Development of sustainability index usingZ-numbers: a new possibilistic hierarchical model in the context ofZ-information

Nowadays sustainability improvement is one of the most important duties of each system and organization. A sustainable system first needs to measure the current condition of sustainability precisely and then tends to apply modifications for the sake of enhancing the quality of performance. Regarding the existence of unreliability in data, and while sustainability measurement always deals with calculations, practitioners and experts are not commonly able to obtain an accurate status for sustainability in associated systems. In light of this exigency, the fuzzy sets have been incorporated with sustainability evaluations in several studies to handle uncertainty and vagueness conditions. Meanwhile, the reliability of the data was still intact. This study aims at satisfying this constraint by adopting the concept ofZ-numbers through sustainability appraisals. By using the proposed model, the unreliable data can be transformed into possibilistic fuzzy sets to remove the mathematical sophistications. TheZ-number-based approach also can be transferred into conventional fuzzy sets when experts are fully confident about deterministic inputs. The proposed model then is applied to a freight transportation sustainability evaluation as an illustrative case to elucidate the application of the proposed model in real-world cases. The elaborated approach is validated by both conventional fuzzy sets and crisp approach, and the superiority of the model is demonstrated by more reasonable results and wide applications. Note that this approach can be used as a benchmark for evaluating sustainability in diverse systems in light of time.