闭区间值鞅及模糊数值鞅

Closed Interval Valued Martingales and Fuzzy Number Valued Martingales

集值上鞅、下鞅和鞅的收敛定理已有不少文章进行了研究[1]、[2][3]。但在这些文章中,集值上(下)鞅并不以经典的上(下)鞅为其特款。在本文中,我们定义了以经典上(下)鞅为其特款的闭区间值上(下)鞅,并讨论了它们的性质及其收敛定理。本文还在此基础上讨论了模糊数值鞅。

The convergence theorems of set valued supermartingales (submartingales, martingales) are studied in the much papers. But, in those papers, classical supermartingale (submartingale) is not a special example of set valued supermartingale (submartingale). In this paper, the new definition of closed interval valued supermartingale (submartingale) is given. By this new definition, classical supermartingale (submartingale) is a special example of closed interval valued supermartingale (submartingale). Then their properties and convergence theorem are discussed. The Fuzzy number Valued martingales are discussed also in this paper.