There are several difficulties in characterizing geological conditions favourable for hydrocarbon accumulation in a frontier region due to the availability and nature of geoscience data. First, geoscience information from various sources requires precise representation for spatial analysis. In many cases, the information to be represented is possibilistic or transient in nature, and it needs a mathematical tool that can adequately represent the information with a degree of possibility and/or uncertainty. Second, the uncertainty of interpreting each geological indicator and of correlating the results with physical parameters of a petroleum accumulation should be expressed explicitly. Third, the evidence and indicators of the existence of a petroleum accumulation come from various data sources, varying in degrees of uncertainty. These uncertainties should be integrated into a petroleum accumulation model so that exploration risk can be objectively evaluated in a subsequent economic analysis. We propose the use of a fuzzy integration method to tackle these problems. The method uses possibility theory to describe the satisfaction levels associated with each of the essentials for the formation of hydrocarbon deposits, such as the presence of reservoir, source rock, trap, top seal and preservation in a spatial domain. The uncertainties associated with data and evaluation are explicitly incorporated in the aggregate of the geological factors. The proposed method was applied to the Heiberg Group/Formation of western Sverdrup Basin in the Canadian Arctic Archipelago to evaluate the geological favourability for petroleum accumulation. The discovered oil and gas fields and the areas with computed high favourability display a good geographical correspondence, indicating that the proposed fuzzy integration method captures the essential spatial characteristics of petroleum accumulations in the western Sverdrup Basin.