| Abstract: | 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. |
