Weight-of-conflict conjecture

Weight-of-conflict conjecture was proposed by Glenn Shafer in his book on the Dempster–Shafer theory titled A Mathematical Theory of Evidence.

It states that if $Q_{1}$ and $Q_{2}$ are commonality functions for two separable support functions $S_{1}$ and $S_{2}$ defined over $\Theta$, and $Q_{1}(A)\leq Q_{2}(A)$, then the corresponding weights of conflict satisfy the condition $W_{S_{1}}\geq W_{S_{2}}$.

$\forall A\subseteq \Theta :Q_{1}(A)\leq Q_{2}(A)\implies W_{S_{1}}\geq W_{S_{2}}$

References

• Zhang, Lian-Wen (April 1986). "Weights of Evidence and Internal Conflict for Support Functions". Journal of Information Science. 38 (2).

Further reading

• Yager, R. R.; Liu, L. (2008). Studies in fuzziness and soft computing. Classic works of the Dempster–Shafer theory of belief functions. Berlin: Springer. ISBN 978-3-540-25381-5.