Intuitive Picture Fuzzy Distance Measure with its Application in Assessing Teaching Quality

Abstract

Considering that picture fuzzy sets (PFSs) is much more efficient in comparison with fuzzy sets at handling the uncertainty in decision-making problems, this paper firstly applies PFSs to depict the indeterminacy and inaccuracy information in the teaching quality assessment (TQA) process. To begin with, the related definitions of PFSs are all profiled successively. Then, we attempt to propose an integrated assessment method with the combined compromise solution (CoCoSo) method and Taxonomy method (TM) to handle the TQA problem with PFSs. In this approach, we define a new cumulative method based on TM to aggregate individual opinion into group opinion. We also develop a weighting strategy based on the CRiteria Importance Through Intercriteria Correlation approach (CRITIC) to evaluate the significance of experts with PFSs. For this, we define a novel generalized chordal picture fuzzy (PF) distance measure that considers the impacts of the degree of the refusal membership, which has a strong capacity of differentiation. Again, a final ranking method is presented with the CoCoSo approach and the Stepwise Weight Assessment Ratio Analysis (SWARA) method. Furthermore, we apply a case study of the TQA to demonstrate the implementation of the newly proposed method. The results obtained from the sensitivity analysis validate that the option “Prof. Cheng” consistently achieves the highest ranking and is independent of variations of balancing factor and weight information of experts and criteria. Finally, a comparison is implemented to confirm the robustness of the suggested integrated framework.