Generalized Aggregate Uncertainty Measure 2 for Uncertainty Evaluation of a Dezert-Smarandache Theory based Localization Problem

Document Type : Research Article

Authors

Dept. of Electrical Engineering, Iran University of Science & Technology, Tehran, Iran

Abstract

In this paper, Generalized Aggregated Uncertainty measure 2 (GAU2), as a new
uncertainty measure, is considered to evaluate uncertainty in a localization problem in which cameras’
images are used. The theory that is applied to a hierarchical structure for a decision making to combine
cameras’ images is Dezert-Smarandache theory. To evaluate decisions, an analysis of uncertainty is
executed at every level of the decision-making system. The second generalization of Aggregated
Uncertainty measure (GAU2) which is applicable for DSmT results is used as a supervisor. The
GAU2 measure in spite of the GAU1 measure can be applied to the problems with vague borders or
continuous events. This measure may help to make decisions based on better preference combinations
of sensors or methods of fusion. GAU2 is used to evaluate uncertainty after applying classic DSmT
and hybrid DSmT with extra knowledge. Therefore by using the decision making system, results with
less uncertainty are generated in spite of high conflict sensory data.

Highlights

[1] P. Pong, S. Challa, Empirical analysis of generalized uncertainty measures with Dempster-Shafer fusion, in:  10th Int. Conf. on Information Fusion, Quebec, Que, 9-12 July, 2007.

[2] J. Esteban, Starr A., Willetts R., Hannah P., Bryanston-Cross P., A review of data fusion models and architectures: towards engineering guidelines, Neural Computing & Application, 14 (2005) 273-281.

[3] G. Shafer, A mathematical theory of evidence, Princeton Univ. Press, Princeton, NJ, 1976.

[4] R.R. Yager, Hedging in the combination of evidence, Journal of Information Optimization Science, 4 (1983) 73-81.

[5] R.R. Yager, On the Dempster–Shafer framework and new combination rules, Information Science, 41 (1987) 93-138.

[6] P. Smets, R. Kennes, The transferable belief model, Artificial Intelligence, 66(2) 191-234.

[7] D. Dubois, H. Prade, Representation and combination of uncertainty with belief functions and possibility measures, Computational Intelligence, 4 (1988) 244-264.

[8] J.P. Yang, H.Z. Huang, Y. Liu, Y.F. Li, Quantification classification algorithm of multiple sources of evidence, International Journal of Information Technology & Decision Making, 14(5) (2015) 1017-1034.

[9] J. Dezert, Foundation for a new theory of plausible and paradoxical reasoning, Information Security Journal, 9 (2002) 13-57.

[10] F. Smarandache, J. Dezert, Advances and applications of DSmT for information fusion, (collected works), vol. 1, American Research Press, 2004.

[11] F. Smarandache, J. Dezert, Advances and applications of DSmT for information fusion, (collected works), vol. 2, American Research Press, 2006.

[12] F. Smarandache, J. Dezert, Advances and applications of DSmT for information fusion, (collected works), vol. 3, American Research Press, 2009.

[13] R.V.L. Hartley, Transmission of information, Bell Systems & Technology Journal, 7(535-563) (1928).

[14] C.E. Shannon, A mathematical theory of communication, Bell Systems & Technology Journal, 27 (1948) 379-423 and 623-656.

[15] G.J. Klir, M.J. Wierman, Uncertainty-based information 2nd ed. series, Studies in Fuzziness and Soft Computing 15, Physica–Verlag, Heidelberg, Germany, 1999.

[16] M. Beynon, D. Cosker, D. Marshall, An expert system for multicriteria decision making using Dempster Shafer theory, Expert Systems with Applications, 20 (2001) 357-367.

[17] Z. Hua, B. Gong, X. Xu, A DS–AHP approach for multiattribute decision making problem with incomplete information, Expert Systems with Applications, 34 (2008) 2221-2227.

[18] J. Dezert, J.M. Tacnet, M. Batton-Hubert, F. Smarandache, Multi- criteria decision making based on DSmT-AHP, in:  Advances and Applications of DSmT for Information Fusion (collected works), American Research Press (ARP), 2015.

[19] N. Abbas, Y. Chibani, A. Martin, F. Smarandache, The effective use of the DSmT for multi-class classification in:  Advances and Applications of DSmT for Information Fusion (collected works), American Research Press (ARP), 2015, pp. 359.

[20] F. Smarandache, J. Dezert, Advances and applications of DSmT for information fusion, (collected works), vol. 4, American Research Press, 2015.

[21] R.R. Yager, Entropy and specificity in a mathematical theory of evidence, International Journal of General Systems, 9(4) (1983) 249-260.

[22] G.J. Klir, A. Ramer, Uncertainty in Dempster–Shafer theory: a critical re-examination, International Journal of General Systems, 18(2) (1990) 155-166.

[23] T. George, N.R. Pal, Quantification of conflict in Dempster–Shafer framework: a new approach, International Journal of General Systems, 24(4) (1996) 407-423.

[24] N.R. Pal, J.C. Bezdek, R. Hemasinha, Uncertainty measures for evidential reasoning I: a review, International Journal of Approximate Reasoning, 7(3/4) (1992) 165-183.

[25] N.R. Pal, J.C. Bezdek, R. Hemasinha, Uncertainty measures for evidential reasoning II: a new measure of total uncertainty, International Journal of Approximate Reasoning, 8(1) (1993) 1-16.

[26] A. Ramer, J. Hiller, Total uncertainty revisited, International Journal of General Systems, 26(3) (1997) 223-237.

[27] J.A. Herencia, M.T. Lamata, A generalization of entropy using Dempster–Shafer theory, International Journal of General Systems, 29(5) (2000) 719-735.

[28] Y. Maeda, H.T. Nguyen, H. Ichihashi, Maximum entropy algorithms for uncertainty measures, International Journal of Uncertainty, Fuzziness & Knowledge Based Systems, 1(1) (1993) 69-93.

[29] D. Harmanec, G.J. Klir, Measuring total uncertainty in Dempster–Shafer theory, International Journal of General Systems, 22(4) (1994) 405-419.

[30] D. Harmanec, Uncertainty in Dempster–Shafer theory, State University of New York, New York, NY, 1996.

[31] A.L. Jousselme, C. Liu, D. Grenier, E. Bosse, IEEE Transaction on Systems, Man and Cybernetics-Part A: Systems and Humans, 36(5) (2006) 890-903.

[32] G.J. Klir, H.W. Lewis, Remarks on measuring ambiguity in the evidence theory, IEEE Transaction on Systems, Man and Cybernetics-Part A: Systems and Humans, 38(4) (2008) 995-999.

[33] M. Vatsa, R. Singh, A. Noore, M.M. Houck, Quality-augmented fusion of level-2 and level-3 fingerprint information using DSm theory, International Journal of Approximate Reasoning, 50 (2008) 51-61.

[34] M. Vatsa, R. Singh, A. Noore, Unification of evidence-theoretic fusion algorithms; a case study in level-2 and level-3 fingerprint features, IEEE Transaction on Systems, Man and Cybernetics-Part A: Systems and Humans, 39(1) (2009) 47-56.

[35] G.J. Klir, Uncertainty and information, foundation of generalized information theory, John Wiley & Sons Inc., Hoboken, NJ, 2006.

[36] M. Khodabandeh, A. Mohammad-Shahri, Two generalizations of aggregated uncertainty measure for evaluation of Dezert-Smarandache theory, International Journal Information Technology & Decision Making (IJITDM), 11(1) (2012) 119-142.

[37] M. Khodabandeh, A. Mohammad-Shahri, Uncertainty evaluation for a Dezert-Smarandache theory based localization problem, International Journal of General Systems, 43(6) (2014) 610-632.

[38] M. Khodabandeh, A. Mohammad-Shahri, Uncertainty evaluation for an ultrasonic data fusion based target differentiation problem using Generalized Aggregated Uncertainty measure 2, Measurement, 59 (2015) 139-144.

[39] E. Garcia, Altamirano L., Multiple cameras fusion based on DSmT for tracking objects on ground plane, in: F. Smarandache, Dezert J. (Eds.) Advances and Applications of DSmT for Information Fusion (collected works), American Research Press (ARP), 2009, pp. 691-704.

Keywords

References

[1] P. Pong, S. Challa, Empirical analysis of generalized uncertainty measures with Dempster-Shafer fusion, in:  10th Int. Conf. on Information Fusion, Quebec, Que, 9-12 July, 2007.
[2] J. Esteban, Starr A., Willetts R., Hannah P., Bryanston-Cross P., A review of data fusion models and architectures: towards engineering guidelines, Neural Computing & Application, 14 (2005) 273-281.
[3] G. Shafer, A mathematical theory of evidence, Princeton Univ. Press, Princeton, NJ, 1976.
[4] R.R. Yager, Hedging in the combination of evidence, Journal of Information Optimization Science, 4 (1983) 73-81.
[5] R.R. Yager, On the Dempster–Shafer framework and new combination rules, Information Science, 41 (1987) 93-138.
[6] P. Smets, R. Kennes, The transferable belief model, Artificial Intelligence, 66(2) 191-234.
[7] D. Dubois, H. Prade, Representation and combination of uncertainty with belief functions and possibility measures, Computational Intelligence, 4 (1988) 244-264.
[8] J.P. Yang, H.Z. Huang, Y. Liu, Y.F. Li, Quantification classification algorithm of multiple sources of evidence, International Journal of Information Technology & Decision Making, 14(5) (2015) 1017-1034.
[9] J. Dezert, Foundation for a new theory of plausible and paradoxical reasoning, Information Security Journal, 9 (2002) 13-57.
[10] F. Smarandache, J. Dezert, Advances and applications of DSmT for information fusion, (collected works), vol. 1, American Research Press, 2004.
[11] F. Smarandache, J. Dezert, Advances and applications of DSmT for information fusion, (collected works), vol. 2, American Research Press, 2006.
[12] F. Smarandache, J. Dezert, Advances and applications of DSmT for information fusion, (collected works), vol. 3, American Research Press, 2009.
[13] R.V.L. Hartley, Transmission of information, Bell Systems & Technology Journal, 7(535-563) (1928).
[14] C.E. Shannon, A mathematical theory of communication, Bell Systems & Technology Journal, 27 (1948) 379-423 and 623-656.
[15] G.J. Klir, M.J. Wierman, Uncertainty-based information 2nd ed. series, Studies in Fuzziness and Soft Computing 15, Physica–Verlag, Heidelberg, Germany, 1999.
[16] M. Beynon, D. Cosker, D. Marshall, An expert system for multicriteria decision making using Dempster Shafer theory, Expert Systems with Applications, 20 (2001) 357-367.
[17] Z. Hua, B. Gong, X. Xu, A DS–AHP approach for multiattribute decision making problem with incomplete information, Expert Systems with Applications, 34 (2008) 2221-2227.
[18] J. Dezert, J.M. Tacnet, M. Batton-Hubert, F. Smarandache, Multi- criteria decision making based on DSmT-AHP, in:  Advances and Applications of DSmT for Information Fusion (collected works), American Research Press (ARP), 2015.
[19] N. Abbas, Y. Chibani, A. Martin, F. Smarandache, The effective use of the DSmT for multi-class classification in:  Advances and Applications of DSmT for Information Fusion (collected works), American Research Press (ARP), 2015, pp. 359.
[20] F. Smarandache, J. Dezert, Advances and applications of DSmT for information fusion, (collected works), vol. 4, American Research Press, 2015.
[21] R.R. Yager, Entropy and specificity in a mathematical theory of evidence, International Journal of General Systems, 9(4) (1983) 249-260.
[22] G.J. Klir, A. Ramer, Uncertainty in Dempster–Shafer theory: a critical re-examination, International Journal of General Systems, 18(2) (1990) 155-166.
[23] T. George, N.R. Pal, Quantification of conflict in Dempster–Shafer framework: a new approach, International Journal of General Systems, 24(4) (1996) 407-423.
[24] N.R. Pal, J.C. Bezdek, R. Hemasinha, Uncertainty measures for evidential reasoning I: a review, International Journal of Approximate Reasoning, 7(3/4) (1992) 165-183.
[25] N.R. Pal, J.C. Bezdek, R. Hemasinha, Uncertainty measures for evidential reasoning II: a new measure of total uncertainty, International Journal of Approximate Reasoning, 8(1) (1993) 1-16.
[26] A. Ramer, J. Hiller, Total uncertainty revisited, International Journal of General Systems, 26(3) (1997) 223-237.
[27] J.A. Herencia, M.T. Lamata, A generalization of entropy using Dempster–Shafer theory, International Journal of General Systems, 29(5) (2000) 719-735.
[28] Y. Maeda, H.T. Nguyen, H. Ichihashi, Maximum entropy algorithms for uncertainty measures, International Journal of Uncertainty, Fuzziness & Knowledge Based Systems, 1(1) (1993) 69-93.
[29] D. Harmanec, G.J. Klir, Measuring total uncertainty in Dempster–Shafer theory, International Journal of General Systems, 22(4) (1994) 405-419.
[30] D. Harmanec, Uncertainty in Dempster–Shafer theory, State University of New York, New York, NY, 1996.
[31] A.L. Jousselme, C. Liu, D. Grenier, E. Bosse, IEEE Transaction on Systems, Man and Cybernetics-Part A: Systems and Humans, 36(5) (2006) 890-903.
[32] G.J. Klir, H.W. Lewis, Remarks on measuring ambiguity in the evidence theory, IEEE Transaction on Systems, Man and Cybernetics-Part A: Systems and Humans, 38(4) (2008) 995-999.
[33] M. Vatsa, R. Singh, A. Noore, M.M. Houck, Quality-augmented fusion of level-2 and level-3 fingerprint information using DSm theory, International Journal of Approximate Reasoning, 50 (2008) 51-61.
[34] M. Vatsa, R. Singh, A. Noore, Unification of evidence-theoretic fusion algorithms; a case study in level-2 and level-3 fingerprint features, IEEE Transaction on Systems, Man and Cybernetics-Part A: Systems and Humans, 39(1) (2009) 47-56.
[35] G.J. Klir, Uncertainty and information, foundation of generalized information theory, John Wiley & Sons Inc., Hoboken, NJ, 2006.
[36] M. Khodabandeh, A. Mohammad-Shahri, Two generalizations of aggregated uncertainty measure for evaluation of Dezert-Smarandache theory, International Journal Information Technology & Decision Making (IJITDM), 11(1) (2012) 119-142.
[37] M. Khodabandeh, A. Mohammad-Shahri, Uncertainty evaluation for a Dezert-Smarandache theory based localization problem, International Journal of General Systems, 43(6) (2014) 610-632.
[38] M. Khodabandeh, A. Mohammad-Shahri, Uncertainty evaluation for an ultrasonic data fusion based target differentiation problem using Generalized Aggregated Uncertainty measure 2, Measurement, 59 (2015) 139-144.
[39] E. Garcia, Altamirano L., Multiple cameras fusion based on DSmT for tracking objects on ground plane, in: F. Smarandache, Dezert J. (Eds.) Advances and Applications of DSmT for Information Fusion (collected works), American Research Press (ARP), 2009, pp. 691-704.
AUT Journal of Modeling and Simulation
Volume 49, Issue 2
December 2017
Pages 153-162

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