Interval-Valued Uncertainty Based on Entropy and Dempster-Shafer Theory
Tóm tắt
This paper presents a new structure as a simple method at two uncertainties (i.e., aleatory and epistemic) that result from variabilities inherent in nature and a lack of knowledge. Aleatory and epistemic uncertainties use the concept of the entropy and Dempster-Shafer (D-S) theory, respectively. Accordingly, we propose the generalized Shannon entropy in the D-S theory as a measure of uncertainty. This theory has been originated in the work of Dempster on the use of probabilities with upper and lower bounds. We describe the framework of our approach to assess upper and lower uncertainty bounds for each state of a system. In this process, the uncertainty bound is calculated with the generalized Shannon entropy in the D-S theory in different states of these systems. The probabilities of each state are interval values. In the current study, the effect of epistemic uncertainty is considered between events with respect to the non-probabilistic method (e.g., D-S theory) and the aleatory uncertainty is evaluated by using an entropy index over probability distributions through interval-valued bounds. Therefore, identification of total uncertainties shows the efficiency of uncertainty quantification.
Tài liệu tham khảo
G. Apostolakis. Science. 250 (1990), 1359–1364.
M.J. Roemer, G.J. Kacprzynski, R.F. Orsagh, IEEE Aerospace Conf. Proc. 6(10–17) (2001), 2979–2988.
M. J. Ducey, For. Ecol. Manage. 150 (2001), 199–211.
G. Shafer. A Mathematical Theory of Evidence. Princeton University Press, Princeton 1976.
M. Beynon, D. Cosker, D. Marshall, Expert Syst. Appl. 20 (2001), 357–367.
S.L. Hé garat-Mascle, Richard D., Ottle C. Integr. Comput. Aid. Eng. 10 (2003), 9–22.
V. Kaftandjian, O. Dupuis, D. Babot, Y.M. Zhu. Pattern Recognit. Lett. 24(1–3) (2003), 547–564.
S. Fabre, A. Appriou, X. Briottet. Inform. Fusion. 2(1) (2001), 49–71.
C.R. Parikh, M.J. Pont, N.B. Jones, Pattern Recognit Lett. 22(6–7) (2001), 777–785.
C. Jiang, Z. Zhang, X. Han, J. Liu, Comput. Struct. 129 (2013), 1–12.
H. Tang, D. Li, J. Li, S. Xue, Int. J. Fatigue. 99(1) (2017), 163–174.
S. Yin, D. Yu, H. Yin, B. Xia, Comput. Methods Appl. Mech. Eng. 322 (2017), 419–440.
S. Yin, D. Yu, H. Yin, H. Lü, B. Xia, Mech. Syst. Signal Process. 93 (2017), 204–224.
T. Jian, W. Zhigang, Y. Chao, Chinese J. Aeronaut. 28(1) (2015), 164–171.
C.E. Shannon, Bell Syst. Tech J. 27(379–423) (1948), 623–656.
R. Thapliyal, H.C. Taneja, J. Stat. Theory Appl. 12(2) (2013), 200–207.
O.A. Olvera-Guerrero, P. Guerrero, G. Espinosa-Paredes, Ann. Nucl. Energy. 108 (2017), 1–9.
R. Gu, Physica A. Stat. Mech. Appl. 484 (2017), 215–224.
R.C. Gupta, H.C. Taneja, R. Thapliyal, J. Stat. Theory Appl. 13(1) (2014), 27–37.
S. Tahmasebi, M. Eskandarzadeh, A.A. Jafari, J. Stat. Theory Appl. 16(2) (2017), 165–177.
A. Toomaj, M. Doostparast, J. Stat. Theory Appl. 13(2) (2014), 189–195.
Z. Sun, P. Liu, Z. Wang, Energy Procedia. 105 (2017), 2354–2359.
R. Kiani Mavi, M. Goh, N. Kiani Mavi, Procedia Soc. Behav. Sci. 235(24) (2016), 216–225.
C.J. Roy, W.L. Oberkampf, Comput. Methods Appl. Mech. Eng. 200 (2011), 2131–2144.
G. Tang, L.P. Swiler, M.S. Eldred, G. Iaccarino, Proceedings of the 12th AIAA Non-Deterministic Approaches Conference, 2010.
F.O. Hoffman, J.S. Hammonds, Risk Anal. 14 (1994), 707–712.
G. Li, Z. Lu, L. Li, B. Ren, Appl. Math. Model. 40(9–10) (2016), 5703–5716.
J.J. Jakeman, B.M. Michael Eldred, D. Xiu. J. Comput. Phys. 229 (2010), 4648–4663.
J.C. Helton, J.D. Johnson, W.L. Oberkampf, C.B. Storlie, A sampling-based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory, Technical Report 5557, Sandia National Laboratories, 2006.
D. Dubois, H. Prade, Possibility Theory: An Approach to Computerized Processing of Uncertainty, Plenum, New York, 1998.
L.P. Swiler, T.L. Paez, R.L. Mayes, and M.S. Eldred. Structural Dynamics, and Materials Conference Palm Springs, CA 2009.
M. M. Granger, M. Henrion, Uncertainty a Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis, University Press, Cambridge, 1992.
J.H. Purba, D.T. Sony Tjahyani, A.S. Ekariansyah, H. Tjahjono, Ann. Nucl. Energy. 85 (2015), 1189–1199.
S. Ferson, J. G. Hajagos, Reliab. Eng. Syst. Safety. 85(1–3) (2004), 135–152.
Q. Zhang, Z. Zeng, E. Zio, R. Kang, Appl. Soft. Comput. 56 (2017), 570–579.
H. Li, Y. Bao, J. Ou. Mech. Syst. Signal Process. 22 (2008), 1427–1440.
J. Guo, J. Intell. Fuzzy Syst. 30 (2016), 869–881.