An integrated method for multi-attribute group decision-making based on the linguistic Z-number and MSM operators

This article extends the ordered weighted average operator (OWA) in the linguistic Z-number (LZN) environment, increasing attention to the distribution of data itself, and this idea can also be combined with other operators. Specifically, for the weight of data, this paper gives consideration to both the preference of attributes and the distribution of data itself, gives the interval distribution induced OWA operator (IDIOWA), and combines the weight of attributes to obtain the LZN interval distribution induced hybrid weighted average operator (LZIDIHWA) in LZN environment. Then, it introduces some good properties of this operator. At the same time, the LZN interval distribution induced weighted Maclaurin symmetric means operator (LZIDIWMSM) is obtained by combining LZN interval distribution induced OWA operator (LZIDIOWA) with the LZN weighted Maclaurin symmetric means operator (LZWMSM), which makes up for the defect that LZWMSM cannot be used for data integration alone. Finally, the two operators are used for multi-attribute group decision-making (MAGDM), and their effectiveness is verified by comparative analysis.