LAUSR

In the practical decision-making process, it is common that more than one type of evaluation information is adopted for comprehensive assessment. For example, decision-makers are accustomed to evaluating quantitative evaluation information with real numbers, whereas evaluating qualitative evaluation information with fuzzy numbers. In this study, a hybrid multi-criteria decision-making (MCDM) method based on an extended acronym in Portuguese of interactive and multiple attribute decision-making (TODIM) approach with unknown weight information is proposed. First, different criteria values are denoted as real numbers and picture fuzzy numbers (PFNs), respectively. Given that weight information is completely unknown, the best–worst method is modified with PFNs to determine subjective weights. Meanwhile, the entropy weight method is recommended to calculate objective weights. Then, a combined criteria weight vector can be obtained by considering subjective preferences and objective facts, simultaneously. Thereafter, the traditional TODIM approach is extended with hybrid evaluation information to obtain final ranking order. Finally, an example of evaluating the performance of cleaner production for coal mines is illustrated to demonstrate the feasibility of the proposed method. Furthermore, the robustness and strengths of this method are verified by sensitivity and comparison analyses. The results show that the proposed method is feasible and provides references for solving hybrid MCDM problems with unknown weight information.