
Third example……Page 44
Fifth example……Page 45
Summary……Page 47
References……Page 49
Introduction……Page 55
Example of the first hyper-power sets……Page 56
Memory size requirements and complexity……Page 57
Monotone Boolean functions……Page 58
Generation of MBF……Page 60
Conclusion……Page 63
References……Page 64
Appendix: MatLab code for generating hyper-power sets……Page 66
Introduction to matrix calculus for belief functions……Page 67
Order based on the enumeration of isotone Boolean functions……Page 69
Ordering based on the DSm cardinality……Page 70
Ordering based on the intrinsic informational content……Page 74
Conclusion……Page 77
References……Page 78
Introduction……Page 79
Definition of the free-DSm model Mf()……Page 80
Example of a free-DSm model……Page 81
Definition……Page 82
Example 1 : hybrid DSm model with an exclusivity constraint……Page 83
Example 2 : hybrid DSm model with another exclusivity constraint……Page 84
Example 4 : Shafer’s model……Page 85
Example 6 : hybrid DSm model with two non-existential constraints……Page 86
Example 7 : hybrid DSm model with a mixed constraint……Page 87
Notations……Page 88
Programming of the u(X) function……Page 89
The hybrid DSm rule of combination for 2 sources……Page 91
On the associativity of the hybrid DSm rule……Page 92
Property of the hybrid DSm Rule……Page 94
On the programming of the hybrid DSm rule……Page 96
Application of the hybrid DSm rule on previous examples……Page 97
Example with more general basic belief assignments m1(.) and m2(.)……Page 107
The hybrid DSm rule versus Dempster’s rule of combination……Page 110
Example 1……Page 111
Example 2……Page 112
Example 3……Page 113
Bayesian mixture of hybrid DSm models……Page 119
Conclusion……Page 120
References……Page 121
Introduction……Page 123
Counter-examples for Bayesian sources……Page 124
Counter-examples for more general sources……Page 126
Zadeh’s example……Page 128
Generalization with ={1,2,3,4}……Page 132
Third infinite class of counter examples……Page 133
Example with ={1,2,3,4,5}……Page 134
Even more general……Page 135
Another example with ={1,…,6}……Page 136
Generalization……Page 137
Conclusion……Page 138
References……Page 139
Introduction……Page 141
General DSm rule of combination……Page 142
Examples……Page 144
Operations on sets……Page 145
DSm rules of combination……Page 148
Example with the DSm classic rule……Page 150
Example with the hybrid DSm rule……Page 152
Generalization of DSm rules for sets……Page 153
Some lemmas and a theorem……Page 154
An example with multiple-interval masses……Page 156
Conclusion……Page 158
References……Page 159
A Generalized Pignistic Transformation……Page 161
A short introduction to the DSm cardinality……Page 162
The Classical Pignistic Transformation (CPT)……Page 163
P{.} is a probability measure……Page 164
Example for the 3D case……Page 166
Conclusion……Page 169
References……Page 170
Appendix: Derivation of the GPT for the 3D free DSm model……Page 171
Introduction……Page 173
Preliminary: about probability……Page 175
Dempster Shafer Theory……Page 179
Transferable Belief Model……Page 180
Dezert Smarandache Theory (DSmT)……Page 181
Dezert Smarandache model……Page 182
Fusion rule……Page 184
Definition……Page 185
A possible modal interpretation……Page 186
Deriving a fusion rule……Page 187
Modal logic……Page 189
A multi-modal logic……Page 193
Some multi-modal theorems……Page 194
Sensor fusion……Page 195
Logical interpretation of the Bayes inference……Page 201
Definitions……Page 202
Properties……Page 204
Conclusion……Page 207
References……Page 208
On conjunctive and disjunctive combination rules of evidence……Page 211
Introduction……Page 212
Source of information and multi-valued mappings……Page 214
Degree of belief……Page 215
The DS combination rule……Page 216
Definition of probability measure over the mapping space……Page 217
Derivation of the DS combination rule……Page 218
New explanations for the problems in DS combination rule……Page 219
Remark about “multi-valued mapping” in Shafer’s paper……Page 221
Derivation of combination rule of probabilities p12…n(i)……Page 222
Combination rule of probability measures in space S……Page 224
The disjunctive combination rule……Page 226
Properties of conjunctive and disjunctive combination rules……Page 228
The combination rules of evidence……Page 229
Properties of combination rules of evidence……Page 231
Example……Page 234
Conclusion……Page 236
References……Page 237
Introduction……Page 241
Conflict in belief combination……Page 242
A system of different types of conflicts……Page 243
Combination on generalized frames of discernment……Page 245
Reallocation of belief masses of conflicts……Page 247
Summary of the idea of the minC combination……Page 248
Comparison of generalized frames of discernment……Page 249
Comparison of principles of combination……Page 250
Two steps of combination……Page 251
The special cases……Page 252
Examples……Page 253
References……Page 258
General Fusion Operators from Cox’s Postulates……Page 261
About uncertainty……Page 262
Probabilistic modelling……Page 263
The mathematical theory of evidence……Page 265
Fuzzy logic……Page 266
Confidence measures……Page 268
Machine on confidence……Page 269
Operator……Page 270
T-norm……Page 271
T-norm description……Page 274
Conclusions……Page 276
References……Page 278
II Applications of DSmT……Page 281
Introduction……Page 283
The Tweety Penguin Triangle Problem……Page 284
The Pearl’s analysis……Page 285
The weakness of the Pearl’s analysis……Page 287
The Dempster-Shafer reasoning……Page 292
The Dezert-Smarandache reasoning……Page 299
Conclusion……Page 304
References……Page 305
Estimation of Target Behavior Tendencies using DSmT……Page 307
Statement of the Problem……Page 308
The fuzzification interface……Page 309
The behavior model……Page 310
State updating using DSmT……Page 312
Simulation study……Page 313
Comparison between DSm and Fuzzy Logic Approaches……Page 317
Conclusions……Page 318
References……Page 319
Generalized Data Association for Multitarget Tracking in Clutter……Page 321
Data Association……Page 322
The Attribute Contribution to GDA……Page 324
The Input Fuzzification Interface……Page 325
Tracks’ Updating Procedures……Page 328
The Generalized Data Association Algorithm……Page 330
Kinematics probability term for generalized data association……Page 332
Attribute probability terms for generalized data association……Page 333
Simulation scenario1: Crossing targets……Page 334
Simulation scenario 2: Closely spaced targets……Page 335
Simulation results: Two crossing targets……Page 336
Simulation results: Four closely spaced targets……Page 337
Simulation results of GDA based on Dempster-Shafer theory……Page 338
Comparative analysis of the results……Page 339
References……Page 341
Introduction……Page 343
Association Problem no. 2……Page 344
The minimum conflict approach……Page 345
Tchamova’s approach……Page 346
The entropy approaches……Page 347
Schubert’s approach……Page 349
DSmT approaches for BAP……Page 351
Monte-Carlo simulations……Page 352
Conclusion……Page 353
References……Page 354
Neutrosophic Frameworks for Situation Analysis……Page 355
Introduction……Page 356
Situation analysis……Page 357
Situation awareness as a mental state……Page 358
Situation Analysis as a process……Page 359
Sources of uncertainty in Situation Analysis……Page 360
Allowing statements and reasoning about uncertainty……Page 363
Contextualization……Page 366
Enrichment of the universe of discourse……Page 368
Autoreference……Page 370
Neutrosophy……Page 371
Neutrosophic logic……Page 372
Dezert-Smarandache theory (DSmT)……Page 373
Possible worlds semantics for neutrosophic frameworks……Page 374
Kripke model……Page 375
Kripke structure for neutrosophic propositions……Page 377
Probability assignments and structures……Page 378
Connection between DSmT and neutrosophic logic in Kripke structures……Page 383
References……Page 384
Application of DSmT for Land Cover Change Prediction……Page 389
Introduction……Page 390
Hierarchization of the factors of land cover change……Page 391
Basic belief assignment……Page 393
Land cover prediction with DSmT……Page 395
Mass belief assignment……Page 396
Results……Page 397
References……Page 399
Power and Resource Aware Distributed Smart Fusion……Page 401
Introduction……Page 402
Discovery of missing information……Page 403
Feature discrimination……Page 405
Measures of value of information……Page 407
Fusion using DSmT……Page 408
Simulated network of radar sensors……Page 409
A real network of spatially DSN with disparate sensors……Page 417
References……Page 426
Biographies of contributors……Page 429