\(\chi\)-linguistic sets and its application for the linguistic multi-attribute group decision making

The information in the real world often contains many properties such as fuzziness, randomness, and approximation. Although existing linguistic collections attempt to solve these problems, with the emergence of more and more constraints and challenges, this information cannot fully express the problem, leading to an increasing demand for methods that can contain multiple uncertain information. In this paper, we comprehensively consider the various characteristics of information including membership degree, credibility and approximation based on rough sets, and propose the concept of \(\chi\) $\chi$ -linguistic sets ( \(\chi\) $\chi$ LSs), which depend on original data rather than prior knowledge and effectively solve the problem of incomplete information representation. At the same time, the corresponding theories such as the comparison method and operational rules have also been proposed. Subsequently, we construct a new \(\chi\) $\chi$ -linguistic VIKOR ( \(\chi\) $\chi$ LVIKOR) method for multi-attribute group decision making (MAGDM) problem with \(\chi\) $\chi$ LSs, and apply it to the risk assessment of COVID-19. Through comparative analysis, we discuss the effectiveness and superiority of \(\chi\) $\chi$ LSs.