Multi-attribute group decision-making method with linguistic q-rung orthopair fuzzy information based on bi-direction Choquet integral

The purpose of this paper is to develop the linguistic q-rung orthopair fuzzy set (LqROFS) information VIKOR method based on the bi-direction Choquet integral (BDCI), taking into account the correlation between information. The method can enrich the existing studies related to LqROFS information and better solve the problem of MAGDM problem.

Since applying Choquet integral (CI) depict information interaction is a common operation in MAGDM. However, the traditional CI has some limitations. The unidirectional alignment may affect the MAGDM results. Therefore, a LqROFS-VIKOR method based on BDCI is proposed, where BDCI is used to aggregate the decision matrix. Furthermore, it is not reasonable to apply exact numbers to express the similarity between two qualitative data. Then a new method of defining similarity using linguistics is proposed. The similarity is used to calculate attribute weights.

The validity and potential application of MAGMD method with linguistic q-rung orthopair fuzzy information based on BDCI are demonstrated in a numerical examples study.

According to the study of available literature, the current research on LqROFS is incomplete. The existing studies of both similarity and aggregate operators have certain shortcomings. The definition of similarity proposed in this paper is more in line with reality. And compared with the existing methods, the BDCI-based aggregate operator can describe the interaction between information more reasonably. Based on this VIKOR method based on BDCI under the LqROFS environment can better select the alternative.