Elsevier

Fuzzy Sets and Systems

Volume 130, Issue 1, 16 August 2002, Pages 75-86
Fuzzy Sets and Systems

Semi-order fuzzy supermartingales and submartingales with continuous time

https://doi.org/10.1016/S0165-0114(02)00118-5Get rights and content

Abstract

A new suitable semi-order in the fuzzy number space (En,D), the semi-order fuzzy supermartingales and submartingales with continuous time and their characteristics are introduced. The famous Riesz decomposition and Doob–Meyer decomposition theorems in standard martingale theory are generalized to semi-order fuzzy supermartingales. The proof of Doob–Meyer decomposition is rather technical and so the theory of fuzzy-valued measures generated by increasing fuzzy processes is developed.

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