Matematiksel kanıt kuramı'nda uzlaşma üretici yöntemler için bir çerçeve

Öz

Anahtar Kelimeler

• -

Matematiksel kanıt kuramı'nda uzlaşma üretici yöntemler için bir çerçeve

Öz

Matematiksel kanıt kuramı’nda, ayrı kanıt kaynaklarından elde edilen kanaat fonksiyonlarının birleştirilmesi için önerilen ilk kural Dempster birleştirme kuralıdır. Bu kural, koşullandırma biçiminde bir birleştirme gerçekleştirmektedir. Literatürde uzlaşma üretici birleştirme yöntemleri de bulunmaktadır. Fakat bu yöntemler, uzlaşma üretici bir yöntemden beklenen eşkuvvetlilik özelliğini sağlamamakta ve birleşen kanaatlerin uyum içinde mi yoksa çelişki içinde mi olduklarını gösteren bir çelişki miktarı da üretmemektedirler. Bu çalışmada, değişim ve eşkuvvetlilik özelliklerine sahip ve anlamlı bir çelişki miktarı üreten uzlaşma üretici bir yöntem için çerçeve sunulmaktadır

Anahtar Kelimeler

• Matematiksel kanıt kuramı, Dempster-Shafer kuramı, Kanaat fonksiyonu, Veri birleştirme, Dempster birleştirme kuralı, Uzlaşma üretici

Kaynakça

1. M. Büyükyazıcı, 2004, Kanıt Kuramında Analitik Birleştirme Süreci, Doktora Tezi, Hacettepe Üniversitesi.
2. F. Campos, S. Cavalcante, 2003, An Extended Approach for Dempster-Shafer Theory, IEEE International Conference on Information Reuse and Integration (IRI 2003), Las Vegas, USA, October, 2003.
3. M.E.G.V. Cattaneo, 2003, Combining belief functions issued from dependent sources, In: J.M. Bernard, T. Seidenfeld, M. Zaffalon (Eds.), Proceedings of the Third International Symposium on Imprecise Probabilities and Their Applications (ISIPTA'03), Carleton Scientific, Lugano, Switzerland. pp. 133-147.
4. R.T. Clemen, R.L. Winkler, 1999, Combining Probability Distributions From Experts in Risk Analysis, Risk Analysis, Vol. 19, No. 2 pp. 187-203.
5. M. Daniel, 2003, Associativity in Combination of belief functions; a derivation of minC combination, Soft Computing, 7(5), pp. 288–296.
6. A.P. Dempster, 1967, Upper and lower probabilities induced by a multi-valued mapping, Ann. Mathematic Statistics, Vol. 38, pp. 325-339.
7. T. Denœux, 2008, Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence, Artificial Intelligence, 172, 234-264.
8. M. Detyniecki, 2001, Fundamentals on Aggregation Operators,

9. http://www.cs.berkeley.edu/~marcin/agop.pdf .
10. J. Dezert, 2002, Foundations for a New Theory of Plausable and Paradoxical Reasoning, Information & Security, Vol. 9, 90-95.
11. D. Dubois, H. Prade, 1988, Representation and combination of uncertainty with belief functions and possibility measures, Computational Intelligence, Volume 4, Issue 3, pp. 244-264.
12. C. Genest, J.V. Zidek, 1986, Combining probability distributions: A critique and a annotated bibliography, Statistical Science, Vol. 1, No. 1, pp.114-148.
13. R. Haenni, 2002, Are alternatives to Dempster’s rule of combination real alternatives? Comments on “About the belief function combination and the conflict management problem”-Lefevre et al, Information Fusion, Vol. 3, pp. 237-239.
14. R. Haenni, 2005, Shedding new light on Zadeh’s Criticism of Dempster’s rule of Combination, Proceedings of Information Fusion 2005, Philadelphia, July 2005.
15. R. Haenni, S. Hartmann, 2006, Modeling partially reliable information source: A general approach based on Dempster-Shafer theory, Information Fusion, Vol. 7, pp. 361-379.
16. R. Haenni, J. Kohlas, N. Lehman, 2000, Probabilistic argumentation systems, J. Kohlas, S. Moral (Eds.), Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vol. 5 of Algorithms for Uncertainty and Defeasible Reasoning, pp. 221-288, Kluwer Academic Publishers.
17. R. Haralick, L. Shapiro, 1993, Computer and Robot Vision, Vol 2, Addison-Wesley Publishing Company, Inc.
18. H.Y. Hau, R.L. Kashyap, 1989, On the Robustness of Dempster’ s Rule of Combination, IEEE International Workshop on Tools for Artificial Intelligence, Fairfax, VA, Oct. 1989, 578-582.
19. A. Josang, 2002, The consensus operator for combining beliefs, Artificial Intelligence, 141, pp. 157-170.
20. A. Josang, M. Daniel, P. Vannoorenberghe, 2003, Strategies for combining conflicting dogmatic beliefs, Applications of plausable, paradoxical, and neutrosophical reasoning for information fusion (The sixth international conference on information fusion), Cairns, Queensland, Australia, July 8-11, 2003.
21. J. Kohlas, P.A. Monney, 1995, A Mathematical Theory of Hints: An Approach to the Dempster-Shafer Theory of Evidence, Vol. 425 of Lecture Notes in Economics and Mathematical Systems, Springer –Verlag.
22. E.S. Lee, Q. Zhu, 1995, Fuzzy and Evidence Reasoning, Physica-Verlag Heidelberg, Germany, 360 s.
23. E. Lefevre, O. Colot, P. Vannoorenberghe, 2002, Belief Function Combination and Conflict Management, Information Fusion, Vol. 3, 149-162.
24. W. Liu, 2001, Propositional Probabilistic and Evidential Reasoning, Physica-Verlag Heidelberg, New York, 274 s.
25. P.A. Monney, M. Chan, 2007, Modelling dependency in Dempster-Shafer theory, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol. 15, No., pp. 93-114.
26. C.K. Murphy, 2000, Combining Belief Functions when Evidence Conflicts, Decision Support Systems, Vol. 29, 1-9.
27. National Technical University of Athens, 2003, Focal Elements and Body of Evidence, http://www.survey.ntua.gr/main/labs/rsens/DeCETI/IRIT/MSI-FUSION/node178.html.
28. K. Sentz, S. Ferson, 2002, Combination of Evidence in Dempster-Shafer Theory, Sandia National Laboratories Report, SAND2002-0835, California, 96 s.
29. G. Shafer, J. Pearl, (edited), 1990, Readings in Uncertain Reasoning, Morgan Kaufmann Publishers, Inc., United States, 768 s.
30. G. Shafer, 1976, A Mathematical Theory of Evidence, Princeton University Press, London, 297 s.
31. Ph. Smets, 2007, Analyzing the Combination of Conflicting Belief Functions, Information Fusion, Vol. 8, pp. 387-412.
32. Ph. Smets, R. Kennes, 1994, The Transferable Belief Model, Artificial Intelligence, Vol. 66, pp. 191-234.
33. F. Voorbraak, 1991, On the justification of Dempster's rule of combination, Artificial Intelligence, 48, pp. 171-197.
34. R. R. Yager, 1987, On the Dempster-Shafer framework and new combination rules, Information Sciences, 41 (2), p.93-137.
35. K. Yamada, 2008, A new combination of evidence based on compromise, Fuzzy Sets and Systems, 159, 1689-1708.
36. L.A. Zadeh, 1979, On the validty of Dempster’s rule of combination of evidence. Technical Report 79/24, University of California, Berkely.
37. L.A. Zadeh, 1984, A mathematical theory of evidence (book review), AI Magazine, 5(3), pp. 81-83.