Foundations for a new theory of plausible and paradoxical reasoning

Jean Dezert

Foundations for a new theory of plausible and paradoxical reasoning

09.01_Dezert.pdf

Publication Type:

Journal Article

Authors:

Jean Dezert

Source:

Information & Security: An International Journal, Volume 9, p.13-57 (2002)

Keywords:

Dempster-Shafer, evidence, plausible and paradoxical reasoning, rule of combination

Abstract:

This paper presents an original comprehensive approach to plausible and paradoxical reasoning. It provides detailed description of a rule of combination of sources of information in a very general framework allowing for both uncertain and paradoxical information. In this new theory, the rule of combination which takes into account explicitly both conjunctions and disjunctions of assertions in the fusion process, appears to be more simple and general than the Dempster's rule of combination. Through several simple examples, where the Dempster-Shafer theory usually fails, the author shows the strong capacity of the new theory to solve difficult practical problems.

20882 reads
Google Scholar
DOI
RTF
EndNote XML

References

Appriou, A.. Proc´edure d’aide `a la d´ecision multi-informateurs. Application `a la classification multi-capteurs de cibles In AGARD Avionics Panel Symposium on Software Engineering and Its Applications. Turkey, 1988.

Ashbacher, C. Introduction to Neutrosophic Logic. American Research Press, 2002.

Bianaghi, E., and P. Madella. Inductive and Deductive Reasoning techniques for Fuzzy Dempster-Shafer Classifiers In 1997 Seventh IFSA World Congress. Prague, 1997.

Blackman, Samuel S., and Robert Populi. Design and Analysis of Modern Tracking Systems. Norwood, MA: Artech House, 1999.

Cheng, Y., and R.L. Kashyap. Study of the Different Methods for Combining Evidence In SPIE on Applications of Artificial Intelligence. Vol. 635., 1986.

Comtet, L.. "Sperner Systems." Advanced Combinatorics: The Art of Finite and Infinite Expansions (1974): 271-273.

Cover, Thomas M., and Thomas Allen. Elements of Information Theory, Wiley Series in Telecommunications. John Wiley & Sons, 1991.

De Brucq, D., A. Sombo, and O. Colot. Identical Foundation of Probability Theory and Fuzzy Set Theory In 5th Intern. Conf. on Inf. Fusion. Annapolis, 2002.

Dempster, A.P.. "Upper and Lower Probabilities Induced by Multivalued Mapping." Annals of Mathematical Statistics 28 (1967): 325-339.

Dempster, A.P.. "A Generalization of Bayesian Inference." Journal of the Royal Statistical Society 30 (1968): 205-247.

Denoeux, T.. "Application of evidence theory to k-NN pattern classification." In Pattern Recognition in Practice IV, edited by E.S. Gelsema and L.N. Kanal, 13-24. Amsterdam: Elsevier, 1994.

Dezert, Jean. Vers un nouveau concept de navigation autonome d’engin. Un lien entre le PDAF et la th´eorie de l’´evidence. Orsay, France: University Paris XI, 1990.

Dezert, Jean. "Autonomous Navigation with Uncertain Reference Points using the PDAF." Multitarget-Multisensor Tracking: Applications and Advances 2 (1991): 271-324.

Dezert, Jean. Optimal Bayesian Fusion of Multiple Unreliable Classifiers In 4th Intern. Conf. on Information Fusion (Fusion 2001). Montreal, 2001.

An introduction to the theory of plausible and paradoxical reasoning In NM&A 02, International Conference on Numerical methods and Applications. Borovetz, Bulgaria, 2002.

Dubois, D., and H Prade. "On the Unicity of Dempster Rule of Combination." International Journal of Intelligent Systems 1 (1986): 133-142.

Dubois, D., Ph. Smets, H Prade, H.E. Kyburg, and P. Garbolino. "Quantified Uncertainty." J. Applied Non-Classical Logics 1 (1991): 105-197.

Dubois, D., and H Prade. "Evidence, Knowledge and Belief Functions." International Journal of Approximate Reasoning 6 (1992): 295-319.

Jaynes, E.T.. Where do we stand on Maximum Entropy In Maximum Entropy Formalism Conference., 1978.

Klawonn, F., and Ph. Smets. "The dynamic of belief in the transferable belief model and specialization-generalization matrices." Uncertainty in Artificial Intelligence 92 (1992): 130-137.

Klopotek, M.A.. "Interpretation of belief function in Dempster-Shafer theory." Foundations of Computing and Decision Sciences 20, no. 40 (1995): 287-306.

Klopotek, M.A.. "Identification of Belief Structure in Dempster-Shafer Theory." Foundations of Computing and Decison Sciences 21, no. 1 (1996): 35-54.

Kyburg, Jr, H.E.. "Bayesian and Non-Bayesian Evidential Updating." Artificial Intelligence 31 (1987): 271-294.

Lowrance, J.D., and T.D. Garvey. "Evidential Reasoning: An Implementation for Multisensor Integration." Technical Note 307 (1983).

Lesh, S.A.. An Evidential Theory Approach to Judgment-Based Decision Making. Durham, NC: Dept. of Forestry and Environmental Studies, Duke University, 1986.

Mahler, R.. "Combining Ambiguous Evidence with Respect to Ambiguous a priori Knowledge, I: Boolean Logic." IEEE Trans. on SMC, Part 1: Systems and Humans 26, no. 1 (1996): 27-41.

Mesalkin, L.D.. "A Generalization of Sperner’s Theorem on the Number of Subsets of a Finite Set." Theory Prob 8 (1963): 203-204.

Milner, E.C.. "A Combinatorial Theorem on Systems of Sets." J. London Math. Soc 43 (1968): 204-206.

Pearl, J.. "Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference." Computer Science, Artificial Intelligence (1988).

Provan, G.M.. "The validity of Dempster-Shafer Belief Functions." International Journal of Approximate Reasoning 6 (1992): 389-399.

Rota, G.C.. "Theory of M¨obius Functions." Zeitung f¨ur Wahrscheinlichkeitstheorie und Verwandte Gebiete 2 (1964).

Ruspini, E.H.. The Logical Foundation of Evidential Reasoning. Menlo park, CA: SRI International, 1986.

Ruspini, E.H., D.J. Lowrance, and T.M. Start. "Understanding Evidential Reasoning." International Journal of Approximate Reasoning 6 (1992): 401-424.

Schubert, J.. "On Nonspecific Evidence." International Journal of Intelligent Systems 8 (1993): 711-725.

Semerdjiev, Emil, and Albena Tchamova. An Approach for a Fast Reduction of the Full Ignorance in the Target Identification Process In the First International Conference on Multisource-Multisensor Information Fusion. Vol. 2. Las Vegas, Nevada, 1998.

Shafer, G.. A Mathematical Theory of Evidence. Princeton Univ. Press, Princeton,NJ, 1976.

Shafer, G., and A. Tversky. "Languages and designs for probability." Cognitive Science 9 (1985): 309-339.

Shafer, G.. "The Combination of Evidence." International Journal of Intelligent Systems (1986): 155-179.

Shafer, G.. "Perspectives on the Theory and Practice of Belief Functions." International Journal of Approximate Reasoning 4 (1990): 323-362.

Smets, Ph.. Quantifying Beliefs by Belief Functions:An Axiomatic Justification In 3th International Joint Conference on Artificial Intelligence. Chamb´ery, France, 1993.

Smets, Ph.. "Belief Function: The Disjunctive Rule of Combination and the Generalized Bayesian Theorem." International Journal of Approximate Reasoning 9 (1993): 1-35.

Zadeh, Lotfi A.. "A Theory of Approximate Reasoning." Machine Intelligence 9 (1979): 149-194.

Denga, Xinyang, Qi Liub, and Yong Deng. "Matrix games with payoffs of belief structures." Applied Mathematics and Computation 273 (2016).

Deepa, R. Design of a clustering protocol and a Trust model for service discovery in Mobile ad hoc networks., 2015.

Neama, Tamer. M. Abo, Ismail. A. Ismail, Tarek. S. Sobh, and M. Zaki. "Aproposed Framework for Information Fusion and Obtain Beliefs from Evidences." Egyptian Computer Science Journal 37 , no. 1 (2013).

Foundations for a new theory of plausible and paradoxical reasoning

Publication Type:

Authors:

Source:

Keywords:

Abstract:

References

Russia at War: Strategic Competition, Confrontation, and Conflict

Democratic Backsliding and Security Governance