Combination of Evidence in Dempster-Shafer Theory

Dempster-Shafer theory offers an alternative to traditional probabilistic theory for the mathematical representation of uncertainty. The significant innovation of this framework is that it allows for the allocation of a probability mass to sets or intervals. Dempster-Shafer theory does not require an assumption regarding the probability of the individual constituents of the set or interval. This is a potentially valuable tool for the evaluation of risk and reliability in engineering applications when it is not possible to obtain a precise measurement from experiments, or when knowledge is obtained from expert elicitation. An important aspect of this theory is the combination of evidence obtained from multiple sources and the modeling of conflict between them. This report surveys a number of possible combination rules for Dempster-Shafer structures and provides examples of the implementation of these rules for discrete and interval-valued data.

[1]  Albena Tchamova.  Evidence reasoning theory with application to the identity estimation and data association systems , 1997 .

[2]  Robert A. Hummel,et al.  On the Use of the Dempster Shafer Model in Information Indexing and Retrieval Applications , 1993, Int. J. Man Mach. Stud..

[3]  D. Dubois,et al.  A set-theoretic view of belief functions: Logical operations and approximations by fuzzy sets , 1986 .

[4]  Xavier Roboam,et al.  IEE Conference Publication , 2000 .

[5]  Isabelle Bloch,et al.  A first step toward automatic interpretation of SAR images using evidential fusion of several structure detectors , 1999, IEEE Trans. Geosci. Remote. Sens..

[6]  David A. Bell,et al.  Using the Dempster‐Shafer orthogonal sum for reasoning which involves space , 1998 .

[7]  Farzin Deravi,et al.  Audio-visual person recognition: an evaluation of data fusion strategies , 1997 .

[8]  R. Huber.  Scene classification of SAR images acquired from antiparallel tracks using evidential and rule-based fusion , 2001 .

[9]  Lian-zeng Zhang,et al.  Representation, independence, and combination of evidence in the Dempster-Shafer theory , 1994 .

[10]  E. M. Oblow.  O-THEORY—A HYBRID UNCERTAINTY THEORY , 1987 .

[11]  R. Cooke.  Elicitation of expert opinions for uncertainty and risks , 2003 .

[12]  Andrea Servida,et al.  Evidence Aggregation in Expert Judgments , 1988, IPMU.

[13]  Quiming Zhu,et al.  Using the Dempster-Shafer reasoning model to perform pixel-level segmentation on color images , 1992, Optics & Photonics.

[14]  Takahiko Horiuchi,et al.  Decision Rule for Pattern Classification by Integrating Interval Feature Values , 1998, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[15]  Rajendra P. Srivastava,et al.  Evidential reasoning for WebTrust assurance services , 1999 .

[16]  Derek R. Peddle,et al.  MERCURY ⊕ : an evidential reasoning image classifier , 1995 .

[17]  D. Peddle.  Knowledge formulation for supervised evidential classification , 1995 .

[18]  Gu Guochang,et al.  AUV obstacle-avoidance based on information fusion of multi-sensors , 1997, 1997 IEEE International Conference on Intelligent Processing Systems (Cat. No.97TH8335).

[19]  F. Golshani,et al.  Uncertain reasoning using the Dempster-Shafer method: an application in forecasting and marketing management , 1990 .

[20]  Eloi Bosse,et al.  Fusion of identity declarations from dissimilar sources using the Dempster-Shafer theory , 1997 .

[21]  J. Kacprzyk,et al.  Advances in the Dempster-Shafer theory of evidence , 1994 .

[22]  Raghu Krishnapuram,et al.  A belief maintenance scheme for hierarchical knowledge‐based image analysis systems , 1991, Int. J. Intell. Syst..

[23]  P. L. Bogler,et al.  Shafer-dempster reasoning with applications to multisensor target identification systems , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[24]  Thierry Toutin,et al.  Dempster-Shafer theory for multi-satellite remotely sensed observations , 2000, SPIE Defense + Commercial Sensing.

[25]  J.R. Boston,et al.  Combination of data approaches to heuristic control and fault detection [heart assist devices] , 2000, Proceedings of the 2000. IEEE International Conference on Control Applications. Conference Proceedings (Cat. No.00CH37162).

[26]  Thierry Denoeux.  An evidence-theoretic neural network classifier , 1995, 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century.

[27]  Robin R. Murphy,et al.  Dempster-Shafer theory for sensor fusion in autonomous mobile robots , 1998, IEEE Trans. Robotics Autom..

[28]  Daniel L. Schmoldt,et al.  A prototype vision system for analyzing CT imagery of hardwood logs , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[29]  Robin R. Murphy,et al.  Ultrasonic robot localization using Dempster-Shafer theory , 1992, Optics & Photonics.

[30]  Forouzan Golshani,et al.  Dynamic route planning with uncertain information , 1996, Knowl. Based Syst..

[31]  J.C. Principe,et al.  Sleep staging automaton based on the theory of evidence , 1989, IEEE Transactions on Biomedical Engineering.

[32]  G. Vachtsevanos,et al.  DETECTION AND IDENTIFICATION OF AXIAL FLOW COMPRESSOR INSTABILITIES , 1992 .

[33]  Wuben Ben Luo,et al.  Using Dempster–Shafer Theory to Represent Climate Change Uncertainties , 1997 .

[34]  Singiresu S Rao,et al.  Generalized hybrid method for fuzzy multiobjective optimization of engineering systems , 1996 .

[35]  P. Smets.  The transferable belief model for expert judgements , 1990, [1990] Proceedings. First International Symposium on Uncertainty Modeling and Analysis.

[36]  M. Beynon,et al.  The Dempster-Shafer theory of evidence: an alternative approach to multicriteria decision modelling , 2000 .

[37]  Richard C. Hughes,et al.  Acoustic signal interpretation: Reasoning with non-specific and uncertain information , 1985, Pattern Recognit..

[38]  F. Pergalani,et al.  Slope Instability Zonation: a Comparison Between Certainty Factor and Fuzzy Dempster–Shafer Approaches , 1998 .

[39]  A. de Korvin,et al.  A Dempster-Shafer-based approach to compromise decision making with multiattributes applied to product selection , 1993 .

[40]  George J. Klir,et al.  On Measuring Uncertainty and Uncertainty-Based Information: Recent Developments , 2001, Annals of Mathematics and Artificial Intelligence.

[41]  Ronald R. Yager,et al.  Decision Making with Belief Structures: an Application in Risk Management , 1996, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[42]  Mounia Lalmas,et al.  Dempster-Shafer's theory of evidence applied to structured documents: modelling uncertainty , 1997, SIGIR '97.

[43]  A. Bastière.  Methods for multisensor classification of airborne targets integrating evidence theory , 1998 .

[44]  C. M. Cheng,et al.  A moving target detector based on information fusion , 1990, IEEE International Conference on Radar.

[45]  Luis Moreno,et al.  Analysis of data fusion methods in certainty grids application to collision danger monitoring , 1991, Proceedings IECON '91: 1991 International Conference on Industrial Electronics, Control and Instrumentation.

[46]  Xianoning Ling,et al.  Combining opinions form several experts , 1989, Appl. Artif. Intell..

[47]  Kamal Kant Bharadwaj,et al.  Hierarchical censored production rules (HCPRs) system employing the dempster-shafer uncertainty calculus , 1994, Inf. Softw. Technol..

[48]  Kimberly Coombs,et al.  Using Dempster-Shafer methods for object classification in the theater ballistic missile environment , 1999, Defense, Security, and Sensing.

[49]  Keith M. Andress.  Evidential reconstruction of vessel trees from rotational angiograms , 1998, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269).

[50]  Michel Chapron,et al.  A color edge detector based on Dempster-Shafer theory , 2000, Proceedings 2000 International Conference on Image Processing (Cat. No.00CH37101).

[51]  Lotfi A. Zadeh,et al.  A Simple View of the Dempster-Shafer Theory of Evidence and Its Implication for the Rule of Combination , 1985, AI Mag..

[52]  Malcolm J. Beynon,et al.  An expert system for multi-criteria decision making using Dempster Shafer theory , 2001, Expert Syst. Appl..

[53]  S. K. Wong,et al.  REPRESENTATION, PROPAGATION AND COMBINATION OF UNCERTAIN INFORMATION , 1994 .

[54]  Mübeccel Demirekler,et al.  A novel rank-based classifier combination scheme for speaker identification , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[55]  Peter Regel-Brietzmann,et al.  Soft-decision vector quantization based on the Dempster/Shafer theory , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[56]  Robin R. Murphy,et al.  Estimating time available for sensor fusion exception handling , 1995, Other Conferences.

[57]  Basel Solaiman,et al.  Combination of fuzzy sets and Dempster-Shafer theories in forest map updating using multispectral data , 2001, SPIE Defense + Commercial Sensing.

[58]  Mark J. Ducey,et al.  Representing uncertainty in silvicultural decisions : an application of the Dempster-Shafer theory of evidence , 2001 .

[59]  Guo Jing,et al.  Multisensor multiple-attribute data association , 1996, Proceedings of International Radar Conference.

[60]  Thierry Denoeux,et al.  Handling possibilistic labels in pattern classification using evidential reasoning , 2001, Fuzzy Sets Syst..

[61]  Ivan Kramosil.  Probabilistic analysis of belief functions , 2001 .

[62]  E. Drakopoulos,et al.  Decision rules for distributed decision networks with uncertainties , 1992 .

[63]  Seema Alim,et al.  Application of Dempster‐Shafer Theory for Interpretation of Seismic Parameters , 1988 .

[64]  Khaled Mellouli,et al.  Pooling expert opinions using Dempster-Shafer theory of evidence , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[65]  Pascal Vasseur,et al.  Perceptual organization approach based on Dempster-Shafer theory , 1999, Pattern Recognit..

[66]  Eric Lefevre,et al.  Knowledge modeling methods in the framework of evidence theory: an experimental comparison for melanoma detection , 2000, Smc 2000 conference proceedings. 2000 ieee international conference on systems, man and cybernetics. 'cybernetics evolving to systems, humans, organizations, and their complex interactions' (cat. no.0.

[67]  G. Klir.  IS THERE MORE TO UNCERTAINTY THAN SOME PROBABILITY THEORISTS MIGHT HAVE US BELIEVE , 1989 .

[68]  Eric Brassart,et al.  Cooperation between two omnidirectional perception systems for mobile robot localization , 2000, Proceedings. 2000 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000) (Cat. No.00CH37113).

[69]  A Gammerman,et al.  SYSEX: An Expert System for Biological Identification , 1987, Other Conferences.

[70]  Robert J. Safranek,et al.  Evidence accumulation using binary frames of discernment for verification vision , 1990, IEEE Trans. Robotics Autom..

[71]  Thierry Denux.  Reasoning with imprecise belief structures , 1999 .

[72]  George J. Klir,et al.  A design condition for incorporating human judgement into monitoring systems , 1999 .

[73]  John Yen.  Can evidence Be combined in the Dempster-shafer theory? , 1987, Int. J. Approx. Reason..

[74]  T. J. Moulsley,et al.  Extension of Dempster-Shafer theory and application to fault diagnosis in communication systems , 1994 .

[75]  G. Quirchmayr,et al.  Evaluating policies based on their long term average cost , 2000 .

[76]  Thierry Denoeux,et al.  Induction of decision trees from partially classified data using belief functions , 2000, Smc 2000 conference proceedings. 2000 ieee international conference on systems, man and cybernetics. 'cybernetics evolving to systems, humans, organizations, and their complex interactions' (cat. no.0.

[77]  Paul Suetens,et al.  Road extraction from multi-temporal satellite images by an evidential reasoning approach , 1991, Pattern Recognit. Lett..

[78]  V. Lesser,et al.  Dempster-Shafer theory and rule strengths in expert systems , 1990 .

[79]  Billur Barshan,et al.  Voting as Validation in Robot Programming , 1999, Int. J. Robotics Res..

[80]  Madan M. Gupta,et al.  Analysis and management of uncertainty : theory and applications , 1992 .

[81]  Dehua Li,et al.  Multi-source information integration in intelligent systems using the plausibility measure , 1994, Proceedings of 1994 IEEE International Conference on MFI '94. Multisensor Fusion and Integration for Intelligent Systems.

[82]  Toshiyuki Inagaki.  Interdependence between safety-control policy and multiple-sensor schemes via Dempster-Shafer theory , 1991 .

[83]  L Chandra Sekhara Sarma,et al.  A prototype expert system for interpretation of remote sensing image data , 1994 .

[84]  Fabrice Janez,et al.  Automatic map updating by fusion of multispectral images in the Dempster-Shafer framework , 2000, SPIE Optics + Photonics.

[85]  George Vachtsevanos,et al.  An application of fuzzy logic and Dempster-Shafer theory to failure detection and identification , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[86]  Mathias Bauer,et al.  Approximation algorithms and decision making in the Dempster-Shafer theory of evidence - An empirical study , 1997, Int. J. Approx. Reason..

[87]  Li Chen,et al.  A MODIFIED DEMPSTER-SHAFER THEORY FOR MULTICRITERIA OPTIMIZATION , 1998 .

[88]  M. Rombaut,et al.  Driving situation recognition in the CASSICE project towards an uncertainty management , 2000, ITSC2000. 2000 IEEE Intelligent Transportation Systems. Proceedings (Cat. No.00TH8493).

[89]  G. Ferrier,et al.  An Integrated GIS and Knowledge-Based System as an Aid for the Geological Analysis of Sedimentary Basins , 1997, Int. J. Geogr. Inf. Sci..

[90]  Thierry Denoeux.  Function approximation in the framework of evidence theory: a connectionist approach , 1997, Proceedings of International Conference on Neural Networks (ICNN'97).

[91]  J.-J. Chao,et al.  An efficient direct-sequence signal detector based on Dempster-Shafer theory , 1990, IEEE Trans. Commun..

[92]  S. S. Rao,et al.  Computer-aided design/engineering of bearing systems using the Dempster-Shafer theory , 1995, Artificial Intelligence for Engineering Design, Analysis and Manufacturing.

[93]  Prakash P. Shenoy,et al.  Using Dempster-Shafer's belief-function theory in expert systems , 1992, Defense, Security, and Sensing.

[94]  R. Yager.  Quasi-associative operations in the combination of evidence , 1987 .

[95]  R. M. Mersereau,et al.  A system for knowledge-based boundary detection of cardiac magnetic resonance image sequences , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[96]  Russell M. Mersereau,et al.  Knowledge-based system for boundary detection of four-dimensional cardiac magnetic resonance image sequences , 1993, IEEE Trans. Medical Imaging.

[97]  Peter M. Williams,et al.  An application of Dempster-Shafer theory to the assessment of biogas technology , 1992 .

[98]  Martin G. Bello,et al.  Representation and transformation of uncertainty in an evidence theory framework , 1989, Proceedings CVPR '89: IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[99]  T. Fine,et al.  The Emergence of Probability , 1976 .

[100]  M. Singh,et al.  An Evidential Reasoning Approach for Multiple-Attribute Decision Making with Uncertainty , 1994, IEEE Trans. Syst. Man Cybern. Syst..

[101]  Harald Ganster,et al.  Active fusion - A new method applied to remote sensing image interpretation , 1996, Pattern Recognit. Lett..

[102]  S. Hasegawa,et al.  Dempster-Shafer theoretic design of a decision support system for a large-complex system , 1994, Proceedings of 1994 3rd IEEE International Workshop on Robot and Human Communication.

[103]  Nii O. Attoh-Okine,et al.  Use of Belief Function in Brownfield Infrastructure Redevelopment Decision-Making , 2001 .

[104]  G. G. Wilkinson,et al.  Evidential reasoning in a pixel classification hierarchy—a potential method for integrating image classifiers and expert system rules based on geographic context , 1990 .

[105]  Andrew P. Sage,et al.  Uncertainty in Artificial Intelligence , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[106]  P. R. Gillett,et al.  Monetary unit sampling: a belief-function implementation for audit and accounting applications , 2000, Int. J. Approx. Reason..

[107]  D. Dubois,et al.  On the Combination of Evidence in Various Mathematical Frameworks , 1992 .

[108]  R. Yager.  On the dempster-shafer framework and new combination rules , 1987, Inf. Sci..

[109]  Ramesh C. Jain,et al.  Evidential reasoning for building environment maps , 1995, IEEE Trans. Syst. Man Cybern..

[110]  T. Denœux.  Modeling vague beliefs using fuzzy-valued belief structures , 2000 .

[111]  G. Isaksen,et al.  Interpretation of molecular geochemistry data by the application of artificial intelligence technology , 1997 .

[112]  Qiang Ji,et al.  Dempster-Shafer and Bayesian Network for CAD-Based Feature Extraction: A Comparative Investigation and Analysis , 1994, AAAI.

[113]  Y. C. Tang,et al.  A geometric feature relation graph formulation for consistent sensor fusion , 1990, 1990 IEEE International Conference on Systems, Man, and Cybernetics Conference Proceedings.

[114]  Thierry Denoeux,et al.  A k-nearest neighbor classification rule based on Dempster-Shafer theory , 1995, IEEE Trans. Syst. Man Cybern..

[115]  J.R. Deller,et al.  An AI-based communication system for motor and speech disabled persons: design methodology and prototype testing , 1989, IEEE Transactions on Biomedical Engineering.

[116]  Y Wu.  MOBILE ROBOT OBSTACLE DETECTION AND ENVIRONMENT MODELING WITH SENSOR FUSION , 1997 .

[117]  Ronald R. Yager,et al.  Arithmetic and Other Operations on Dempster-Shafer Structures , 1986, Int. J. Man Mach. Stud..

[118]  Henry Lum,et al.  Application of Plausible Reasoning to AI-Based Control Systems , 1987, 1987 American Control Conference.

[119]  Axel Pinz,et al.  A comparison of three uncertainty calculi for building sonar-based occupancy grids , 2001, Robotics Auton. Syst..

[120]  Horace Ho-Shing Ip,et al.  Human face recognition using Dempster-Shafer theory , 1994, Proceedings of 1st International Conference on Image Processing.

[121]  Xavier Briottet,et al.  Sensor Fusion Integrating Contextual Information , 2001, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[122]  Patrick Vannoorenberghe,et al.  Color image segmentation using Dempster-Shafer's theory , 1999, Proceedings 1999 International Conference on Image Processing (Cat. 99CH36348).

[123]  Sally McClean,et al.  Knowledge discovery in distributed databases using evidence theory , 2000, Int. J. Intell. Syst..

[124]  Jürg Kohlas,et al.  Theory of evidence — A survey of its mathematical foundations, applications and computational aspects , 1994, Math. Methods Oper. Res..

[125]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[126]  Michael J. Pont,et al.  Application of Dempster-Shafer theory in condition monitoring applications: a case study , 2001, Pattern Recognit. Lett..

[127]  Qiang Ji,et al.  An evidential reasoning approach for recognizing shape features , 1995, Proceedings the 11th Conference on Artificial Intelligence for Applications.

[128]  M. Kawade.  Object recognition system in a dynamic environment , 1995, Proceedings of 1995 IEEE International Conference on Fuzzy Systems..

[129]  Isabelle Bloch,et al.  Some aspects of Dempster-Shafer evidence theory for classification of multi-modality medical images taking partial volume effect into account , 1996, Pattern Recognit. Lett..

[130]  Jerome J. Braun.  Dempster-Shafer theory and Bayesian reasoning in multisensor data fusion , 2000, SPIE Defense + Commercial Sensing.

[131]  Jean-Marc Boucher,et al.  Multiscale and multisource classification using Dempster-Shafer theory , 1999, Proceedings 1999 International Conference on Image Processing (Cat. 99CH36348).

[132]  Mounia Lalmas,et al.  Representing and retrieving structured documents using the Dempster-Shafer theory of evidence: modelling and evaluation , 1998, J. Documentation.

[133]  Madan M. Gupta,et al.  Uncertainty modelling and analysis : theory and applications , 1994 .

[134]  Pratyush Sen,et al.  Multiple Attribute Design Evaluation of Complex Engineering Products Using the Evidential Reasoning Approach , 1997 .

[135]  Thierry Denoeux,et al.  A neural network classifier based on Dempster-Shafer theory , 2000, IEEE Trans. Syst. Man Cybern. Part A.

[136]  Adam Krzyżak,et al.  Methods of combining multiple classifiers and their applications to handwriting recognition , 1992, IEEE Trans. Syst. Man Cybern..

[137]  Philippe Mulhem,et al.  Labeling update of segmented images using conceptual graphs and Dempster-Shafer theory of evidence , 2000, 2000 IEEE International Conference on Multimedia and Expo. ICME2000. Proceedings. Latest Advances in the Fast Changing World of Multimedia (Cat. No.00TH8532).

[138]  G. Klir,et al.  Uncertainty-based information: Elements of generalized information theory (studies in fuzziness and soft computing). , 1998 .

[139]  Jacques Verly,et al.  Automatic Object Recognition from Range Imagery Using Appearance Models , 1987 .

[140]  Bernard A. Engel.  Evidential reasoning for assessing environmental impact , 1996 .

[141]  Pepe Siy,et al.  2-D and 3-D touching part recognition using the theory of evidence , 1990, IEEE International Symposium on Circuits and Systems.

[142]  Horace H. S. Ip,et al.  Evidential reasoning for facial gestures recognition from cartoon images , 1994, Proceedings of ANZIIS '94 - Australian New Zealnd Intelligent Information Systems Conference.

[143]  Alain Billat,et al.  A smart flat-coil eddy-current sensor for metal-tag recognition , 2000 .

[144]  V. Kreinovich,et al.  How far are we from the complete knowledge? Complexity of knowledge acquisition in the Dempster-Shafer approach , 1994 .

[145]  J. C. Helton,et al.  Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty , 1997 .

[146]  Clement T. Yu,et al.  Evaluating strategies and systems for content based indexing of person images on the Web , 2000, ACM Multimedia.

[147]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

[148]  Robert M. Kleyle,et al.  The object recognition problem when features fail to be homogeneous , 1993, Int. J. Approx. Reason..

[149]  Edward H. Shortliffe,et al.  The Dempster-Shafer theory of evidence , 1990 .

[150]  P. Smets.  Data fusion in the transferable belief model , 2000, Proceedings of the Third International Conference on Information Fusion.

[151]  M.F. Shipley,et al.  Project management: using fuzzy logic and the Dempster-Shafer theory of evidence to select team members for the project duration , 1999, 18th International Conference of the North American Fuzzy Information Processing Society - NAFIPS (Cat. No.99TH8397).

[152]  C. S. George Lee,et al.  Optimal strategic recognition of objects based on candidate discriminating graph with coordinated sensors , 1992, IEEE Trans. Syst. Man Cybern..

[153]  J. Robert Boston.  A signal detection system based on Dempster-Shafer theory and comparison to fuzzy detection , 2000, IEEE Trans. Syst. Man Cybern. Part C.

[154]  J. Flamm,et al.  Reliability data collection and analysis , 1992 .