Delphi multi-round survey is a procedure that has been widely and successfully used to aggregate experts’ opinions about some previously established statements or questions. Such opinions are usually expressed as real numbers and some commentaries. The evolution of the consensus can be shown by an increase in the agreement percentages, and a decrease in the number of comments made. A consensus is reached when this percentage exceeds a certain previously set threshold. If this threshold has not been reached, the moderator modifies the questionnaire according to the comments he/she has collected, and the following round begins. In this paper, a new fuzzy Delphi method is introduced. On the one hand, the experts’ subjective judgments are collected as fuzzy numbers, enriching the approach. On the other hand, such opinions are collected through a computerized application that is able to interpret the experts’ opinions as fuzzy numbers. Finally, we employ a recently introduced fuzzy ranking methodology, satisfying many properties according to human intuition, in order to determine whether the expert’s fuzzy opinion is favorable enough (comparing with a fixed fuzzy number that indicates Agree or Strongly Agree). A cross-cultural validation was performed to illustrate the applicability of the proposed method. The proposed approach is simple for two reasons: it does not need a defuzzification step of the experts’ answers, and it can consider a wide range of fuzzy numbers not only triangular or trapezoidal fuzzy numbers.

中文翻译：

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基于模糊排序的模糊 Delphi 共识方法

Delphi 多轮调查是一种程序，已被广泛并成功地用于汇总专家对某些先前确定的陈述或问题的意见。这些意见通常以实数和一些评论的形式表达。共识的演变可以通过同意百分比的增加和评论数量的减少来显示。当这个百分比超过某个先前设定的阈值时，就会达成共识。如果没有达到这个门槛，主持人根据他/她收集的评论修改问卷，下一轮开始。本文介绍了一种新的模糊Delphi方法。一方面，将专家的主观判断收集为模糊数，丰富了方法。另一方面，这些意见是通过计算机应用程序收集的，该应用程序能够将专家的意见解释为模糊数字。最后，我们采用最近引入的模糊排序方法，根据人类直觉满足许多属性，以确定专家的模糊意见是否足够有利（与表示同意或非常同意的固定模糊数进行比较）。进行了跨文化验证以说明所提出方法的适用性。所提出的方法很简单，原因有两个：它不需要专家答案的去模糊化步骤，并且它可以考虑范围广泛的模糊数，而不仅仅是三角形或梯形模糊数。我们采用最近引入的模糊排序方法，根据人类直觉满足许多属性，以确定专家的模糊意见是否足够有利（与表示同意或非常同意的固定模糊数进行比较）。进行了跨文化验证以说明所提出方法的适用性。所提出的方法很简单，原因有两个：它不需要专家答案的去模糊化步骤，并且它可以考虑范围广泛的模糊数，而不仅仅是三角形或梯形模糊数。我们采用最近引入的模糊排序方法，根据人类直觉满足许多属性，以确定专家的模糊意见是否足够有利（与表示同意或非常同意的固定模糊数进行比较）。进行了跨文化验证以说明所提出方法的适用性。所提出的方法很简单，原因有两个：它不需要专家答案的去模糊化步骤，并且它可以考虑范围广泛的模糊数，而不仅仅是三角形或梯形模糊数。进行了跨文化验证以说明所提出方法的适用性。所提出的方法很简单，原因有两个：它不需要专家答案的去模糊化步骤，并且它可以考虑范围广泛的模糊数，而不仅仅是三角形或梯形模糊数。进行了跨文化验证以说明所提出方法的适用性。所提出的方法很简单，原因有两个：它不需要专家答案的去模糊化步骤，并且它可以考虑范围广泛的模糊数，而不仅仅是三角形或梯形模糊数。