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Weight-of-conflict conjecture

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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 {\displaystyle Q_{1}} and Q 2 {\displaystyle Q_{2}} are commonality functions for two separable support functions S 1 {\displaystyle S_{1}} and S 2 {\displaystyle S_{2}} defined over Θ {\displaystyle \Theta } , and Q 1 ( A ) ≤ Q 2 ( A ) {\displaystyle Q_{1}(A)\leq Q_{2}(A)} , then the corresponding weights of conflict satisfy the condition W S 1 ≥ W S 2 {\displaystyle W_{S_{1}}\geq W_{S_{2}}} .

∀ A ⊆ Θ : Q 1 ( A ) ≤ Q 2 ( A ) ⟹ W S 1 ≥ W S 2 {\displaystyle \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.
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