  Due to the low power consumption and low cost nature of transmissive
reconfigurable intelligent surface (RIS),in this paper, we propose a downlink
multi-user rate-splitting multiple access (RSMA) architecture based on the
transmissive RIS transmitter, where the channel state information (CSI) is only
accquired partially. We investigate the weighted sum-rate maximization problem
by jointly optimizing the power, RIS transmissive coefficients and common rate
allocated to each user. Due to the coupling of optimization variables, the
problem is nonconvex, and it is difficult to directly obtain the optimal
solution. Hence, a block coordinate descent (BCD) algorithm based on sample
average approximation (SAA) and weighted minimum mean square error (WMMSE) is
proposed to tackle it. Numerical results illustrate that the transmissive RIS
transmitter with ratesplitting architecture has advantages over conventional
space division multiple access (SDMA) and non-orthgonal multiple access (NOMA).
