In multiattribute decision making, the analytic network process (ANP) is an important methodology to derive the subjective weights of attributes when the dependence and feedback relations exist between attributes, and the number of attributes should be no more than seven in a comparison matrix. To reduce the dimensions of attributes, we propose a hybrid hesitant fuzzy linguistic factor analysis method to cluster the attributes into main factors. The method takes multiple forms of decision‐making information into consideration, such as single linguistic terms, hesitant fuzzy linguistic terms, and numeric values. Meanwhile, the objective weights of the main factors are obtained as well. As for the subjective weights of main factors, the incomplete probabilistic linguistic ANP is developed after improving the incomplete probabilistic linguistic preference relation with multiplicative consistency. At last, the final weights of the main factors are calculated by combining the objective and subjective weights. A questionnaire survey about assessing the weights of the main factors influencing graduate students' physical health is designed to explain the application of the proposed methodology. To sum up, the main importance and contributions of this study are as following: (1) developing a hybrid hesitant fuzzy linguistic factor analysis method and incomplete probabilistic linguistic ANP, (2) proposing a novel weight‐derived method from both objective and subjective perspectives, and (3) applying it to graduate students' physical health assessment.

中文翻译：

---

一种新的体重衍生方法及其在研究生身体健康评估中的应用

在多属性决策中，当属性之间存在依赖和反馈关系时，分析网络过程（ANP）是推导属性主观权重的重要方法，比较矩阵中属性的数量不应超过7个。为了降低属性的维度，我们提出了一种混合犹豫模糊语言因素分析方法，将属性聚类为主要因素。该方法考虑了多种形式的决策信息，如单一语言项、犹豫模糊语言项和数值。同时，也得到了主要因素的客观权重。对于主要因素的主观权重，不完全概率语言ANP是在改进具有乘法一致性的不完全概率语言偏好关系后开发的。最后结合客观权重和主观权重计算主要因素的最终权重。一项关于评估影响研究生身体健康的主要因素的权重的问卷调查旨在解释所提出的方法的应用。综上所述，本研究的主要意义和贡献如下：(1) 开发了一种混合犹豫模糊语言因素分析方法和不完全概率语言 ANP，(2) 从客观和主观的角度提出了一种新的权重导出方法(3) 将其应用于研究生的身体健康评估。