For the multi-criteria group decision-making problem where the criterion value is a normal interval number and the weight information is incomplete, the normal interval number and its compromise expected value, compromise mean square error, algorithm, weighted arithmetic average of normal interval number (ININWAA) Operator, the ordered weighted average (ININOWA) operator of normal interval numbers and the mixed weighted average (ININHA) operator of normal interval numbers, and a multi-criteria group with incomplete information based on normal interval numbers is proposed. Decision-making methods. This method uses ININWAA operator and INNHA operator to integrate criterion values, uses the compromise mean square error of criterion values, establishes an optimisation model to solve the optimal criterion weights and uses the expectation variance criterion to determine the order of the schemes. The case analysis shows the effectiveness and feasibility of this method.