Leigh Mercer: Difference between revisions

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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 $Q_{1}$ and $Q_{2}$ are commonality functions for two separable support functions $S_{1}$ and $S_{2}$ defined over $Θ$ , 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 Θ : Q_{1} (A) \leq Q_{2} (A) ⟹ W_{S_{1}} \geq W_{S_{2}}

References

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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''.
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+It states that if <math>Q_1</math> and <math>Q_2</math> are [[commonality function]]s for two [[separable]] [[support function]]s <math>S_1</math> and <math>S_2</math> defined over <math>\Theta</math>, and <math>Q_1(A) \le Q_2(A)</math>, then the corresponding [[weight of conflict|weights of conflict]] satisfy the condition <math>W_{S_1} \ge W_{S_2}</math>.
+:<math>\forall A \subseteq \Theta : Q_1(A) \le Q_2(A) \implies W_{S_1} \ge W_{S_2}</math>
+==References==
+{{Reflist}}
+* {{cite journal |last=Zhang |first=Lian-Wen |title=Weights of Evidence and Internal Conflict for Support Functions |journal=Journal of Information Sciences |volume=38 |issue=2 |date=April 1986}}
+==Further reading==
+* {{cite book |last=Yager |first=R. R. |last2=Liu |first2=L. |year=2008 |series=Classic works of the Dempster–Shafer theory of belief functions |title=Studies in fuzziness and soft computing |location=Berlin |publisher=[[Springer Science+Business Media|Springer]] |isbn=978-3-540-25381-5}}
+[[Category:Dempster–Shafer theory]]

Leigh Mercer: Difference between revisions

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