The aim of this paper is to present a multiple-attribute group decision-making (MAGDM) framework based on a new single-valued neutrosophic linguistic (SVNL) distance measure. By unifying the idea of the weighted average and ordered weighted averaging into a single-valued neutrosophic linguistic distance, we first developed a new SVNL weighted distance measure, namely a SVNL combined and weighted distance (SVNLCWD) measure. The focal characteristics of the devised SVNLCWD are its ability to combine both the decision-makers’ attitudes toward the importance, as well as the weights, of the arguments. Various desirable properties and families of the developed SVNLCWD were contemplated. Moreover, a MAGDM approach based on the SVNLCWD was formulated. Lastly, a real numerical example concerning a low-carbon supplier selection problem was used to describe the superiority and feasibility of the developed approach.

In this paper, by unifying the dual roles of order-inducing variables, a PF weighted induced generalized weighted averaging (PFWIGOWA) operator is presented to facilitate the PF information. The key feature of the proposed operator is that it can improve the existing aggregation operators by the dual roles of its order-inducing variables. In addition, the PFWIGOWA's desirable properties and different families are also discussed. Furthermore, an approach based on the developed operator is presented for solving multi-attribute group decision making (MAGDM) problems with PF information. Finally, the usefulness of the proposed method is illustrated in a research and development (R&D) projects selection problem.

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