Considering regret psychology and non-cooperative competition among alternatives for heterogeneous multi-attribute group decision making

• A new method is proposed for heterogeneous multi-attribute group decision making . • A regret theory-based expert weight determination model is proposed. • The individual decision matrices are aggregated into a collective decision matrix. • A regret theory-based interval DEA game cross-efficiency model is proposed. • The model calculates the comprehensive values of alternatives. In reality, to select the best one from a set of alternatives, there are widespread situations that require several experts to assess the attribute values of each alternative with heterogeneous information. The purpose of this paper is to solve the heterogeneous multi-attribute group decision making (HMAGDM) problems with attribute values involving real numbers, intervals, intuitionistic fuzzy sets, interval type-2 fuzzy sets, and interval-valued hesitant fuzzy sets from the perspective that alternatives have regret psychology with respect to the assessment information and that there is a non-cooperative competitive relationship among alternatives. Therefore, a method based on regret theory and interval data envelopment analysis (DEA) game cross-efficiency model is proposed for HMAGDM. The method adopts a process of aggregation followed by exploration. In the aggregation phase, a regret theory-based expert weight determination model is constructed to derive the weights of experts, and the individual decision matrices provided by individual experts are further aggregated into a collective decision matrix. Then, the heterogeneous information in the collective decision matrix is uniformly converted into intervals, which are represented as variables with unknown parameters. According to these variables, a regret theory-based interval DEA game cross-efficiency model is proposed to calculate the comprehensive values of alternatives and thus rank alternatives. The feasibility and effectiveness of the proposed method are illustrated by a supplier selection example.