The intent of this paper is to schedule short-term hydrothermal system probabilistically considering stochastic operating cost curves for thermal power generation units and uncertainties in load demand and reservoir water inflows. Therefore, the stochastic multi-objective hydrothermal generation scheduling problem is formulated with explicit recognition of uncertainties in the system production cost coefficients and system load, which are treated as random variable. Fuzzy methodology has been exploited for solving a decision making problem involving multiplicity of objectives and selection criterion for best compromised solution. A real-coded genetic algorithm with arithmetic-average-bound-blend crossover and wavelet mutation operator is applied to solve short-term variable-head hydrothermal scheduling problem. Initial feasible solution has been obtained by implementing the random heuristic search. The search is performed within the operating generation limits. Equality constraints that satisfy the demand during each time interval are considered by introducing a slack thermal generating unit for each time interval. Whereas the equality constraint which satisfies the consumption of available water to its full extent for the whole scheduling period is considered by introducing slack hydro generating unit for a particular time interval. Operating limit violation by slack hydro and slack thermal generating unit is taken care using exterior penalty method.The effectiveness of the proposed method is demonstrated on two sample systems.