A new method to analyze evidence conflict

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1 : (2011) Control Theory & Applications Vol. 28 No. 6 Jun ,2, 2, 2, 1 (1., ; 2., ) :, DS, DS.. k,, k., -,,,. 1, 0.. : D-S ; ; ; ; : TP273 : A A new method to analyze evidence conflict DENG Yong 1,2, WANG Dong 2, LI Qi 2, ZHANG Ya-juan 1 (1. College of Computer and Information Sciences, Southwest University, Chongqing , China; 2. School of Electronic, Information and Electrical Engineering, Shanghai Jiaotong University, Shanghai , China) Abstract: Dempster Shafer evidence theory is widely used in data fusion. However, incorrect results may be obtained by classical Dempster combination rule when collected evidence highly conflict with each other. Extensive work has been done to improve the DS combination rule, but how to measure the conflict among two pieces of evidence is an issue which has not been well considered. We define a new factor, the relative coefficient, for measuring the conflict between two pieces of evidence based on the partial entropy and the mixture entropy. When the relative coefficient is close to one, the conflict degree between two pieces of evidence is very low. On the other hand, when the relative coefficient is close to zero, the conflict degree between two pieces of evidence is very high. Some numerical examples are given to illustrate the efficiency of the proposed method. Key words: D-S evidence theory; combination rule; evidence conflict; partial entropy; relative coefficient 1 (Introduction) D-S, [1 3].,,, [4 6]. D-S, D-S [7 10]. [10]., k., k, : k.,.,,,.,,. 1,, 0,. D-S. 2 D-S (The basic concepts of D-S evidence theory), D-S : ; : : ( ); (NCET ); (09QA ); (CSCT, 2010BA2003); (11GFF 17); (SWU110021).

2 840 28, [11]. U X, U, U X. U, U 2 U 2 U. U n, 2 n. 1 U, U 2 U 2 U, A Θ, m : 2 U [0, 1] : m (Φ) = 0, (1) m (A) = 1, (2) A U m U (BPA). BPA A, m(a). A Θ, m(a) > 0, A.. D-S, A [Bel (A), Pl (A)], Bel Pl (belief function) (plausibility function). D-S : m(a) = 1 1 k A i B j C l =A k = A i B j C l =φ [m 1 (A i )m 2 (B j )m 3 (C l ) ], (3) [m 1 (A i )m 2 (B j )m 3 (C l ) ]. (4) k,. 3 Dempster (The existing problems of Dempster combination rule) Dempster, k. k = 1, Dempster ; k 1,. 1 [6], U = (a, b, c), 1: m 1 {a} = 0.99, m 1 {b} = 0.01; 2: m 2 {b} = 0.01, m 2 {c} = m 1 m 2, D-S m 1 m 2 m 1 {a} = 0, m 1 {b} = 1, m 1 {c} = 0., {b}.,,, D-S.,,?,?? D-S k,,, k : U = {a, b, c, d, e}, m 1 {a}=m 1 {b}=m 1 {c}=m 1 {d}=m 1 {e}=0.2; m 2 {a}=m 2 {b}=m 2 {c}=m 2 {d}=m 2 {e} =0.2. D-S k, k = 0.8,,.,,. D-S k.? 2006 Liu [12],., k, pignistic, k. cf (m 1, m 2 ) = k, difbetp,,, D-S. difbetp : BetP m (A) = BetP m (ω), (5) ω A difbetp m2 m 1 = max ( BetP m1 (A) BetP m2 (A) ). (6) A Ω, 4 : A) k, difbetp, m 1, m 2, D-S. B) k, difbetp, m 1, m 2, D- S. C) k, difbetp, m 1, m 2, D-S. D) k, difbetp, m 1, m 2,, D-S. Liu k, difbetp,.,,

3 6 : 841.,,?, [13 16],, [17 20].,,,,,,. 4 (Characterization of evidential conflict with correlation coefficient),,,,, :,,,., [21],, [22]. 2 X Y { } { } a1 a X = k b1 b, Y = k, p 1 p k q 1 q k X Y : H Y (X) = n q k log p k, (7) H (X) = n q k log q k. (8) 3 X Y, 4 : H (X, Y ) = H Y (X) + H X (Y ). (9) r Y (X) = H (Y ) H Y (X), (10) r X (Y ) = H (X) H X (Y ), (11) r (X, Y )= H (X Y ) H (X) + H (Y ) = H (X, Y ) H Y (X) + H X (Y ). (12) : 0 r X (Y ), r Y (X), r (X, Y ) 1, X, Y, r X (Y ) = r Y (X) = r (X, Y ) = 1. r X Y,. { }, X = a1 a k a 1,, a k, p 1 p k p 1,, p k,.,, 1, 1 m(c) = 0, 2 m(c) = 0.99, 0.99 log 0=,, r,, 0. 0, 0,, 0,., [23], 0, log 0 =,, ,., : 3 U = (a, b, c), 1: m 1 {a} = 0.01, m 1 {b} = 0.99; 2: m 2 {b} = 0.99, m 2 {c} = r = ,,,,,, 0,.,, X Y : H Y (X) = n q k 5p k, (13) H (X) = n q k 5q k. (14), log 0-1, 0-1, e log, e log. e p k 0-1, e p k, e 5p k, log., (9) (12)., 3, r = ,, 0, 0,.

4 842 28, m 1 {a} = 0.1, m 1 {b} = 0.8, Y =DY = = m 1 {a, c} = 0.1, , c.,, ;,.,,,., Θ,., [20] BPA, BPA, D., D,. D,, : : D(A, B) = A B A B, A, B 2Θ. (15) D, v = D (i, j) v. (16).,. 1,, r = : { } m (a) m (b) m (c) m1 =, { } m (a) m (b) m (c) m2 = , {a} {b} {c} {a} D = {b} 0 1 0, {c} X = [ ] T, Y = [ ] T, X =DX = = 0.01, , : H Y (X) = , H X (Y ) = , H(X) = , H(Y ) = , r(x, Y ) = = ,, 1 a 0.99, 2 a 0,,. k.,,, 0,, D-S. 2, 1,,,,. 5 (The analysis of evidential conflict) k,., r = 1,,,.,.. 4 U = (a, b, c), 1: m 1 {a}=0.8, m 1 {b}=0.1, m 1 {c}=0.1; 2: m 2 {a} = 0.1, m 2 {b} = 0.8, m 2 {a, c} = 0.1. r = U = (a, b, c), 1: m 1 {a} = 0.8, m 1 {b} = 0.1, m 1 {c} = 0.1; 2: m 2 {a} = 0.8, m 2 {b} = 0.1, m 2 {a, c} = 0.1. r = ,,,.

5 6 : 843,?,,,,. 6 U = (a, b), 1: m 1 {a} = 0.8, m 1 {b} = 0.2; 2: m 2 {a} = 0.2, m 2 {b} = 0.8. r = U = (a, b), 1: m 1 {a} = 0.9, m 1 {b} = 0.1; 2: m 2 {a} = 0.1, m 2 {b} = 0.9. r = , 6 7, 6,, 7 6,., 0 1, 1,,, ; 0,,., k,., [24] Liu pignistic. 8 [24], Ω = {1, 2, 3,, 20}, : 1: m 1 (2, 3, 4) = 0.05, m 1 (5) = 0.05, m 1 (Ω) = 0.1, m 1 (A) = 0.8; 2: m 2 (1, 2, 3, 4, 5) = 1. A {1}, {1, 2}, {1, 2, 3},, {1, 2, 3,, 20}. 1 A 20 m 1 m 2 pignistic. 1 A. 1, Liu pignistic difbetp, difbetp,, difbetp,,.,,,. 1 Table 1 Comparison of new proposed conflict coefficient with classical conflict coefficient difbetp r k A ={1} A ={1, 2} A ={1, 2, 3} A ={1,, 4} A ={1,, 5} A ={1,, 6} A ={1,, 7} A ={1,, 8} A ={1,, 9} A ={1,, 10} A ={1,, 11} A ={1,, 12} A ={1,, 13} A ={1,, 14} A ={1,, 15} A ={1,, 16} A ={1,, 17} A ={1,, 18} A ={1,, 19} A ={1,, 20} Fig. 1 Comparison of new proposed conflict coefficient with classical conflict coefficient 6 (Conclusion) k D-S, k, k.,, D-S. :, (13)(14) 5, log,.,.

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