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In competitive environment, customer outage cost may be taken into account for the delivery of energy services. Based on a probabilistic approach the outage cost can be evaluated from the Interrupted Energy Assessment Rate (IEAR) which normally requires customer perception on the damages occurred from an electricity interruption. In general the IEAR is only calculated based on mean values, even though the obtained customer damage information usually contains fairly large deviation. To cope with the large deviation of the data, this paper employs fuzzy arithmetic to model the customer damage function which is consequently used in association with power interruption statistics, rather than conventional probabilistic reliability calculation, to calculate the Fuzzy Interrupted Energy Assessment Rate (FIEAR). The proposed method has been tested with a distribution system of which more than 40,000 actual interruptions were recorded. The results show that the FIEAR normally covers the IEAR and provides flexibility to allow the customer outage cost to be implemented in real competitive environment.