In this case, DCR does not work since it gets an undefined division 0/0. 

In Smets' TBM (Transferable Believe Model), the total conflicting mass, 0.4 + 0.5 + 0.1 = 1, is transferred to the empty set, since TBM considers an open world (non-exhaustive hypotheses). 

See row \# 6.

With DSm first conditioning rule (row \# 7) the total conflicting mass, 1, is transferred to the whole set that the truth belongs to, T∪D. So, mDSmT1(T∪D |T∪D) = (m1+ m2)( T∪D) + 1 = 1.

In DSm second conditioning rule (row \# 8) the total conflicting mass is 1. Since C(B∪D) = 0, the total conflicting mass 1 is uniformly transferred to the sets T, D, and T∪D {i.e. the singletons and unions of singletons included in T∪D}, therefore each such set receives 1/3. 

## Conclusion.

We have examined Dempster's Conditioning Rule in terms of bba. We saw that in the second military example, using DCR for target identification, the procedure failed mathematically. That's why we designed two DSm simple conditioning rules and could complete the procedure of target identification. We have compared these approaching of target identification using DCR, 
TBM conditioning, and the two DSm conditioning rules that got better results than DCR and TBM. We also observed from these examples that the two DSm simple conditioning rules give almost similar results. 

## References:

[1] Milan Daniel, Analysis of DSm belief conditioning rules and extension of their applicability, Chapter 10 in [5], 2009. [2] Glenn Shafer, A Mathematical Theory of Evidence, Princeton Univ. Press, Princeton, New Jersey, 1976. 

[3] F. Smarandache, Unification of Fusion Theories (UFT), International Journal of Applied Mathematics & Statistics, Vol. 2, 1-14, 2004; Presented at NATO Advanced Study Institute, Albena, Bulgaria, 16-27 May 2005. [4] F. Smarandache, J. Dezert (Editors), Advances and Applications of DSmT for Information Fusion, Volume 2, American Research Press, Rehoboth, 2006. 

[5] F. Smarandache & J. Dezert, "Advances and Applications of DSmT for Information Fusion", Vol. 3, Arp, 2009. 