Most linguistic-based approaches to multi-attribute group decision making (MAGDM) use symmetric, uniformly distributed sets of additive linguistic terms to express the opinions of decision makers. However, in reality, there are also some problems that require the use of asymmetric, uneven, i.e., non-equilibrium, multiplicative linguistic term sets to express the evaluation. The purpose of this paper is to propose a new approach to MAGDM under multiplicative linguistic information. The aggregation of linguistic data is an important component in MAGDM. To solve this problem, we define a chi-square for measuring the difference between multiplicative linguistic term sets. Furthermore, the linguistic generalized weighted logarithm multiple averaging (LGWLMA) operator and linguistic generalized ordered weighted logarithm multiple averaging (LGOWLMA) operator are proposed based on chi-square deviation. On the basis of the proposed two operators, we develop a novel approach to GDM with multiplicative linguistic term sets. Finally, the evaluation of transport logistics enterprises is developed to illustrate the validity and practicality of the proposed approach.

As the increasingly serious water pollution problem affects the sustainable development of the ecological environment, the research of water pollution treatment engineering cannot be delayed. Among them, the performance evaluation of water pollution treatment engineering is a major focus. After reading the existing studies, it is found that most of the existing performance evaluation indicators of water pollution treatment engineering have qualitative indicators and there is an unbalanced preference representation. Intuitionistic multiplicative linguistic sets can be a good representation of the qualitative preference and non-preference of decision-makers in the context of decision-making containing unbalanced phenomena. Therefore, to better solve the problem of water pollution treatment engineering, this paper introduces intuitionistic multiplicative linguistic sets to the problem of water pollution treatment engineering and proposes an effective theory for it. First, considering the multiplicative nature of the intuitionistic multiplicative linguistic set, a new score function and accuracy function are defined, and on this basis, the priority rules of intuitionistic multiplicative linguistic set are given to prepare for the subsequent water pollution treatment engineering performance ranking. And the distance measure of intuitionistic multiplicative linguistic set is introduced and a CRITIC attribute weight determination model under intuitionistic multiplicative linguistic set is obtained on this basis. Secondly, the Choquet integral operator is applied to better represent the correlation between elements. However, the nature of membership degree and non-membership degree shows that it is not reasonable to aggregate the information of intuitionistic multiplicative linguistic sets with a single increasing and decreasing transformation. Therefore, in this paper, we propose the IMLS bi-direction exponent Choquet integral operator, which is inspired by the bi-direction Choquet integral. Lastly, we improve the original preference function of the classical PROMETHEE II method to obtain the bi-directional PROMETHEE II method in intuitionistic multiplicative linguistic information. Finally, a numerical case is also provided to illustrate the scientific and rational application of the bi-directional PROMETHEE II method in intuitionistic multiplicative linguistic information for the performance evaluation of water pollution treatment engineering.

PurposeThe 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.Design/methodology/approachSince 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.FindingsThe validity and potential application of MAGMD method with linguistic q-rung orthopair fuzzy information based on BDCI are demonstrated in a numerical examples study.Originality/valueAccording 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.

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