A novel bi-objective R-mathematical programming method for risk group decision making

Most risk-based multi-attribute group decision-making (R-MAGDM) frameworks often assume that attributes are independent and rarely consider the decision-maker’s (DM) psychological behaviours. However, in many cases, attributes tend to interact with each other, and DMs often display bounded rationality during the decision-making process. A new R-mathematical programming method is developed to address these issues by integrating R-sets, regret theory, the Banzhaf function, and the LINMAP method. Initially, a novel exp operation and a method for defuzzification of R-numbers are introduced, enabling the utilisation of R-numbers in decision-making problems. Subsequently, an R-utility function and an R-regret/rejoice function are defined to calculate the Banzhaf R-perceived utility of each alternative. Following this, R-group consistency (RGCI) and inconsistency indexes (RGII) are introduced for pair-wise rankings of alternatives. Furthermore, a bi-objective R-programming model is formulated to maximise RGCI and minimise RGII to identify the R-ideal solution and optimal weights of criteria and DMs. An optimisation algorithm utilising the non-dominated sorting genetic algorithm-II (NSGA-II) is proposed to solve the constructed model and obtain the non-dominated set. Four decision-making schemes are presented to determine the best trade-off solution from this non-dominated set. Finally, a numerical case is presented to demonstrate the proposed approach’s practicality, effectiveness, and superiority.