格值模糊测度的可能性分布表示  

Representing Capacities as Families of Possibility Distributions

作　　者：倪煜博 李永明[1] NI Yu-bo;LI Yong-ming(College of Mathematics and Information Science,Shaanxi Normal University,Xi'an 710119,China)

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710119

出　　处：《模糊系统与数学》2018年第6期89-96,共8页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11271237;61228305);教育部博士点基金资助项目(200807180005)

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。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.

关 键 词：模糊测度 可能性测度 必要性测度 MOBIUS变换 DE MORGAN type格 并既约元 

分 类 号：O159[理学—数学]