Interpretable Robust Multicriteria Ranking with TODIM in Generalized Orthopair Fuzzy Settings

The endeavor to align TODIM (an acronym in Portuguese for interactive and multicriteria decision making) with prospect theory has given rise to the development of several variant methods, including power TODIM, exponential TODIM, and logarithmic TODIM. However, these existing methods fail to address high-order uncertainty within generalized orthopair fuzzy environments. To overcome this limitation, we propose an interpretable robust TODIM approach tailored for generalized orthopair fuzzy settings. First, we extend these TODIM methods to accommodate generalized orthopair fuzzy settings, integrating them into a unified framework. Second, we introduce a set of robustness analysis measures for the extended TODIM method, accounting for simultaneous uncertainty in criteria weights, value function coefficients, and the membership and non-membership degrees of generalized orthopair fuzzy sets. Third, we develop a programming model to determine representative criteria weights based on these robustness analysis measures, followed by an approach to recommend an interpretable and robust ranking within the extended TODIM framework. Finally, we present an illustrative example to demonstrate the application of this interpretable and robust TODIM approach, accompanied by a comparative analysis to highlight its advantages.