By analyzing three parts of interval valued intuition fuzzy sets (IVIFS), we provide a novel framework constructing risk function with IVIFS information for risk analysis of outsourced software project. First, we introduced some risk factors of outsourced software project according to their hierarchical levels, and present a general risk function model. And then, some useful mathematical properties of this risk function are proved. Based on the mathematical properties of general risk function, all these presented specific risk functions are classified into four types: incentive function, punitive function, incentive-punitive function and equilibrium function. Especially, two kinds of incentive-punitive risk functions are focused on and a construction method for them is proposed. Finally, an application example for the risk assessment of outsourced software project illustrates the use of this decision making method. The simulation results show that these functions are effective in risk prediction.
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