Picture Fuzzy Extension of DEMATEL and its Usage in Educational Quality Evaluation

Multiple attribute decision-making (MADM) models are strength tools for assessing alternatives when more than one attribute should be considered. The experts consulted need scales to state their judgments and preferences. The contemporary versions of fuzzy sets provide various kinds of scales to let the experts specify different characteristics of their ideas. The concept of picture fuzzy sets (PFS) includes four elements. The first three of them can be independently assignable: the positive, the neutral, and the negative membership degrees. The only constraint is that their sum must not exceed 1. The difference between 1 and the sum of the assigned degrees is called refusal degree and it represents the expert’s choice of refusing the sharing of the preference. PFS has greater representation strength than other fuzzy extensions have since it exposes an additional fourth component, refusal degree. In this study, picture fuzzy version of DEMATEL (DEcision-MAking Trial and Evaluation Laboratory), which is developed for revealing the potential causal dependencies among the multiple attributes, is introduced for considering the hesitancy and refusal degrees of experts. In this new version, no constant linguistic evaluation scale is proposed. Instead, the evaluations of experts are grouped into four categories: YES, NO, ABSTAIN, and REFUSE. The strength of the influence between two attributes is determined according to the aggregation of these statements. The proposition is applied to a real case regarding an evaluation of the educational quality and a comparative analysis including different applications is conducted to validate the method.