An introduction to DSmT. First part

Authors

  • Jean Dezert
  • Florentin Smarandache

Keywords:

Dezert-Smarandache Theory, DSmT, quantitative and qualitative reasoning, information fusion

Abstract

The management and combination of uncertain, imprecise, fuzzy and even paradoxical or highly conflicting sources of information has always been, and still remains today, of primal importance for the development of reliable modern information systems involving artificial reasoning. In this introduction, we present a survey of our recent theory of plausible and paradoxical reasoning, known as DezertSmarandache Theory (DSmT), developed for dealing with imprecise, uncertain and conflicting sources of information. We focus our presentation on the foundations of DSmT and on its most important rules of combination, rather than on browsing specific applications of DSmT available in literature. Several simple examples are given throughout this presentation to show the efficiency and the generality of this new theory.

References

Bolanos, L.M. De Campos, S. Moral, Propagation of linguistic labels in causal networks, Proc. of 2nd IEEE Int. Conf. on Fuzzy Systems, Vol. 2, pp. 863–870, 28 March – 1 April, 1993.

L. Comtet, Sperner Systems, Sec.7.2, Advanced Combinatorics: The Art of Finite and Infinite Expansions, D. Reidel Publ. Co., 1974, pp. ?271-273.

R. Dedekind, Über Zerlegungen von Zahlen durch ihre grössten gemeinsammen Teiler, Gesammelte Werke, Bd. 1. pp. ?103-148, 1897.

T. Denœux, Reasoning with imprecise belief structures, Technical Report Heudiasys 97/44; available at http://www.hds.utc.fr/~tdenoeux/; International Journal of Approximate Reasoning, 20, pp. 79-111, 1999.

J. Dezert J., F. Smarandache, DSmT: A New Paradigm Shift for Information Fusion, Proceedings of Cogis ' 06 Conference, Paris, March 2006.

J. Dezert, A. Tchamova, F. Smarandache, P. Konstantinova, Target Type Tracking with PCR5 and Dempster's rules: A Comparative Analysis, Proceedings of Fusion 2006 International conference on Information Fusion, Firenze, Italy, July 10-13, 2006.

J. Dezert, F. Smarandache, A new probabilistic transformation of belief mass assignment, Proceedings of Fusion 2008 Conference, Cologne, Germany, July 2008.

D. Dubois, H. Prade, On the unicity of Dempster rule of combination, International Journal of Intelligent Systems, 1, pp. 133-142, 1986.

D. Dubois, H. Prade, Representation and combination of uncertainty with belief functions and possibility measures, Computational Intelligence, 4, pp. 244-264, 1988.

M.C. Florea, Combinaison dèinformations hétérogènes dans le cadre unificateur des ensembles aléatoires : Approximations et robustesse, Ph.D. Thesis, Laval University, Canada, July 2007.

J.W. Guan, D.A. Bell, Generalizing the Dempster-Shafer rule of combination to Boolean algebras, Proc. of IEEE/ACM Int. Conf. on Developing and Managing Projects, Washington, March, 1993, pp. 229-236.

T. Inagaki, Interdependence between safety-control policy and multiple-sensor schemes via

Dempster-Shafer theory, IEEE Trans. on reliability, 40, 2, pp. 182-188, 1991.

M. Lamata, S. Moral, Calculus with linguistic probabilities and beliefs, in: R. R. Yager, M. Fedrizzi, and J. Kacprzyk (editors), Advances in Dempster-Shafer Theory of Evidence, Wiley, pp. 133-152.

E. Lefevre, O. Colot, P. Vannoorenberghe, Belief functions combination and conflict management, Information Fusion Journal, Elsevier Publisher, 3, 2, pp. 149-162, 2002.

E. Lefevre, O. Colot, P. Vannoorenberghe, Reply to the Comments of R. Haenni on the paper ''Belief functions combination and conflict management", Information Fusion Journal, Elsevier Publisher, Vol. 4, pp. 63-65, 2003.

C.K. Murphy, Combining belief functions when evidence conflicts, Decision Support Systems, Elsevier Publisher, Vol. 29, pp. 1-9, 2000.

J.B. Paris, The uncertain reasoner's companion, a mathematical perspective, Cambridge University Press, 1994.

J. Pearl, Probabilistic reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan Kaufmann Publishers, San Mateo, CA, 1988.

A. Robinson, Non-Standard Analysis, North-Holland Publ. Co., 1966.

K. Sentz, S. Ferson, Combination of evidence in Dempster-Shafer Theory, SANDIA Tech. Report, SAND2002-0835, 96 pages, April 2002.

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

C.E. Shannon, A Mathematical Theory of Communication, Bell Syst. Tech. J., 27, pp. 379-423 and 623-656, 1948.

N.J.A. Sloane, The On-line Encyclopedia of Integer Sequences 2003 (Sequence No. A014466); http://www.research.att.com/~njas/sequences/

F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Probability, and Statistics (4th Ed.), Amer. Research Press, Rehoboth, 2005.

F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic, Multiple-valued logic, An international journal, 8, 3, pp. 385-438, 2002.

F. Smarandache, Neutrosophy: A new branch of philosophy, Multiple-valued logic, An international journal, 8, 3, pp. 297-384, 2002.

F. Smarandache (Editor), Proceedings of the First International Conference on Neutrosophics, Univ. of New Mexico, Gallup Campus, NM, USA, 1-3 Dec. 2001, Xiquan, Phoenix, 2002.

F. Smarandache, J. Dezert (Editors), Applications and Advances of DSmT for Information Fusion, Am. Res. Press, Rehoboth, 2004; http://www.gallup.unm.edu/~smarandache/DSmT-book1.pdf

F. Smarandache, Unification of Fusion Theories (UFT), Presented at NATO Advanced Study Institute, Albena, Bulgaria, 16-27 May 2005 also in International Journal of Applied Mathematics & Statistics, Vol. 2, 1-14, 2004 and on http://arxiv.org/abs/cs/0409040.

Published

2011-06-05