Abstract
Doob decomposition and Riesz decomposition theorems in standard martingale theory are generalized to fuzzy martingales. The concepts of two types of Riesz decomposition for fuzzy supermartingales are given and the necessary and sufficient conditions of that fuzzy supermartingale or submartingale (resp. supermartingale) has Doob decomposition (resp. Riesz decomposition) are discussed in detail.
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