A New Neutrosophic Multigranulation Model for Multi-Attribute Group Decision Making

1. Introduction

With the advent of big data era, complex decision making situations are common in numerous realistic applications (Qudrat-Ullah et al., 2008). In general, there are two major challenges in addressing practical complex decision making situations, the one is the information depiction, and another one is the information fusion and analysis. For the sake of coping with the above two challenges, plenty of scholars and practitioners have started their researches from the perspective of fuzzy MAGDM. In specific, the fuzzy context is intended to precisely depict complex decision making scenarios, whereas MAGDM acts as a powerful tool for handling information fusion and analysis issues (Liu & You, 2018). In light of the above two challenges, we review some significant development trends as follows:

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  The review of the fuzzy context. Since Zadeh (Zadeh, 1965) initiated the notion of fuzzy sets, many generalized fuzzy sets along with their applications were successively explored over the past 50 years or more. Among the fuzzy set community, neutrosophic sets (NSs), initiated by Smarandache (Smarandache, 1998; Smarandache, 1999), play a vital role in both theoretical and application studies in the family of generalized fuzzy sets. In a NS, there exist three different components for describing the truth aspect, the indeterminacy aspect and the falsity aspect, which have enlarged the conceptual implication of classic fuzzy sets, thus NSs are conducive to combating the challenges of the impreciseness and uncertainty in various decision making information. Ever since the birth of neutrosophic theories and methods, single-valued neutrosophic sets (SVNSs) were later put forward to provide a formal mathematical expression for solving realistic complex problems via the notion of neutrosophy (Wang et al., 2005). Recently, many realistic complex problems have been efficiently addressed in the context of SVNSs, such as decision making (Abdel-Basset et al., 2019; Alias et al., 2018; Deli et al., 2015; Zhang et al., 2017), graph theories (Akram et al., 2018; Broumi & Smarandache, 2013; Broumi et al., 2019; Ishfaq et al., 2018; Sayed et al., 2018), etc.

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  The review of MAGDM. The core of MAGDM lies in involving an expert group to solve complex decision making problems from the aspect of multiple attributes, and viable information fusion and analysis rules need to be designed in corresponding problem solving processes. There are plenty of classic MAGDM methods, and it is widely recognized that granular computing-based ones act as powerful methods in terms of granularity features in complex decision making situations. In the community of granular computing, the rough set theory is a significant representative which does well in providing solvable approximations. In this chapter, due to the feature of group decision making, we aim to utilize multigranulation rough set (MGRS) models (Qian et al., 2010; Sun & Ma, 2015; Sun et al., 2017; Zhan et al., 2019; Zhang, Li, & Liang, 2020; Zhang et al., 2019) to explore a new solution path for MAGDM.