Semi-order fuzzy supermartingales and submartingales with continuous time

Authors:
Yuhu Feng;Xinglong Zhu
Affiliations:
Department of Applied Mathematics, Dong Hua University, 1882 Yan An West Road, Shanghai 200051, People's Republic of China;Department of Applied Mathematics, Dong Hua University, 1882 Yan An West Road, Shanghai 200051, People's Republic of China
Venue:
Fuzzy Sets and Systems
Year:
2002

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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.