可信性空间上关于模糊变量的强大数定律

目前,关于强大数定律的研究仍集中在概率测度(可加性测度)空间上。但是,概率测度的可加性条件太强,限制了强大数定律的研究范围。为了扩大其研究范围和应用领域,强大数定律将被推广到一种非可加测度空间——可信性空间上进行研究。可信性测度是一种比概率测度更广泛的、自对偶的测度,它的性质将得到更进一步的讨论。利用概率论中类似的方法,在可信性空间上给出依可信度1收敛的概念、重新提出基于模糊变量的强大数定律的定义;进而提出并证明强大数定律的相关引理;最后给出强大数定律的证明,从而获得了可信性空间上关于模糊变量的强大数定律。这一工作扩大了强大数定律的研究范围,达到了推广强大数定律应用领域的目的。

Strong law of large numbers about fuzzy variables on credibility space

At present,the researches about strong law of large numbers still focus on probability measure(additive measure) space.But the additional condition of the probability is very strict and the condition restrains the generalization and application of strong law of large numbers.In order to generalize its study and application ranges,this paper explores the strong law of large numbers on a kind of non-additive measure space-credibility space,which is wider than probability space.Credibility measure is a self-dual measure;its properties are further discussed.By using analogy method,the concept of converges with credibility 1 and the definition of strong law of large numbers will be given on credibility space;some correlation theorems about strong law of large numbers are proven;finally,the strong law of large numbers about fuzzy variables are proposed and proven.The work of this paper generalizes the study and application ranges of strong law of large numbers.