The purpose of this paper is to discuss fuzzy valued Gaussian processes and mar-tingales with continuous parameter. We mainly obtain a representation theorem for fuzzy valued Gaussian processes after proving a new embedding theorem. Based on previous results about set valued and fuzzy valued martingales (cf. [S. Li, Y. Ogura, J. Fuzzy Math. 4 (1996) 905; S. Li, Y. Ogura, Fuzzy Sets and Systems 101 (1999) 453; S. Li, Y. Ogura, Ann. Probab. 26 (1998) 1384-1402; S. Li, Y. Ogura, in: Proc. IFSA '97, vol. 4, 1997, pp. 9-13; S. Li, Y. Ogura, in: C. Bertoluzza, M.A. Gil, D.A. Ralescu (Eds.), Statistical Modeling, Analysis and Management of Fuzzy Data, Physica (in press); Y. Ogura, S. Li, Fuzzy Sets and Systems (in press)]), we prove optional sampling theo- rems for set valued and fuzzy valued martingales with continuous parameter.