Linguistic Z-number preference relation for group decision making and its application in digital transformation assessment of SMEs

In the new phase of technological revolution and industrial transformation, the digital transformation (DT) of small and medium-sized enterprises (SMEs) has become a critical strategic issue. Assessing the DT of SMEs as a crucial link can be viewed as a group decision making (GDM) problem with uncertain linguistic information. Recently, the linguistic Z-number (LZN) has demonstrated benefits in the representation of uncertain linguistic information due to the characteristics of simultaneous representation of linguistic evaluation and corresponding credibility. However, rather of providing direct evaluation, decision makers (DMs) of the DT assessment prefer to pairwise compare alternatives. To this end, we put forward linguistic Z-number preference relations (LZPRs) as an assessment tool for expressing DMs' preferences and credibilities. Following that, novel operational rules of LZNs are proposed to correspond with LZPRs. After considering the difference between the importance of the two parts A and B in LZNs, we further propose the weighted Euclidean distance and the improved comparison method of LZNs. In addition, the additive consistency of the LZPR is discussed, as well as a consistency index for determining its consistency. The automatic improvement algorithm and the feedback improvement method are used to enhance the consistency of LZPRs that have unacceptable consistency. Furthermore, a GDM model of LZPRs is built using DMs' combined weights based on the credibility and the novel linguistic Z-number weighted averaging (NLZWA) operator. Finally, a case study and comparative analysis of SMEs' DT assessment demonstrate the effectiveness, flexibility and superiority of the proposed method.