Development of sustainability index using Z -numbers: a new possibilistic hierarchical model in the context of Z -inform
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Development of sustainability index using Z‑numbers: a new possibilistic hierarchical model in the context of Z‑information Sepehr Hendiani1 · Morteza Bagherpour1 Received: 22 February 2019 / Accepted: 26 August 2019 © Springer Nature B.V. 2019
Abstract 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 of Z-numbers through sustainability appraisals. By using the proposed model, the unreliable data can be transformed into possibilistic fuzzy sets to remove the mathematical sophistications. The Z-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. Keywords Z-numbers · Sustainability · Fuzzy sets · Performance evaluation · Reliability
* Morteza Bagherpour [email protected] Sepehr Hendiani [email protected] 1
Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran
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S. Hendiani, M. Bagherpour
1 Introduction The context of sustainability, which is widely known in the past decades, refers to a situation in which three pillars, including environmental, economic and social, are simultaneously optimized by their influential factors. In other words, the word sustainable will be defined as the act of improving quality of life for today and future’s generations by enhancing the performance of social, environmental and economic aspects at the same time (Ortiz et al. 2009). According to government’s rigid regulations and alternatively beneficial visions, firms cannot hesitate the inclusion of sustainability practices (Govindan et al. 2016) and they are moving toward implementing sustainability practices in their business models as soon as possible. In light of the inclusion of sustainability, some measurement techniques charact
