Cognitively Inspired Group Decision-Making with Linguistic q-Rung Orthopair Fuzzy Preference Relations

In actual decision-making problems, it is very difficult to appropriately depict the cognitive information of the relevant experts because cognition is usually diverse and contains uncertainties and fuzziness. The recently introduced linguistic q-rung orthopair fuzzy set (Lq-ROFS), which determines the linguistic preferred degree and linguistic nonpreferred degree within a wider space, has been shown to be effective in representing cognitive information. However, the corresponding preference relation has yet to be studied. Pairwise comparison is an effective way for decision-makers to express their preferences, especially when cognition is complex and indeterminate. Therefore, this paper employs linguistic q-rung orthopair fuzzy preference relations (Lq-ROFPRs) to express the cognitive information of experts. The additive consistency of Lq-ROFPR is introduced to rank the objects, and a consistency-based model is built to obtain the normalized linguistic q-rung orthopair fuzzy priority weight vector (Lq-ROFPWV). Then, several models are constructed to estimate missing values and improve the additive consistency level. For the group decision-making (GDM) problem, a model is first built with which to gain the weights of decision-makers. When group consensus is not achieved, a consensus-reaching model is designed as a means of increasing the consensus level. This study designs a decision support model to address GDM problem with incomplete Lq-ROFPRs and presents a step-by-step algorithm. The proposed method is utilized to assess four Chinese shopping platforms, and the comprehensive ranking result is reasonable and reliable. This is the first time to investigate GDM with Lq-ROFPRs based on consistency and consensus analysis, the newly studied Lq-ROFPRs not only extend the applications for linguistic preference relations but also endow experts with more flexibility in denoting their cognitive preferences. Compared to the latest published work in this domain, the novel approach conducts a reasonable decision-making process and has some advantages.