【摘要】 Dubois,Prade和Rico等对取值为有限全序集上的模糊测度与可能性测度的关系上做了深入研究,本文推广了他们的这一结果,研究了取值在De Morgan代数上的模糊测度,并通过置换与内M?bius变换,构造出两种可能性分布,证明了取值在De Morgan代数上的模糊测度可以通过一些可能性测度的下确界表示,而通过外M?bius变换,可构造出一种必要性分布,证明了取值在De Morgan代数上的模糊测度可以通过一些必要性测度的上确界表示。更多还原

【Abstract】 Dubois, Prade and Rico study the relation between capacity and possibility measure ranging on a finite totally ordered set. This paper studies the capacity ranging on De Morgan algebra and constructs two types of possibility distributions by permutation and inner M"obius transform. We prove that capacity ranging on De Morgan algebra can be represented by a infimum of possibility measures. We also construct a type of possibility distributions by outer M"obius transform and prove that supremum of Necessity measure can represent capacity ranging on De Morgan algebra.更多还原