The multi-attribute and group-decision problem in the selection of a construction diversion scheme for large hydropower projects often involves multi-decision subjects and schemes. Each scheme includes multiple attributes, and the attribute values and weights are multi-attribute group decision-making problems with interval numbers. In this study, a new method for solving the multi-attribute group-decision problem is proposed by integrating regret theory, negotiation gathering theory, and the Monte Carlo simulation technique. Firstly, decision-makers’ comprehensive perception utility for each scheme is calculated based on the regret theory. Then, non-uniform and fuzzy opinion of different decision subjects are negotiated and gathered, and negotiation intervals of the attribute weights are calculated through group negotiation gathering theory. Moreover, fuzzy complementary judgment matrixes describing an excellent degree of the diversion schemes are obtained by conducting Monte Carlo simulations. Finally, the alternative diversion schemes are sorted in terms of their priorities, and the reliability of the sorting procedure is confirmed. The multi-attribute group-decision problem in the selection of a construction diversion scheme for Jinping I Hydropower Station is effectively solved by the proposed method. The proposed method is reliable and may significantly contribute to engineering decision-making.

Introduction: Arithmetic calculation is a fundamental skill for mathematical learning and daily life. However, elementary school students often make errors in practice.Methods: Grounded in the schema theory and the memory retrieval theory of mental arithmetic, this study employs a controlled experiment to investigate the effect of a schema-based method in correcting persistent errors in mental arithmetic, specifically in the context of simple addition operations. The experimental group utilizes a schema-based method to help participants rectify incorrect answers in memory retrieval, while the control group did not receive this treatment.Results: The results showed that significant differences emerged between the experimental and control groups in both the post-test performance and the reduction of persistent error count, indicating that the experimental group had rectified incorrect answers in memory; and persistent errors in simple addition were indeed caused by interference from incorrect answers during memory retrieval; and the schema-based method proves to be effective.Discussion: The findings of this study contribute to enhancing practical mental arithmetic instruction, assisting students in correcting relevant errors, and improving their mental arithmetic abilities. Not only does it offer directive guidance for teaching practices, but it also provides an enlightening reference for promoting innovative teaching methods.