Transformation of Discrete Z-Numbers into Normal Cloud Models and Their Applications

Z-numbers incorporate a reliability measure for fuzzy evaluations, enabling the representation of more complex uncertain information. The uncertainty in Z-numbers stems from both the fuzziness of linguistic variables and their inherent randomness. However, existing methods predominantly focus on the fuzziness aspect of Z-numbers, often overlooking their randomness. To better address the randomness in Z-numbers, this study proposes a novel strategy that quantifies them using normal cloud models. First, we introduce a latent probability measure designed to preserve ordinal relationships, it provides a unified quantification of the fuzziness and randomness inherent in discrete Z-numbers. Subsequently, we develop a backward cloud generator based on this latent probability measure to transform discrete Z-numbers into normal cloud models. We then construct a cloud dominance function to evaluate the dominance relationships between two cloud models. Building on this, we integrate the cloud model with the TODIM method to propose an enhanced TODIM approach for solving multi-attribute decision-making (MADM) problems in discrete Z-number environments. Finally, we validate the effectiveness and broad applicability of the proposed approach through experimental analysis in a case study.