Sequential funding the venture project or not? A prospect consensus process with probabilistic hesitant fuzzy preference information

Abstract Sequential investment problem is a widespread issue in venture capital (VC) process and it is an important key for the success of VC as well. Not only the basic information of projects but also the sunk cost, the network of venture capitalists (VCs), etc., should be considered in the sequential decision-making. In this paper, we study the sequential investment from building a decision-making index system firstly. Then, because of complex and uncertain decision-making circumstance, it is hard for the VCs to give their evaluation information for each alternative as crisp numbers, but it may be easy for them to provide their preferences over each pair of alternatives. Motivated by which, the probabilistic hesitant fuzzy preferences (P-HFPs) are adopted by the VCs in their evaluation process. Moreover, considering the bounded rational psychological characteristic of the VCs in decision-making, the prospect theory has been introduced. Therefore, a prospect consensus with P-HFPs has been constructed due to the grouping of sequential decision-making. It has been applied to a practical case, and an expected consensus under rational framework has been used to analyze the case. The superiority of prospect consensus with P-HFPs has been correspondingly demonstrated in this paper through the comparative analyses of the expected consensus with P-HFPs, the prospect consensus with HFPs and the expected consensus with HFPs.