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Kanıt kuramında yeni bir birleştirme yöntemi "Analitik Birleştirme Süreci"

Year 2020, Volume: 13 Issue: 2, 78 - 100, 31.12.2020

Murat Büyükyazıcı , Meral Sucu

Abstract

Bu çalışmada, eşit derecede güvenilir ve bağımsız bilgi kaynaklarından elde edilen iki kanaat fonksiyonunu birleştiren bir uzlaşma oluşturucu ile ilgileniyoruz. Burada bahsedilen bağımsızlık, bilgi kaynaklarının oluşumları arasındadır. Eş kuvvetlilik ve değişme özelliklerini sağlayan "Analitik Birleştirme Süreci" adlı yeni bir uzlaşma oluşturucu öneriyoruz. Bu yöntem aynı zamanda orijinal kanaatlerin uyum içinde mi yoksa çelişki halinde mi olduğunu gösteren bir çelişki ölçüsü üretir. Diğer bir avantaj, bu yöntemle üretilen çelişki ölçüsünün hem nitel hem de nicel çelişkiyi yansıtmasıdır.

Keywords

Kanıt kuramı Dempter-Shafer kuramı Kanaat fonksiyonu Veri birleştirme Uzlaşı üretici Analitik birleştirme süreci Tam sayılı programlama

References

  • F. Campos, S. Cavalcante, An Extended Approach for Dempster-Shafer Theory, IEEE International Conference on Information Reuse and Integration (IRI 2003), Las Vegas, USA, October, 2003.
  • M.E.G.V. Cattaneo, 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), 2003, Carleton Scientific, Lugano, Switzerland. pp. 133-147.
  • R.T. Clemen, R.L. Winkler, Combining Probability Distributions From Experts in Risk Analysis, Risk Analysis, (1999) Vol. 19, No. 2 pp. 187-203.
  • M. Daniel, Associativity in Combination of belief functions; a derivation of minC combination, Soft Computing, 7(5), (2003), pp. 288–296.
  • A.P. Dempster, Upper and lower probabilities induced by a multi-valued mapping, Ann. Mathematic Statistics, (1967) Vol. 38, pp. 325-339.
  • T. Denœux, Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence, Artificial Intelligence, 172, (2008), 234-264.
  • M. Detyniecki, Fundamentals on Aggregation Operators, http://www.cs.berkeley.edu/~marcin/agop.pdf , 2001.
  • D. Dubois, H. Prade, Representation and combination of uncertainty with belief functions and possibility measures, Computational Intelligence, Volume 4, Issue 3, (1988), pp. 244-264.
  • D. Dubois, H. Prade, On the combination of evidence in various mathematical frameworks, J. Flamm and T. Luisi (Eds.), Reliability Data Collection and Analysis, Brussels, ECSC, EEC, EAFC: pp. 213-241, 1992.
  • S. Ferson, V. Kreinovich, L. Ginzburg, D.S. Myers, K. Sentz, Constructing Probability Boxes and Dempster-Shafer Structures, Sandia National Laboratories Report, SAND2002-4015, California, 2003.
  • C. Genest, J.V. Zidek, Combining probability distributions: A critique and a annotated bibliography, Statistical Science, Vol. 1, No. 1, (1986), pp.114-148.
  • R. Haenni, 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 (2002), pp. 237-239.
  • R. Haenni, Shedding new light on Zadeh’s Criticism of Dempster’s rule of Combination, Proceedings of Information Fusion 2005, Philadelphia, July 2005.
  • R. Haenni, S. Hartmann, Modeling partially reliable information source: A general approach based on Dempster-Shafer theory, Information Fusion, Vol. 7 (2006), pp. 361-379.
  • R. Haenni, J. Kohlas, N. Lehman, 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, 2000.
  • H.Y. Hau, R.L. Kashyap, On the Robustness of Dempster’ s Rule of Combination, IEEE International Workshop on Tools for Artificial Intelligence, Fairfax, VA, Oct. (1989), pp. 578-582.
  • A. Josang, The consensus operator for combining beliefs, Artificial Intelligence, 141 (2002), pp. 157-170.
  • A. Josang, M. Daniel, P. Vannoorenberghe, 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.
  • J. Kohlas, P.A. Monney, 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, 1995.
  • E. Lefevre, O. Colot, P. Vannoorenberghe, Belief Function Combination and Conflict Management, Information Fusion, Vol. 3 (2002), pp. 149-162.
  • W. Liu, Analyzing the degree of conflict among belief functions, Artificial Intelligence, Vol. 170 (11) (2006), pp. 909-924.
  • P.A. Monney, M. Chan, Modelling dependency in Dempster-Shafer theory, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol. 15, No. 1 (2007), pp. 93-114.
  • C.K. Murphy, Combining Belief Functions when Evidence Conflicts, Decision Support Systems, Vol. 29 (2000), pp. 1-9.
  • K. Sentz, S. Ferson, Combination of Evidence in Dempster-Shafer Theory, Sandia National Laboratories Report, SAND2002-0835, California, 2002.
  • G. Shafer, A Mathematical Theory of Evidence, Princeton University Press, London, 1976.
  • F. Smarandache, J. Dezert (Eds.), Advances and Applications of DSmT for Information Fusion, Smarandache, Vol 2. American Research Press, Rehoboth, 2006.
  • F. Smarandache, J. Dezert, Proportional Conflict Redistribution Rules for Information Fusion, arXiv Archives, Los Alamos National Laboratory; the Abstract and the whole paper are available at http://arxiv.org/PS_cache/cs/pdf/0408/0408064.pdf , 2005.
  • Ph. Smets, Analyzing the Combination of Conflicting Belief Functions, Information Fusion, Vol. 8, (2007), pp. 387-412.
  • Ph. Smets, R. Kennes, The Transferable Belief Model, Artificial Intelligence, Vol. 66 (1994), pp. 191-234.
  • F. Voorbraak, On the justification of Dempster's rule of combination, Artificial Intelligence, 48, (1991), pp. 171-197.
  • W.L. Winston, Operations Research Aplications and Algorithms, Duxbury Press, Belmont, 1994.
  • L.A. Wolsey, Integer Programming, Wiley-Interscience Series in Discrete Mathematics and Optimization, Wiley-Interscience Publication, NewYork, 1998.
  • R. R. Yager, On the Dempster-Shafer framework and new combination rules, Information Sciences, (1987), 41 (2), p.93-137.
  • B.B. Yaghlane, P. Smets, K. Mellouli, Belief function independence: I. The marginal case, International Journal of Approximate Reasoning, Vol. 29, (2002), pp. 47-70.
  • B.B. Yaghlane, P. Smets, K. Mellouli, Belief function independence: II. The conditional case, International Journal of Approximate Reasoning, Vol. 31, (2002), pp. 31-75.
  • K. Yamada, A new combination of evidence based on compromise, Fuzzy Sets and Systems, 159, (2008), 1689-1708.
  • L.A. Zadeh, On the validty of Dempster’s rule of combination of evidence. Technical Report 79/24, University of California, Berkely, 1979.
  • L.A. Zadeh, A mathematical theory of evidence (book review), AI Mag. 5(3) (1984), pp. 81-83.
  • Fuyuan Xiao, Evidence combination based on prospect theory for multi-sensor data fusion, ISA Transactions, Volume 106, (2020), Pages 253-261.
  • Jiang W., Zhan J., A modified combination rule in generalized evidence theory, Appl. Intell., (2017), 46 (3) pp. 630-640.
  • Jian W., Kuoyuan Q., Zhiyong Z., An improvement for combination rule in evidence theory, Future Generation Computer Systems, (2019), Volume 91, Pages 1-9.
  • Wenjun M., Yuncheng J., Xudong L., A flexible rule for evidential combination in Dempster–Shafer theory of evidence, Applied Soft Computing, (2019), Volume 85.

A new combination method in mathematical theory of evidence “Analytic Fusion Process”

Year 2020, Volume: 13 Issue: 2, 78 - 100, 31.12.2020

Murat Büyükyazıcı , Meral Sucu

Abstract

In this paper, we are interested in a consensus generator which combine two belief functions obtained from equally reliable and independent sources of information. The independence mentioned here is between occurrences of the sources of information. We propose a new consensus generator called “Analytic Fusion Process” which satisfy the idempotent and commutative law. Furthermore, this method also produces a measure of conflict shows whether the original beliefs were in harmony or in conflict. Another advantage is that the measure of conflict produced by this method reflects both qualitative and quantitative conflict.

Keywords

Mathematical theory of evidence Dempster-Shafer theory Belief function Data fusion Consensus generator Analytic fusion process Integer programming

References

  • F. Campos, S. Cavalcante, An Extended Approach for Dempster-Shafer Theory, IEEE International Conference on Information Reuse and Integration (IRI 2003), Las Vegas, USA, October, 2003.
  • M.E.G.V. Cattaneo, 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), 2003, Carleton Scientific, Lugano, Switzerland. pp. 133-147.
  • R.T. Clemen, R.L. Winkler, Combining Probability Distributions From Experts in Risk Analysis, Risk Analysis, (1999) Vol. 19, No. 2 pp. 187-203.
  • M. Daniel, Associativity in Combination of belief functions; a derivation of minC combination, Soft Computing, 7(5), (2003), pp. 288–296.
  • A.P. Dempster, Upper and lower probabilities induced by a multi-valued mapping, Ann. Mathematic Statistics, (1967) Vol. 38, pp. 325-339.
  • T. Denœux, Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence, Artificial Intelligence, 172, (2008), 234-264.
  • M. Detyniecki, Fundamentals on Aggregation Operators, http://www.cs.berkeley.edu/~marcin/agop.pdf , 2001.
  • D. Dubois, H. Prade, Representation and combination of uncertainty with belief functions and possibility measures, Computational Intelligence, Volume 4, Issue 3, (1988), pp. 244-264.
  • D. Dubois, H. Prade, On the combination of evidence in various mathematical frameworks, J. Flamm and T. Luisi (Eds.), Reliability Data Collection and Analysis, Brussels, ECSC, EEC, EAFC: pp. 213-241, 1992.
  • S. Ferson, V. Kreinovich, L. Ginzburg, D.S. Myers, K. Sentz, Constructing Probability Boxes and Dempster-Shafer Structures, Sandia National Laboratories Report, SAND2002-4015, California, 2003.
  • C. Genest, J.V. Zidek, Combining probability distributions: A critique and a annotated bibliography, Statistical Science, Vol. 1, No. 1, (1986), pp.114-148.
  • R. Haenni, 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 (2002), pp. 237-239.
  • R. Haenni, Shedding new light on Zadeh’s Criticism of Dempster’s rule of Combination, Proceedings of Information Fusion 2005, Philadelphia, July 2005.
  • R. Haenni, S. Hartmann, Modeling partially reliable information source: A general approach based on Dempster-Shafer theory, Information Fusion, Vol. 7 (2006), pp. 361-379.
  • R. Haenni, J. Kohlas, N. Lehman, 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, 2000.
  • H.Y. Hau, R.L. Kashyap, On the Robustness of Dempster’ s Rule of Combination, IEEE International Workshop on Tools for Artificial Intelligence, Fairfax, VA, Oct. (1989), pp. 578-582.
  • A. Josang, The consensus operator for combining beliefs, Artificial Intelligence, 141 (2002), pp. 157-170.
  • A. Josang, M. Daniel, P. Vannoorenberghe, 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.
  • J. Kohlas, P.A. Monney, 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, 1995.
  • E. Lefevre, O. Colot, P. Vannoorenberghe, Belief Function Combination and Conflict Management, Information Fusion, Vol. 3 (2002), pp. 149-162.
  • W. Liu, Analyzing the degree of conflict among belief functions, Artificial Intelligence, Vol. 170 (11) (2006), pp. 909-924.
  • P.A. Monney, M. Chan, Modelling dependency in Dempster-Shafer theory, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol. 15, No. 1 (2007), pp. 93-114.
  • C.K. Murphy, Combining Belief Functions when Evidence Conflicts, Decision Support Systems, Vol. 29 (2000), pp. 1-9.
  • K. Sentz, S. Ferson, Combination of Evidence in Dempster-Shafer Theory, Sandia National Laboratories Report, SAND2002-0835, California, 2002.
  • G. Shafer, A Mathematical Theory of Evidence, Princeton University Press, London, 1976.
  • F. Smarandache, J. Dezert (Eds.), Advances and Applications of DSmT for Information Fusion, Smarandache, Vol 2. American Research Press, Rehoboth, 2006.
  • F. Smarandache, J. Dezert, Proportional Conflict Redistribution Rules for Information Fusion, arXiv Archives, Los Alamos National Laboratory; the Abstract and the whole paper are available at http://arxiv.org/PS_cache/cs/pdf/0408/0408064.pdf , 2005.
  • Ph. Smets, Analyzing the Combination of Conflicting Belief Functions, Information Fusion, Vol. 8, (2007), pp. 387-412.
  • Ph. Smets, R. Kennes, The Transferable Belief Model, Artificial Intelligence, Vol. 66 (1994), pp. 191-234.
  • F. Voorbraak, On the justification of Dempster's rule of combination, Artificial Intelligence, 48, (1991), pp. 171-197.
  • W.L. Winston, Operations Research Aplications and Algorithms, Duxbury Press, Belmont, 1994.
  • L.A. Wolsey, Integer Programming, Wiley-Interscience Series in Discrete Mathematics and Optimization, Wiley-Interscience Publication, NewYork, 1998.
  • R. R. Yager, On the Dempster-Shafer framework and new combination rules, Information Sciences, (1987), 41 (2), p.93-137.
  • B.B. Yaghlane, P. Smets, K. Mellouli, Belief function independence: I. The marginal case, International Journal of Approximate Reasoning, Vol. 29, (2002), pp. 47-70.
  • B.B. Yaghlane, P. Smets, K. Mellouli, Belief function independence: II. The conditional case, International Journal of Approximate Reasoning, Vol. 31, (2002), pp. 31-75.
  • K. Yamada, A new combination of evidence based on compromise, Fuzzy Sets and Systems, 159, (2008), 1689-1708.
  • L.A. Zadeh, On the validty of Dempster’s rule of combination of evidence. Technical Report 79/24, University of California, Berkely, 1979.
  • L.A. Zadeh, A mathematical theory of evidence (book review), AI Mag. 5(3) (1984), pp. 81-83.
  • Fuyuan Xiao, Evidence combination based on prospect theory for multi-sensor data fusion, ISA Transactions, Volume 106, (2020), Pages 253-261.
  • Jiang W., Zhan J., A modified combination rule in generalized evidence theory, Appl. Intell., (2017), 46 (3) pp. 630-640.
  • Jian W., Kuoyuan Q., Zhiyong Z., An improvement for combination rule in evidence theory, Future Generation Computer Systems, (2019), Volume 91, Pages 1-9.
  • Wenjun M., Yuncheng J., Xudong L., A flexible rule for evidential combination in Dempster–Shafer theory of evidence, Applied Soft Computing, (2019), Volume 85.
There are 42 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Murat Büyükyazıcı 0000-0002-8622-4659

Meral Sucu 0000-0002-7991-1792

Publication Date December 31, 2020
Published in Issue Year 2020 Volume: 13 Issue: 2

Cite

IEEE M. Büyükyazıcı and M. Sucu, “A new combination method in mathematical theory of evidence ‘Analytic Fusion Process’”, JSSA, vol. 13, no. 2, pp. 78–100, 2020.