Risk interval-valued three-way decisions model with regret theory and its application to project resource allocation

Psychology of regret often affects how people work in their daily lives. Due to the effects of psychology of regret, decision-makers can make irrational decisions in the face of uncertain decision risks. As a classic model, three-way decisions (TWD) are to divide a universal set into three pair-wise disjoint regions by developing an appropriate strategy and also have been widely applied in the area of risk decision-making. However, in the existing theoretical research of TWD, few studies mention the influence of psychology of regret on risk behaviours of decision-makers. In order to expand the theories of TWD and build contacts, we have introduced the influence of psychology of regret on decision-makers’ risk behaviours into TWD with decision-theoretic rough sets (DTRS). In thisarticle, we specifically adopt regret theory to depict the decision-makers’ risk behaviours on the loss function. Regret theory as one type of generalised psychology, considers the psychological comparison between the current choice and other choices made by decision-makers. In light of the Bayesian decision procedure and a basic model of interval-valued DTRS, we reinterpret TWD and construct a new risk interval-valued TWD model. At the same time, we explore the influence of the regret behaviour to TWD by using the simulation experiment and validate the effectiveness of the new risk model. Then, we further apply the risk interval-valued TWD model to support the project resource allocation. From two different viewpoints, we establish two adjustment targets to meet the actual needs of decision-makers in project allocation, which improves our decision’s flexibility in the resource restriction. Target 1 is to minimise the utility loss of the entire field. Target 2 is to maximise the utility of the positive region in each field. Finally, a case of popular entrepreneurship of online movie is used to illustrate and validate our proposed methods.