Estimating sustainability dimensions using fuzzy inverse directional distance model with flexible measures: a health sector application

Appraising some sustainability indicators for changes of others, or comprehensively assessing all metrics, while maintaining sustainability performance, is a crucial consideration for decision-makers. Moreover, numerous real-world applications involve factors that possess an ambiguous status as either input or output, commonly referred to as flexible measures, as well as imprecise measures. Accordingly, this research introduces a fuzzy flexible directional distance model for evaluating sustainable systems with fuzzy flexible measures. Subsequently, a fuzzy inverse directional distance approach, founded on data envelopment analysis and incorporating flexible measures, is proposed to assess the alteration of some imprecise sustainability criteria in response to changes in other measures while maintaining sustainability performance. Also, the modifications of all sustainability dimensions are dealt with while the sustainability performance level remains unchanged. An instance of numerical illustration and practical implementation within the healthcare industry has been presented to showcase the introduced methodology. The findings suggest that the technique proposed in this study has proven to be advantageous and enlightening for evaluating specific dimensions of sustainability in relation to alternations of other indicators or comprehensively addressing modifications of all sustainability indicators, while simultaneously preserving the ability of entities with fuzzy flexible measures.