In the intricate decision-making problems, the preference information of decision makers may be difficultly stated by numerical values due to the ambiguity of human thinking about the complex objective things in the real world, and sometimes, it may be easily expressed by LTs (linguistic terms). Thus, how to solve fuzzy MAGDM (multiple attribute group decision-making) problem in which the attributes are described by neutrosophic linguistic information and weights for the attributes and decision makers are fully unknown, has become an important research direction. To achieve this goal, this paper briefly reviews the basic concept of LTs, SVLNN (single-valued linguistic neutrosophic number), and the closeness degree, then we put forward the closeness degree between the LNNs (linguistic neutrosophic numbers) and the distance formula between LNNs, and they can be used to determine the weights of experts and attributes. Then, a MAGDM method based on the extended VIKOR (Visekriterijumska Optimizacija I Kom-promisno Resenje) method is established under the single-valued linguistic neutrosophic numbers (SVLNN) environment. Further, an illustrative example about selecting problems of fault handling point is presented to demonstrate the application of the developed approach, and the feasibility and effectiveness of the proposed method are proved by comparing this method with WAA (Weighted Arithmetic Averaging) and TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) method.
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