Semi-order Fuzzy Supermartingales and Submartingales

There are some mathematical models(see Example2.4)and analogous results in standard martingale theorywhich can not be described by the usual fuzzy martingaletheory because of the lack of corresponding semi-orderin the fuzzy number space(E~n,D).In this paper,asuitable semi-order in the fuzzy number space(E~n,D)and the semi-order fuzzy supermartingale and submar-tingale are introduced,the charaterlstics of semi-ordersupermartingales and submartingales,as well as theDood's stopping theorem for them(the bounded stoppingtimes theorem and the general stopping times theoremfor a class of closable semi-order fuzzy supermartin-gales and submartingales)are established.

Semi-order Fuzzy Supermartingales and Submartingales

There are some mathematical models (see Example 2.4) and analogous results in standard martingale theory which can not be described by the usual fuzzy martingale theory because of the lack of corresponding semi - order in the fuzzy number space (En, D). In this paper, a suitable semi - order in the fuzzy number space (EA, D) and the semi - order fuzzy supermartingale and submar-tingalc are introduced, the charateristics of semi - order supcrmartingalcs and submartingales, as well as the Dood's stopping theorem for them(the bounded stopping times theorem and the general stopping times theorem for a class of closable semi - order fuzzy supermartin-galcs and submartingale s) are established.