The deregulation of the electricity industry has prompted a wide interest, especially among generation companies, in developing optimum bidding strategies in order to maximize profits. The paper presents an approach to strategic bidding using a fuzzy methodology that is able to handle uncertainty in market parameters such as load demand, generator bid, power dispatch, price, cost, revenue and profit. A multi-level fuzzy system is developed to model a generator bidding system. This system is able to extract market behaviors from historical market data, and is used to calculate optimum bid multipliers. The optimum bid multipliers are tested on a simplified electricity market model, namely a four-generator two-bus system. The results show that the proposed fuzzy approach is effective in formulating optimum bids for generators.