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The selection of venture capital investment projects is one of the most important decision-making activities for venture capitalists. Due to the complexity of investment market and the limited cognition of people, most of the venture capital investment decision problems are highly uncertain and the venture capitalists are often bounded rational under uncertainty. To address such problems, this article presents an approach based on regret theory to probabilistic hesitant fuzzy multiple attribute decision-making. Firstly, when the information on the occurrence probabilities of all the elements in the probabilistic hesitant fuzzy element (P.H.F.E.) is unknown or partially known, two different mathematical programming models based on water-filling theory and the maximum entropy principle are provided to handle these complex situations. Secondly, to capture the psychological behaviours of venture capitalists, the regret theory is utilised to solve the problem of selection of venture capital investment projects. Finally, comparative analysis with the existing approaches is conducted to demonstrate the feasibility and applicability of the proposed method. [ABSTRACT FROM AUTHOR]

The multi-stage uncertain risk decision-making problems are very common in production and life, such as emergency decision-making problems, batch product sampling inspection, etc. It’s very complex and interesting in applications. The multi-stage uncertain risk decision-making process often involves multiple reference points owing to decision-making environment and decision-makers’ mentalities. This paper aims to solve the multi-stage uncertain risk decision-making problems without probability information. Decision makers’ psychological behaviors are considered by setting the thresholds of possibility degree in different states. The attribute weight optimization model is established based on the extended LINMAP method through a two-stage model, considering the principle of maximizing the ranking consistency of alternatives in all states. The stage weight optimization model is established in the viewpoint of minimizing the opportunity loss. The optimal alternative is selected according to the compromise ranking values, which consider the satisfaction of decision makers. A case is presented to illustrate the feasibility and validity of the proposed method. [ABSTRACT FROM AUTHOR]

Two types of information, collectively referred to as double information, are usually required in management decision-making. The first is preference information expressed in a judgment matrix. The second is reference information expressed in a multi-attribute decision matrix. In this paper, we investigate large-scale group clustering problems with double information in group decision-making. We first establish a novel three-dimensional gray correlation degree index, which integrates the alternative decision-making vector, index vector and alternative preference vector, to fully excavate the correlation between decision makers with double information. We then develop a new clustering procedure combining three-dimensional gray relational analysis and the concept of hierarchical clustering. Moreover, a model for determining clustering centers is established on the basis of the maximum gray correlation degree within each cluster and minimum gray correlation degree among clusters. A heuristic algorithm for the model to identify the core decision maker in each cluster is proposed. Finally, we illustrate the applications of the developed procedures with a practical case. The rationality of the proposed method is demonstrated by comparing results with results obtained using other methods, including the traditional gray clustering method and hierarchical clustering method with single information; i.e., preference information or reference information. [ABSTRACT FROM AUTHOR]