The problem of volatility forecasting with and without consideration of weekly seasonality effect (the weekend effect) is examined in this research. The question of the seasonality existence is understood in the following sense: do models, which incorporate seasonality, feature better forecasts? The fuzzy GARCH model, which accounts for a weekly seasonality effect is presented in the paper. This model is based on the ordinary GARCH model but allows for the use different dependences in different clusters (both of volatility and seasonality), as well as for the so-called soft switching between the clusters. The suggested method is applied to two indices, which can be deemed as indicators of the Russian stock market condition. The indices are the MOEX Russia Index and the RTS Index. The proposed model is challenged against a fuzzy model without seasonality and a classic GARCH model. The conducted calculations suggest that there is no significant improvement of a forecast if a seasonality is embedded into the fuzzy GARCH model. Fuzzy models show comparable results with regards to the conventional autoregressive conditional heteroskedasticity model. Thus, fuzzy models can be used along with traditional models, however day of the week consideration doesn’t yield a greater quality of volatility forecasts, at least on the samples used. The fuzzy GARCH model may be useful for financial risks estimation and for evaluation of the Value at Risk metric in particular.