证据合成与结合律

THE COMBINATION OF EVIDENCES AND THE ASSOCIATION LAW

设Ｂｅｌ＿１，Ｂｅｌ＿２，Ｂｅｌ＿３是有限论域上的三个信任测度，它们的基本概率分布各为ｍ＿１，ｍ＿２ｍ＿３。Ｄｅｍｐｓｔｅｒ给出了两个信任测度的合成规则。张连文、汪培庄等把Ｄｅｍｐｓｔｅｒ合成规则改进为证据的λ－合成规则。还认为λ－合成规则满足结合律，但是没有证明。本文证明了在一般情况下，无论是Ｄｅｍｐｓｔｅｒ的合成规则，或是λ－合成规则，或是改进了的λ－合成规则都不满足结合律。

Let Bel_1,Bel_2,Bel_3,be three belief measures on the finite domain of discourse.Their basicprobatility assignments are m_1,respectively.Dempster has given the combinationrule of two belief measures.The λ-combination rule as the improvement on Dempster’s rule has been given by Zhang Lianwen and Wang Peizhuang.Without proving,it has been reportedin their paper that the λ-combination rule satiafies the associative law.In this paper acounterexample is shown that in general the λ-combination rule does not satisfy the associative law.