How to determine a suitable security algorithm for a special application scenario is a complex problem. In this paper, this complex problem is formulated as a multicriteria decision-making (MCDM) problem, and we propose a novel MULTIMOORA (multiobjective optimization on the basis of a ratio analysis plus the full MULTIpevaluation information in the security algorithms evaluation problem. The MULTIMOORA method is an excellent decision method, which owns strong robustness. However, it has not been used to process the complex information structure of q-rung orthopair fuzzy sets. Moreover, it cannot solve the problem that the extreme values negatively influence the ranking results, and it also cannot capture the interrelationship hiding behind the criteria. To overcome the above challenges, we propose novel q-rung orthopair fuzzy Dombi power Heronian mean (DPHM) operator and q-rung orthopair fuzzy Dombi power geometric Heronian mean (DPGHM) operator. Based on these two operators, the MULTIMOORA method is improved for solving the security algorithms’ evaluation problem. Finally, a practical example for evaluating five security algorithms is used to illustrate the decision process of the proposed q-rung orthopair fuzzy MULTIMOORA method.