A novel weight‐derived method and its application in graduate students' physical health assessment

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. K E Y W O R D S analytic network process, factor analysis, hybrid decision-making information, incomplete probabilistic linguistic preference relation, physical health assessment 1 | INTRODUCTION In multiattribute decision making, analytic hierarchic process (AHP) 1 is a classic and essential methodology to derive the weights of the pairwise elements (objectives, attributes, or alternatives) with layered and interlaced structure, which has various applications: social vulnerability assessment of earthquake disaster, 2 safety measures in the chemical industry 3 and risk management in distributed wind energy, 4 and so forth. Moreover, other researches about AHP have been developed. 5,6 However, if the dependence and feedback relations exist between the pairwise elements, the AHP method is unsuitable for solving such issues. Thus, Saaty 7 proposed another important method called the "analytic network process" (ANP) to tackle more practical problems. In the ANP, all attributes or alternatives are grouped into different clusters, and the preference matrix shows the dependence and feedback relations between these elements. Then, the initial weight of each element is derived and the final comprehensive weight is calculated. 8 Because of its practicability, the ANP has been utilized to solve many complex and practical problems, such as the modeling the drivers of urban land use changes in Lusaka, 9 analysis in referrals of children and adolescent victims of violence 10 and the priori...

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“…, m denotes the sample size, and P denotes the number of indicators whose calculation formula is shown in equation (5).…”