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The aim of this research is to establish a new type of aggregation operator based on Hamacher operational law of spherical uncertain linguistic numbers (SULNs).

First, the authors define spherical uncertain linguistic sets and develop some operational laws of SULNs. Furthermore, the authors extended these operational laws to the aggregation operator and developed spherical uncertain linguistic Hamacher averaging and geometric aggregation operators.

The authors were limited in achieving a consistent opinion on the fusion in group decision-making problem with the SULN information.

In order to give an application of the introduced operators, the authors first constrict a system of multi-attribute decision-making algorithm.

Single-valued neutrosophic sets (SVNSs) are efficient models to address the complexity issues potentially with three components, namely indeterminacy, truthness and falsity. Taking advantage of SVNSs, this paper introduces some new aggregation operators (AOs) for information fusion of single-valued neutrosophic numbers (SVNNs) to meet multi-criteria group decision-making (MCGDM) challenges.

Einstein operators are well-known AOs for smooth approximation, and prioritized operators are suitable to take advantage of prioritized relationships among multiple criteria. Motivated by the features of these operators, new hybrid aggregation operators are proposed named as “single-valued neutrosophic Einstein prioritized weighted average (SVNEPWA) operator” and “single-valued neutrosophic Einstein prioritized weighted geometric (SVNEPWG) operators.” These hybrid aggregation operators are more efficient and reliable for information aggregation.

A robust approach for MCGDM problems is developed to take advantage of newly developed hybrid operators. The effectiveness of the proposed MCGDM method is demonstrated by numerical examples. Moreover, a comparative analysis and authenticity analysis of the suggested MCGDM approach with existing approaches are offered to examine the practicality, validity and superiority of the proposed operators.

The study reveals that by choosing a suitable AO as per the choice of the expert, it will provide a wide range of compromise solutions for the decision-maker.

Reverse logistics (RL) is a type of supply chain management that moves goods from the end customer to the original manufacturer for reuse, remanufacturing and disposal purposes. Owing to growing environmental legislations and the development of new technologies in marketing, RL has attracted more significance among experts and academicians. Outsourcing RL practices to third-party reverse logistics provider (3PRLP) has been identified as one of the most important management strategies due to complexity of RL operations and the lack of available resource. Current sustainability trends have made 3PRLP assessment and selection process more complex. In order to select the 3PRLP, the existence of several aspects of sustainability motivates the experts to establish a new multi-criteria decision analysis (MCDA) approach.

With the growing complexity and high uncertainty of decision environments, the preference values of 3PRLPs are not always expressed with real numbers. As the generalized version of fuzzy set, intuitionistic fuzzy set and Fermatean fuzzy set, the theory of q-rung orthopair fuzzy set (q-ROFS) is used to permit decision experts (DEs) to their assessments in a larger space and to better cope with uncertain information. Given that the combined compromise solution (CoCoSo) is an innovative MCDA approach with higher degree of stability and reliability than several existing methods.

To exhibit the potentiality and applicability of the presented framework, a case study of S3PRLPs assessment is taken from q-rung orthopair fuzzy perspective. The assessment process consists of three sustainability aspects namely economic, environment and social dimensions related with a total of 14 criteria. Further, sensitivity and comparative analyses are made to display the solidity and strength of the presented approach. The results of this study approve that the presented methodology is more stable and efficient in comparison with other methods.

Thus, the objective of the study is to develop a hybrid decision-making methodology by combining CoCoSo method and discrimination measure with q-ROFS for selecting an appropriate sustainable 3PRLP (S3PRLP) candidate under uncertain environment. In the proposed method, a novel procedure is proposed to obtain the weights of DEs within q-ROFS context. To calculate the criteria weights, a new formula is presented based on discrimination measure, which provides more realistic weights. In this respect, a new discrimination measure is proposed for q-ROFSs.

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.