Neutrosophic TOPSIS Method for Sustainable Supplier Selection in a Discount Market Chain

Introduction

Sustainability is one of the most vital elements that is integrated into the corporate strategy of many organizations. Developing models to guide decisions in achieving sustainability goals is one of the main challenges, as described in the Brundtland Commission report, which emphasizes the relationships between society, environment, and economic development. In this case, organizations will be increasingly dependent on the performance of their suppliers. Therefore, companies will not only have to monitor and evaluate the sustainability performance of their operations, but also disseminate this assessment to their suppliers and other stakeholders. Institutions that can protect their resources and realize their core competencies without harming the environment will be able to continue their strong sustainable activities against their competitors in the future.

In sustainable supply chain management, one of the most important strategic decisions of a firm regarding sustainability performance is the selection of sustainable suppliers and their performance evaluation (Chen et al., 2006; Chai et al., 2013; Luthra et al., 2017; Giannakis et al., 2020). Since sustainability has become a strategically central goal for many businesses, sustainable supplier selection can also be considered as a multi-criteria decision-making (MCDM) problem for them within the framework of strategic decision-making. Multi-criteria decision-making (MCDM) approaches such as AHP, ANP, SAW, VIKOR, TOPSIS, and many others can be easily applied to the sustainable supplier selection problem which contains many quantitative and/or qualitative criteria generally conflicting. In the MCDM methods, decision makers evaluate both criteria and alternatives according to their preferences/judgments. However, evaluations of decision makers cannot express by crisp (exact) numbers in real-life applications. In such cases, fuzzy sets have been adapted to MCDM methods in order to overcome this deficiency.

Fuzzy set (FS) theory is first proposed by Zadeh (1965) to deal with fuzzy information. In the FS, only one membership exists and it cannot express non-membership. Based on the FS, the intuitionistic fuzzy set (IFS) by adding a non-membership is introduced by Atanassov (1986). The FS and IFS can only handle incomplete information but not indeterminate information and inconsistent information. By adding an independent indeterminacy-membership based on the IFS, neutrosophic logic and neutrosophic sets (NSs) are first proposed by Smarandache (1998, 1999). The NS is a generalization of the IFS, and it is very helpful for decision makers to express their opinions more accurately in detail. A neutrosophic set is characterized by three independent degrees, i.e. truth-membership degree (T), indeterminacy-membership degree (I), and falsity-membership degree (F) is more capable to catch up on incomplete or unobtainable information. An important feature of NS is that every element of the universe has not only a certain degree of truth, but also a falsity degree and indeterminacy degree. Afterwards, Rivieccio (2008) pointed out that a NS is a set where each element of the universe has a degree of truth, indeterminacy and falsity and it lies within ]0^‑,1⁺[, the non-standard unit interval. Wang et al. (2005) presented interval neutrosophic sets (INSs) in which the truth-membership, indeterminacy-membership, and falsity membership are considered as interval numbers and demonstrated various properties of INSs.