• 대한수학회지
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• 제35권3호
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• pp.765-782
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• 1998

The purpose of this paper is to give convergence theorems both for closed convex set valued and relative fuzzy valued martingales, and sub- and super- martingales. These kinds of martingales, sub- and super-martingales are the extension of classical real valued martingales, sub- and super-martingales. Here we compare two kinds of convergences, in the Hausdorff metric and in the Kuratowski-Mosco sense. We also introduce a new convergence for the fuzzy valued case in the graph sense and obtain convergence theorems.

• Journal of the Korean Statistical Society
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• 제28권1호
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• pp.21-34
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• 1999

In this paper, conditional expectation of a fuzzy random variable is introduced and its properties are investigated. Using this, we introduce the concept of fuzzy martingales and prove some convergence theorems which generalize te corresponding results for the classical martingales.