Abstract: Failure probability assessment is the key of quantitative risk assessment of pipeline. The interval-valued intuitionistic fuzzy number (IVIFN) is introduced into the expert's assessment of failure probability in order to present the expert's conclusions comprehensively as regards to support, objection and hesitation in the form of interval. Assuming that the interval score function of the IVIFN is subject to normal distribution, an interval point operator is defined considering the risk appetite of information users. Assessment results of many experts are integrated using D-S evidence theory and grey relational analysis. Different risk appetite factors are selected to identify the trends of failure probability and priority of structural importance. Moreover, the assessment of pipeline failure probability is improved, while the uncertainty of failure event sources is reduced. In this paper, this method of failure probability assessment is used for a pipe welding failure, and its effectiveness is verified.