This presentation focuses on a probabilistic-fuzzy IF-THEN rules system, where antecedents carry fuzzy information and consequents are represented by quantile functions, enabling a probabilistic description of output variables. The inference process is based on the L1-fuzzy transform. First, we introduce a simple yet effective method for determining consequent quantiles, in addition to the traditional linear programming approach. Then, we examine the behavior of running and inferred quantiles, assessing their consistency with the underlying probability distribution. Finally, we discuss potential applications in time series forecasting.