Advances and Applications of DSmT for Information Fusion (Collected Works) : Volume 3

By Smarandache, Florentin

Book Id: WPLBN0002828228
Format Type: PDF eBook:
File Size: 23.22 MB
Reproduction Date: 7/17/2013

Title:	Advances and Applications of DSmT for Information Fusion (Collected Works) : Volume 3
Author:	Smarandache, Florentin
Volume:	Volume 3
Language:	English
Subject:	Non Fiction, Education, Dezert-Smarandache Theory (DSmT)
Collections:	Authors Community, Mathematics
Historic Publication Date:	2013
Publisher:	World Public Library

Member Page:	Florentin Smarandache
Citation APA MLA Chicago Smarandache, B. F., & Dezert, J. (2013). Advances and Applications of DSmT for Information Fusion (Collected Works) : Volume 3. Retrieved from http://gutenberg.cc/

Description
Applications demonstrate the power of the DSmT framework. In this third Volume, DSmT is applied to the entire spectrum of the Information Fusion that would interest any reader in data, sensor, information, and mathematical fusion topics. Highlighted in Figure 1 are the contemporary issues that include the links between (1) data conditioning and information management, (2) combined situation and impact assessment, and (2) knowledge representation between machine processing and user coordination. Various applications leverage DSmT “Advances” listed above along with DSmH (hybrid), DSmP (Probabilistic), and DSmT theoretical insights. The third volume attacks these application issues of coordination between the “levels” of information fusion.

Summary
Some works in this book are at their preliminary stages, others are under progress, and some are at their final stages of development. We hope that this third volume on DSmT will bring help and suscitate new ideas to researchers and engineers working in quantitative and qualitative information fusion under uncertainty. This third volume has about 760 pages, split into 25 chapters, from 41 contributors.

Table of Contents
Part I Advances on DSmT 1 Chapter 1 An introduction to DSmT 3 by J. Dezert and F. Smarandache 1.1 Introduction . . . . . . . . . . 4 1.2 Foundations of DSmT . . . . . . . . . 4 1.2.1 The power set, hyper-power set and super-power set . . 6 1.2.2 Notion of free and hybrid DSm models . . . . 18 1.2.3 Generalized belief functions . . . . . . 20 1.2.4 The classic DSm rule of combination . . . . . 21 1.2.5 The hybrid DSm rule of combination . . . . . 22 1.2.6 Examples of combination rules . . . . . . 24 1.2.7 Fusion of imprecise beliefs . . . . . . 29 1.3 Proportional Conflict Redistribution rule . . . . . 33 1.3.1 PCR formulas . . . . . . . . . 34 1.3.2 Examples . . . . . . . . . 35 1.3.3 Zadeh’s example . . . . . . . . 39 1.4 Uniform and partially uniform redistribution rules . . . 41 1.5 RSC Fusion rules . . . . . . . . . 43 1.6 The generalized pignistic transformation (GPT) . . . . 45 1.6.1 The classical pignistic transformation . . . . 45 1.6.2 Notion of DSmcardinality . . . . . . 46 1.6.3 The Generalized Pignistic Transformation . . . 47 1.7 The DSmP transformation . . . . . . . 48 1.7.1 The Probabilistic Information Content (PIC) . . . 49 1.7.2 The DSmP formula . . . . . . . 50 1.7.3 Examples for DSmP and BetP . . . . . . 51 1.8 Fusion of qualitative beliefs . . . . . . . 54 1.8.1 QualitativeOperators . . . . . . . 54 1.8.2 Qualitative Belief Assignment . . . . . . 55 1.8.3 Qualitative Conjunctive Rule . . . . . . 56 1.8.4 QualitativeDSm Classic rule . . . . . . 56 1.8.5 Qualitative hybrid DSm rule . . . . . . 57 1.8.6 Qualitative PCR5 rule (qPCR5) . . . . . 58 1.8.7 A simple example of qualitative fusion of qba’s . . . 58 1.8.8 A simple example for the qDSmP transformation . . . 60 1.9 Belief Conditioning Rules . . . . . . . 62 1.9.1 Shafer’s Conditioning Rule (SCR) . . . . . 62 1.9.2 Hyper-Power Set Decomposition (HPSD) . . . 63 1.9.3 Quantitative belief conditioning rules (BCR) . . . 63 1.9.4 Qualitative belief conditioning rules . . . . . 66 1.10 Conclusion . . . . . . . . . . 68 1.11 References . . . . . . . . . . . 68 Chapter 2 DSm field and linear algebra of refined labels 75 by F. Smarandache, J. Dezert and X. Li 2.1 Introduction . . . . . . . . . . 76 2.2 DSm field and linear algebra of refined labels . . . . 77 2.2.1 Qualitative operators on DSm-LARL . . . . . 77 2.2.2 The DSm field of refined labels . . . . . . 79 2.3 New operators . . . . . . . . . 81 2.4 Working with 2-tuple labels . . . . . . . 83 2.5 Working with interval of labels . . . . . . . 83 2.6 Concluding remark . . . . . . . . . 83 2.7 References . . . . . . . . . . . 84 Chapter 3 Transformations of beliefmasses into subjective probabilities 85 by J. Dezert and F. Smarandache 3.1 Introduction . . . . . . . . . . 86 3.2 Classical and generalized pignistic probabilities . . . . 86 3.2.1 Classical pignistic probability . . . . . . 86 3.2.2 Generalized pignistic probability . . . . . 87 3.3 Sudano’s probabilities . . . . . . . . . 87 3.4 Cuzzolin’s intersection probability . . . . . . 89 3.4.1 Definition . . . . . . . . . 89 3.4.2 Remarks . . . . . . . . . 90 3.5 A new generalized pignistic transformation . . . . . 90 3.5.1 The DSmP formula . . . . . . . 91 3.5.2 Advantages of DSmP . . . . . . . 92 3.6 PIC metric for the evaluation of the transformations . . . 95 3.6.1 Shannon entropy . . . . . . . . 95 3.6.2 The probabilistic information content . . . . 96 3.7 Examples and comparisons on a 2D frame . . . . . 96 3.7.1 Example 1: Shafer’s model with a general source . . . 96 3.7.2 Example 2: Shafer’s model with the ignorant source . . 100 3.7.3 Example 3: Shafer’s model with a probabilistic source . 102 3.7.4 Example 4: Shafer’s model with a non-Bayesian mass . 103 3.7.5 Example 5: Free DSm model . . . . . . 103 3.8 Examples on a 3D frame . . . . . . . . 111 3.8.1 Example 6: Shafer’s model with a non-Bayesian mass . 111 3.8.2 Example 7: Shafer’s model with another non-Bayesian mass . . . . . . . . . . 114 3.8.3 Example 8: Shafer’s model with yet another non-Bayesian mass . . . . . . . . . . 118 3.8.4 Example 9: Shafer’s model with yet another non-Bayesian mass . . . . . . . . . . 118 3.8.5 Example 10: Hybrid DSm model . . . . . 119 3.8.6 Example 11: Free DSmmodel . . . . . . 127 3.9 Extension of DSmP for qualitative belief . . . . . 131 3.10 Example for qualitative DSmP . . . . . . . 133 3.11 Conclusions . . . . . . . . . . 134 3.12 References . . . . . . . . . . . 134 Chapter 4 Probabilistic PCR6 fusion rule 137 by F. Dambreville, F. Celeste, J. Dezert and F. Smarandache 4.1 Introduction . . . . . . . . . . 138 4.2 PCR6 formula for probabilities . . . . . . . 139 4.2.1 Definition and justification of PCR6 . . . . . 139 4.2.2 Reformulation of PCR6 . . . . . . . 141 4.2.3 Definition of probabilistic PCR6 (p-PCR6) . . . 142 4.2.4 Reformulation of p-PCR6 . . . . . . 144 4.2.5 Extension of p-PCR6 on continuous propositions . . . 144 4.2.6 Sampling method . . . . . . . . 146 4.3 Bayes versus p-PCR6 . . . . . . . . . 147 4.3.1 Bayesian fusion rule . . . . . . . 147 4.3.2 Fusion based on p-PCR6 for Gaussian distributions . . 150 4.4 A distributed sequential filtering application . . . . . 151 4.4.1 Whitened p-PCR6 rule . . . . . . . 151 4.4.2 Theoretical setting . . . . . . . 151 4.4.3 Scenario and tests . . . . . . . 153 4.5 Conclusions . . . . . . . . . . 159 4.6 References . . . . . . . . . . . 160 Chapter 5 A class of fusion rules based on the belief redistribution to subsets or complements 161 by F. Smarandache, A. Martin and J. Dezert 5.1 Introduction . . . . . . . . . . 162 5.2 Fusion rules based on RSC . . . . . . . 162 5.2.1 RSC rule no 1 . . . . . . . . . 163 5.2.2 RSC rule no 2 . . . . . . . . . 163 5.2.3 RSC rule no 3 . . . . . . . . . 164 5.2.4 RSC rule no 4 . . . . . . . . . 164 5.2.5 RSC rule no 5 . . . . . . . . . 165 5.2.6 RSC rule no 6 . . . . . . . . . 165 5.2.7 RSC rule no 7 . . . . . . . . . 166 5.2.8 RSC rule no 8 . . . . . . . . . 166 5.2.9 Remarks . . . . . . . . . 167 5.3 A new class of RSC fusion rules . . . . . . . 167 5.4 A general formulation . . . . . . . . . 168 5.4.1 A general formula for the class of RSC fusion rules . . . 169 5.4.2 Example . . . . . . . . . 170 5.5 A general formulation including reliability . . . . . 172 5.5.1 Examples . . . . . . . . . 172 5.6 A new rule including reliability . . . . . . . 176 5.6.1 The fusion of two experts including their reliability . . . 176 5.6.2 Some examples . . . . . . . . . 179 5.6.3 The fusion of s ≥ 2 experts including their reliability . . 180 5.7 Conclusions . . . . . . . . . . 182 5.8 References . . . . . . . . . . . 182 Chapter 6 Definition of evidence fusion rules based on referee functions 185 by F. Dambreville 6.1 Introduction . . . . . . . . . . 186 6.2 Belief fusion . . . . . . . . . . 187 6.2.1 Lattices . . . . . . . . . 187 6.2.2 Belief functions . . . . . . . . . 189 6.2.3 Fusion rules . . . . . . . . . 189 6.2.4 Disjunctive rule . . . . . . . . . 190 6.3 Referee function and fusion rules . . . . . . 191 6.3.1 Referee function . . . . . . . . 191 6.3.2 Properties . . . . . . . . . 192 6.3.3 Sampling process . . . . . . . . 195 6.3.4 Algorithmic definition of fusion rules . . . . . 196 6.4 Example of referee functions . . . . . . . 197 6.4.1 Dempster-Shafer rule . . . . . . . 197 6.4.2 Disjunctive rule . . . . . . . . . 197 6.4.3 Dubois & Prade rule . . . . . . . 198 6.4.4 Averaging rule . . . . . . . . . 199 6.4.5 PCR6 rule . . . . . . . . . 200 6.4.6 Non conjunctive rejection . . . . . . 201 6.4.7 Any rule? . . . . . . . . . 202 6.5 A new rule: PCR_ . . . . . . . . . 203 6.5.1 Limitations of PCR6 . . . . . . . 203 6.5.2 Algorithm . . . . . . . . . 203 6.5.3 Referee function . . . . . . . . 205 6.5.4 Variants of PCR_ . . . . . . . . 206 6.6 Numerical examples . . . . . . . . . 208 6.6.1 Convergence . . . . . . . . . 208 6.6.2 Comparative tests . . . . . . . 211 6.7 Conclusion . . . . . . . . . . 213 6.8 References . . . . . . . . . . . 214 Chapter 7 Implementing general belief function framework with a practical codification for low complexity 217 by A. Martin 7.1 Introduction . . . . . . . . . . 218 7.2 Short background on theory of belief functions . . . . 219 7.3 A general belief function framework . . . . . . 221 7.3.1 A practical codification . . . . . . . 221 7.3.2 Adding constraints . . . . . . . 224 7.3.3 Codification of the focal elements . . . . . 224 7.3.4 Combination . . . . . . . . . 225 7.3.5 Decision . . . . . . . . . 226 7.3.6 Generation of DΘ r . . . . . . . 230 7.3.7 Decoding . . . . . . . . . 231 7.4 Concluding remarks . . . . . . . . . 232 7.5 MATLABTM codes . . . . . . . . . 233 7.5.1 Codification . . . . . . . . . 238 7.5.2 Combination . . . . . . . . . 243 7.5.3 Decision . . . . . . . . . 250 7.5.4 Decoding and generation of DΘ r . . . . . . 264 7.6 Acknowledgments . . . . . . . . . 271 7.7 References . . . . . . . . . . . 271 Chapter 8 Fusion of qualitative information using imprecise 2 -tuple labels 275 by X. Li, X. Huang, J. Dezert, F. Smarandache and L. Duan 8.1 Introduction . . . . . . . . . . 276 8.2 DSmT for the fusion of beliefs . . . . . . . 278 8.2.1 Basic belief mass . . . . . . . . 278 8.2.2 Fusion of quantitative beliefs . . . . . . 278 8.3 Linguistic models of qualitative beliefs . . . . . . 280 8.3.1 The 1-tuple linguistic model . . . . . . 280 8.3.2 The 1-tuple linguistic enriched model . . . . 281 8.3.3 The precise 2-tuple linguistic model . . . . . 282 8.3.4 The imprecise 2-tuple linguistic model . . . . 284 8.4 Fusion of qualitative beliefs . . . . . . . 287 8.4.1 Fusion of precise qualitative beliefs . . . . . 287 8.4.2 Fusion of imprecise qualitative beliefs . . . . 289 8.5 Examples of fusion of qualitative beliefs . . . . . 291 8.5.1 Example of fusion of precise qualitative beliefs . . . 292 8.5.2 Example of fusion of imprecise qualitative beliefs . . . 294 8.6 Conclusion . . . . . . . . . . 295 8.7 References . . . . . . . . . . . 296 Chapter 9 Non-numeric labels and constrained focal elements 299 by C. Osswald and A. Martin 9.1 Introduction . . . . . . . . . . 300 9.2 Theories of belief functions . . . . . . . 301 9.2.1 Basic belief assignments . . . . . . . 301 9.2.2 Decision-aid functions . . . . . . . 301 9.2.3 Usual combination operators . . . . . . 302 9.2.4 Enough operators available? . . . . . . 303 9.2.5 Operators for the usual bba operations . . . . 304 9.3 Extending the definition of labels . . . . . . 305 9.3.1 Discrete and totally ordered labels . . . . . 306 9.3.2 Max-Min algebra . . . . . . . . 306 9.3.3 Auto-indenting labels . . . . . . . 307 9.3.4 Soft auto-indenting labels . . . . . . 308 9.3.5 Example . . . . . . . . . 308 9.3.6 Lattice Labels . . . . . . . . . 309 9.3.7 Intervalmasses . . . . . . . . . 310 9.4 Constraints over the focal elements . . . . . . 311 9.4.1 Ordered set . . . . . . . . . 311 9.4.2 Intervals of RN . . . . . . . . . 312 9.4.3 Partitions . . . . . . . . . 313 9.4.4 Hierarchies . . . . . . . . . 314 9.4.5 Binary clustering systems . . . . . . 316 9.4.6 Semantic assertions . . . . . . . 316 9.5 Conclusion . . . . . . . . . . 317 9.6 References . . . . . . . . . . . 317 9.7 Appendix: algebras . . . . . . . . . 319 9.7.1 Orders and partial orders . . . . . . 319 9.7.2 Lattice . . . . . . . . . 320 9.7.3 Ring and semi-ring . . . . . . . 320 9.7.4 Field . . . . . . . . . . 321 9.7.5 Vector space . . . . . . . . . 321 9.7.6 Algebra over a field . . . . . . . 321 Chapter 10 Analysis of DSm belief conditioning rules and extension of their applicability 323 by M. Daniel 10.1 Introduction . . . . . . . . . . 324 10.2 Brief preliminaries . . . . . . . . . 324 10.3 Belief conditioning rule BCR1 . . . . . . . 325 10.4 Belief conditioning rules BCR2–BCR11 . . . . . 326 10.4.1 Belief conditioning rules BCR2–BCR6 . . . . 326 10.4.2 Belief conditioning rules BCR7–BCR11 . . . . 329 10.5 Belief conditioning rules BCR12–BCR31 . . . . . 329 10.5.1 Belief conditioning rules BCR12–BCR16 . . . . 329 10.5.2 Belief conditioning rules BCR17–BCR21 . . . . 331 10.5.3 The remaining belief conditioning rules . . . . 331 10.6 Comparison of BCRs with the classic rules . . . . . 332 10.6.1 BCR1 . . . . . . . . . 332 10.6.2 BCR2–BCR6 . . . . . . . . . 332 10.6.3 BCR7–BCR11 . . . . . . . . . 332 10.6.4 BCR12–BCR16 . . . . . . . . . 332 10.6.5 BCR17–BCR21 . . . . . . . . . 333 10.6.6 BCR22–BCR31 . . . . . . . . . 333 10.6.7 Comparison of definition domains . . . . . 333 10.7 Extension of applicability of BCRs . . . . . . 334 10.7.1 Extension of applicability in general DSm models . . . 334 10.7.2 Extension of applicability in the free DSm model . . . 337 10.7.3 Extended definition of BCR12 . . . . . . 337 10.8 Summary of comparison . . . . . . . . 338 10.8.1 Summary of coincidence of BCRs with DRC . . . 338 10.8.2 Comparison of BCR1, BCR12 and BCR17 with classic rules of conditioning . . . . . . . 339 10.9 Conclusions . . . . . . . . . . 340 10.10References . . . . . . . . . . . 340 10.11Appendix: comments to implementation . . . . . 342 Part II Applications of DSmT 345 Chapter 11 Attribute information evaluation in C&C systems 347 by K. Krenc and A. Kawalec 11.1 Introduction . . . . . . . . . . 348 11.2 Assessing information . . . . . . . . . 348 11.2.1 Evaluation factors . . . . . . . 348 11.2.2 Not only distancematters . . . . . . 349 11.3 The attribute information evaluation model . . . . . 350 11.3.1 The types of sensors . . . . . . . 351 11.3.2 Classifier . . . . . . . . . 354 11.3.3 Evaluator . . . . . . . . . 354 11.4 Numerical experiments . . . . . . . . . 359 11.4.1 Assumptions . . . . . . . . . 359 11.4.2 Settings and other model information . . . . 360 11.4.3 Results . . . . . . . . . 361 11.4.4 Discussion . . . . . . . . . 367 11.5 Latest concepts . . . . . . . . . 368 11.6 Conclusion . . . . . . . . . . 370 11.7 References . . . . . . . . . . . 370 Chapter 12 Utilizing classifier conflict for sensor management and user interaction 371 by W.L. van Norden and C.M. Jonker 12.1 Introduction . . . . . . . . . . 372 12.2 Combination rules . . . . . . . . . 372 12.3 Classification and sensor management . . . . . . 373 12.3.1 Sensormanagement . . . . . . . 374 12.3.2 Modeling the classification space . . . . . 374 12.3.3 Intersection between elements . . . . . . 375 12.3.4 Interaction with the user . . . . . . 376 12.4 Conflict . . . . . . . . . . . 377 12.4.1 Tracking conflict in PCR6 . . . . . . 377 12.4.2 Redistribution of remaining conflict . . . . . 379 12.5 Utilizing the conflict in sensor management . . . . . 382 12.5.1 Conflict per source . . . . . . . 382 12.5.2 Conflict per hypotheses . . . . . . . 384 12.6 Conclusions . . . . . . . . . . 384 12.7 References . . . . . . . . . . . 384 Chapter 13 Automatic goal allocation for a planetary rover with DSmT 387 by M. Vasile and M. Ceriotti 13.1 Introduction . . . . . . . . . . 388 13.2 Plausible and paradoxical reasoning . . . . . . 390 13.3 Modeling interest for a planetary rover . . . . . . 391 13.3.1 Modeling of sensor information . . . . . . 392 13.3.2 Definition of the Interest Map . . . . . . 392 13.4 Some results with DSmT . . . . . . . 397 13.4.1 DST applied the generation of the Interest Map . . . 403 13.5 Final remarks . . . . . . . . . 409 13.6 Acknowledgments . . . . . . . . . 409 13.7 References . . . . . . . . . . . 409 Chapter 14 Performance evaluation of a tracking algorithm including attribute data 411 by J. Dezert, A. Tchamova, L. Bojilov and P. Konstantinova 14.1 Introduction . . . . . . . . . . 412 14.2 Problemformulation . . . . . . . . . 412 14.2.1 Kinematic likelihood ratios for GDA . . . . . 413 14.2.2 Attribute likelihood ratios for GDA . . . . . 414 14.3 Scenario of simulations and results . . . . . . 415 14.3.1 Scenario of simulations . . . . . . . 415 14.3.2 Numerical results . . . . . . . 416 14.4 Conclusions . . . . . . . . . . 421 14.5 References . . . . . . . . . . . 421 Chapter 15 New fusion rules for solving Blackman’s association problem 425 by A. Tchamova, J. Dezert and F. Smarandache 15.1 On Blackman’s association problem . . . . . . 426 15.1.1 Blackman’s association problem. . . . . . 427 15.2 State-of-the-art to find a correct solution . . . . . 428 15.3 Basics of Dezert-Smarandache theory . . . . . . 428 15.3.1 Free DSmmodel . . . . . . . . 429 15.3.2 Hybrid DSm model . . . . . . . 429 15.3.3 Hyper-power set and classical DSm fusion rule . . . 429 15.4 Proportional conflict redistribution rule no.5 . . . . . 430 15.5 T-conorm/T-norm based combination rules . . . . . 431 15.6 Measure of estimation based on generalized pignistic probabilities433 15.7 Simulation results . . . . . . . . . 434 15.8 Conclusions . . . . . . . . . . 435 15.9 References . . . . . . . . . . . 435 Chapter 16 Target type tracking with DSmP 437 by J. Dezert, F. Smarandache, A. Tchamova and P. Konstantinova 16.1 Introduction . . . . . . . . . . 438 16.2 A short introduction of DSmT . . . . . . . 438 16.3 DSmH and PCR5 combination rules . . . . . . 440 16.3.1 DSmH combination rule . . . . . . . 440 16.3.2 PCR5 combination rule . . . . . . . 440 16.3.3 How to choose between PCR5 and DSmH . . . 441 16.4 Probabilistic belief transformations . . . . . . 442 16.4.1 Classical and generalized pignistic probabilities . . . 442 16.4.2 A new generalized pignistic transformation . . . 443 16.5 The target type tracking problem . . . . . . 445 16.6 Simulations results . . . . . . . . . 447 16.6.1 Results based on DSmH fusion . . . . . . 448 16.6.2 Results based on PCR5 fusion . . . . . . 450 16.6.3 Results based on Dempster-Shafer rule . . . . 450 16.7 Conclusions . . . . . . . . . . 453 16.8 References . . . . . . . . . . . 453 Chapter 17 Framework for biometric match score fusion using statistical and belief models 455 by M. Vatsa, R. Singh and A. Noore 17.1 Introduction . . . . . . . . . . 456 17.2 Overview of belief function theory based fusion algorithms . . . 457 17.3 Framework for biometric match score fusion . . . . . 459 17.3.1 Match score fusion . . . . . . . 460 17.3.2 Statistical classification . . . . . . . 461 17.4 Algorithms and databases used for evaluation . . . . 462 17.4.1 Face verification algorithms . . . . . . 462 17.4.2 Fingerprint verification algorithm. . . . . 462 17.4.3 Biometric databases used for evaluation . . . . 463 17.5 Experimental evaluation . . . . . . . . 463 17.6 Unification of fusion rules . . . . . . . 465 17.7 Conclusion . . . . . . . . . . 466 17.8 Acknowledgments . . . . . . . . . 467 17.9 References . . . . . . . . . . . 467 Chapter 18 Multimodal information retrieval based on DSmT. Application to computer-aided medical diagnosis 471 by G. Quellec, M. Lamard, G. Cazuguel, B. Cochener and C. Roux 18.1 Introduction . . . . . . . . . . 472 18.2 Objectives . . . . . . . . . . . 473 18.3 Shafer’smodel for information retrieval . . . . . 473 18.3.1 Image processing . . . . . . . . 474 18.3.2 Estimation of the degree of match for a feature Fi . . . 475 18.3.3 Designing the frame of discernment . . . . . 475 18.3.4 Defining the belief mass functions . . . . . 476 18.3.5 Fusing the belief mass functions . . . . . 476 18.3.6 Identifying the most similar cases . . . . . 477 18.3.7 Managingmissing values . . . . . . . 477 18.4 Hybrid DSm model for information retrieval . . . . . 478 18.4.1 Designing the frame of discernment . . . . . 478 18.4.2 Defining the belief mass functions . . . . . 479 18.4.3 Fusing the belief mass functions . . . . . 480 18.4.4 Identifying the most similar cases . . . . . 483 18.4.5 Managingmissing values . . . . . . . 483 18.5 Application to computer-aided medical diagnosis . . . 483 18.5.1 Diabetic retinopathy database (DRD) . . . . 483 18.5.2 Digital database for screening mammography . . . 487 18.5.3 Objective of the computer-aided diagnosis system . . . 488 18.5.4 Features of the patient records . . . . . . 488 18.5.5 Training and evaluation datasets . . . . . 488 18.5.6 Results . . . . . . . . . 488 18.6 Discussion and conclusion . . . . . . . 491 18.7 References . . . . . . . . . . . 492 18.8 Appendix: PCR rule with polynomial complexity . . . 495 18.8.1 Algorithm for the conjunctive rule . . . . . 496 18.8.2 Proposed PCR rule of combination . . . . . 499 18.8.3 Conclusion . . . . . . . . . 502 Chapter 19 Fusion of ESM allegiance reports using DSmT 503 by P. Djiknavorian, P. Valin and D. Grenier 19.1 Background . . . . . . . . . . 504 19.1.1 An interpretation of STANAG 1241 . . . . . 504 19.1.2 Another interpretation of STANAG 1241 . . . 505 19.2 Dezert-Smarandache theory . . . . . . . 506 19.2.1 Formulae for DST and DSmT . . . . . . 506 19.2.2 A typical simulation scenario . . . . . . 508 19.3 Results for the simulated scenario . . . . . . 509 19.3.1 DST results . . . . . . . . . 510 19.3.2 DSmH results . . . . . . . . . 511 19.3.3 PCR5 results . . . . . . . . . 511 19.3.4 Decision-making threshold . . . . . . 512 19.4 Monte-Carlo results . . . . . . . . . 513 19.4.1 DST results . . . . . . . . . 513 19.4.2 DSmH results . . . . . . . . . 514 19.4.3 PCR5 results . . . . . . . . . 514 19.4.4 Effect of varying the ESM parameters . . . . 514 19.5 Conclusions . . . . . . . . . . 517 19.6 References . . . . . . . . . . . 518 Chapter 20 Object identification using T-conorm/norm fusion rule 519 by A. Tchamova, J. Dezert and F. Smarandache 20.1 Introduction . . . . . . . . . . 520 20.2 Approach description . . . . . . . . . 520 20.3 Simulation scenario and results . . . . . . . 522 20.4 Conclusions . . . . . . . . . . 526 20.5 References . . . . . . . . . . . 526 Chapter 21 Map regenerating forest stands based on DST and DSmT combination rules 529 by B. Mora, R.A. Fournier and S. Foucher 21.1 Introduction . . . . . . . . . . 530 21.2 Reasoning theories . . . . . . . . . 530 21.2.1 Dempster-Shafer theory (DST) . . . . . . 530 21.2.2 Dezert-Smarandache theory (DSmT) . . . . . 532 21.2.3 Decision rule . . . . . . . . . 532 21.3 Information used in this work . . . . . . . 532 21.3.1 Study area . . . . . . . . . 532 21.3.2 Satellite imagery . . . . . . . . 533 21.3.3 Sample plots . . . . . . . . . 533 21.3.4 Drainage and surface deposit . . . . . . 534 21.4 Methods . . . . . . . . . . . 535 21.4.1 Referencemethods . . . . . . . 536 21.4.2 Data fusion methods . . . . . . . 536 21.5 Results and their interpretation . . . . . . . 540 21.5.1 Results based on the maximum likelihood algorithm . . 540 21.5.2 Results based on the fusion in DST framework . . . 540 21.5.3 Results based on the fusion in DSmT framework . . . 542 21.6 Sensitivity analysis . . . . . . . . . 542 21.6.1 Mass functions of the ancillary sources . . . . 542 21.6.2 Discounting coefficient . . . . . . . 542 21.7 Discussion . . . . . . . . . . . 544 21.8 Conclusion . . . . . . . . . . 545 21.9 References . . . . . . . . . . . 546 Chapter 22 Satellite image fusion using Dezert-Smarandache theory 549 by A. Bouakache, A. Belhadj-Aissa and G.Mercier 22.1 Introduction . . . . . . . . . . 550 22.2 Dezert Smarandache theory basis . . . . . . 551 22.2.1 Mass functions . . . . . . . . . 551 22.2.2 Decision Rule . . . . . . . . . 552 22.3 Implementation of the free and hybrid models . . . . 552 22.3.1 Implementation of the freemodel . . . . . 552 22.3.2 Implementation of the hybrid model . . . . . 554 22.4 Application . . . . . . . . . . 556 22.4.1 Site of study and data used . . . . . . 556 22.4.2 Fusion based on the freemodel . . . . . . 557 22.4.3 Fusion based on the hybridmodel . . . . . 560 22.4.4 Comparison between the free and hybrid models . . . 562 22.5 Conclusion . . . . . . . . . . 562 22.6 References . . . . . . . . . . . 563 Chapter 23 Information fusion for natural hazards in mountains 565 by J.-M. Tacnet, M. Batton-Hubert and J. Dezert 23.1 Introduction . . . . . . . . . . 566 23.1.1 Natural hazards in mountains . . . . . . 566 23.1.2 Experts are expected to manage and integrate the overall uncertainty . . . . . . . . . 568 23.1.3 A more realistic description of the expertise process . . 570 23.2 Backgrounds on MCDA and evidential reasoning . . . 572 23.2.1 Multi-criteria decision analysis . . . . . . 572 23.2.2 Evidential reasoning (ER) . . . . . . 579 23.2.3 Mixing MCDA and evidential reasoning . . . . 582 23.3 ER-MCDAmethodology . . . . . . . . 585 23.3.1 Possibility and Evidence Theory: why and what for? . . 586 23.3.2 AHP and ER within uncertain and complex context . . 587 23.3.3 Step 1: Problemmodeling . . . . . . 591 23.3.4 Step 2: Mapping quantitative criterion into a common frame . . . . . . . . . 596 23.3.5 Step 3: Mapping qualitative criterion into a common frame603 23.3.6 Decision-making . . . . . . . . 617 23.4 Applications: Sensitivity index in a multi-experts environment 619 23.4.1 Sensitivity index in a multi-experts environment . . . 619 23.5 Discussion . . . . . . . . . . . 643 23.5.1 Mixing uncertainty, imprecision, importance and traceability . . . . . . . . . 643 23.5.2 Advantages and lacks of the ER-MCDA framework . . . 644 23.5.3 The question of the validation . . . . . . 645 23.5.4 Towards an improved ER-MCDA framework . . . 647 23.6 Conclusion . . . . . . . . . . 648 23.7 Acknowledgments . . . . . . . . . 650 23.8 References . . . . . . . . . . . 651 Chapter 24 Improvement of multiple ground targets tracking with fusion of identification attributes 661 by B. Pannetier and J. Dezert 24.1 Introduction . . . . . . . . . . 662 24.2 Motionmodel . . . . . . . . . 663 24.2.1 Introduction . . . . . . . . . 663 24.2.2 GIS description . . . . . . . . . 663 24.2.3 Target state under constraint . . . . . . 664 24.3 Measurementmodel . . . . . . . . . 667 24.3.1 GMTI model . . . . . . . . . 667 24.3.2 IMINT model . . . . . . . . . 669 24.3.3 Ontologicmodel . . . . . . . . 670 24.4 VS-IMMwith road constraints (VS-IMMC) . . . . . 670 24.4.1 Track definitions and notations . . . . . . 670 24.4.2 IMM with only one road segment constraint . . . 671 24.4.3 Variation of the set of constrained motion models . . . 673 24.4.4 VS-IMMC within the SB-MHT . . . . . . 674 24.4.5 OOSMalgorithm . . . . . . . . 676 24.5 Target type tracking . . . . . . . . . 677 24.5.1 PCR5 combination rule . . . . . . . 677 24.5.2 Principle of the target type tracker . . . . . 678 24.5.3 Working with multiple sensors . . . . . . 679 24.5.4 Data attributes in the VS IMMC . . . . . 679 24.6 Simulations and results . . . . . . . . 680 24.6.1 Scenario description . . . . . . . 680 24.6.2 Filter parameters . . . . . . . . 684 24.6.3 Results . . . . . . . . . 685 24.7 Conclusion . . . . . . . . . . 688 24.8 References . . . . . . . . . . . 689 Chapter 25 Multiple cameras fusion based on DSmT for tracking objects on ground plane 691 by E. Garcia and L. Altamirano 25.1 Introduction . . . . . . . . . . 692 25.2 DSm hybridmodel . . . . . . . . . 693 25.3 Multiple cameras fusion . . . . . . . . 694 25.4 Results and discussion . . . . . . . . . 697 25.4.1 Probabilistic fusion module . . . . . . 698 25.5 Conclusions . . . . . . . . . . 703 25.6 References . . . . . . . . . . . 703 Biographies of contributors 705 List of Figures 720 List of Tables 727 Index 731