Some novel concave and convex risk functions with interval valued intuitionistic fuzzy sets (IVIFS) information are proposed. By analyzing the factors of outsourced software project risk, we provide some risk functions with IVIFS information for outsourced software project. All these risk functions are classified into three types: incentive function, punitive function and equilibrium function, and some useful mathematical properties of these risk functions are proved. Finally, a practical risk assessment example to outsourced software project is given to illustrate the application of this decision making method. The simulation results show the effectiveness of these functions compared with that of some conventional functions.
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