Single-valued neutrosophic sets (SVNSs) can effectively describe the multi-attribute decision-making (MADM) problems which are characterized by incompleteness and uncertainty. Aiming at the MADM problem of SVNSs, a series of methods are proposed to solve the problem, such as the TODIM and PROMETHEE methods. The main idea of the TODIM method is to establish a relative superiority function of scheme relative to other schemes based on the value function of prospect theory, and the ranking of alternatives is determined according to the obtained superiority. In the PROMETHEE method, the decision maker selects the preference function for each attribute according to their preference, and then calculates the priority index, inflow, outflow and net flow according to the difference of the attribute values of scheme, so as to determine the ranking of alternatives. In this paper, a new method based on PROMETHEE and TODIM is proposed to solve the MADM problem under the single-valued neutrosophic environment. Based on the calculation formula of inflow and outflow in PROMETHEE method, and the calculation formula of overall dominance in the TODIM method, a new integrated formula is obtained.

中文翻译：

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基于PROMETHEE和TODIM的单值中智集多属性决策新方法

单值中智集（SVNS）可以有效地描述以不完整和不确定性为特征的多属性决策（MADM）问题。针对SVNS的MADM问题，提出了TODIM和PROMETHEE等一系列解决方法。TODIM方法的主要思想是基于前景理论的价值函数建立一个方案相对于其他方案的相对优势函数，并根据获得的优势确定备选方案的排名。在PROMETHEE方法中，决策者根据每个属性的偏好选择偏好函数，然后根据方案的属性值的差异计算优先级指标，流入，流出和净流量，以确定替代品的排名。提出了一种基于PROMETHEE和TODIM的新方法来解决单值中智环境下的MADM问题。根据PROMETHEE方法的流入和流出计算公式，以及TODIM方法的总体支配性计算公式，得出了一个新的综合公式。