Deriving priorities from the fuzzy best-worst method matrix and its applications: A perspective of incomplete reciprocal preference relation.

Preference relation is an effective tool in multi-criteria decision making (MCDM). The fuzzy best -worst method (FBWM), which is an extension of the BWM, is proposed to determine weights for criteria. In the FBWM, the Fuzzy Best-to-others Vector (FBV) and Fuzzy others-to-Worst Vector (FWV) are given. The FBV and FWV can intrinsically formulate one incomplete reciprocal pref-erence relation (IRPR), which we call the FBWM matrix. As the FBWM is designed mainly to determine the weights, and the existing FBWM only uses the min-max problem to derive the weights. Therefore, it is important to develop other effective methods to derive the weights from the FBWM matrix. Deriving the weights from FBWM matrix is converted into deriving the pri-orities from the corresponding IRPR. In this view, two groups of methods are proposed. One group is for a single FBWM matrix, and the other group is for a group of FBWM matrices. To show the effectiveness and performance of the developed methods, Monte Carlo simulations were imple-mented. Finally, two examples were used to show how these methods are applied in real decision -making problems. Comparative analyses were performed to show the differences and usefulness of the proposed methods.