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Abstract: Offshore platforms oil and gas day to day operations themselves involve an undeterminable list of risk. Some of them can be prevent or at least mitigate as a result of an experience of a former disaster. Indeed, although computational mathematical technologies grows so fast helping the engineers to estimate and mitigate the risk much uncertainties remains in a way of vagueness, which is many times impossible to measure precisely due to the imprecision and the lake of data. In such cases fuzzy logic is the mathematical treatment indicated to deal with these problems. As insurance is one of the most important economic form to mitigate risk the purpose of this paper is to verify the viability of purchasing a business interruption cover (BIC) for an offshore production unit using the fuzzy net present value (FNPV) that results of the discounted cash flow (DFC) involving much vagueness and uncertainties in these available information. [Copyright &y& Elsevier]