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.

There are many practical decision-making problems in people’s lives, but the information given by decision makers (DMs) is often unclear and how to describe this information is of critical importance. Therefore, we introduce interval neutrosophic linguistic numbers (INLNs) to represent the less clear and uncertain information and give their operational rules and comparison methods. In addition, since the Maclaurin symmetric mean (MSM) operator has the special characteristic of capturing the interrelationships among multi-input arguments, we further propose an MSM operator for INLNs (INLMSM). Furthermore, considering the weights of attributes are the important parameters and they can influence the decision results, we also propose a weighted INLMSM (WINLMSM) operator. Based on the WINLMSM operator, we develop a multiple attribute decision making (MADM) method with INLNs and some examples are used to show the procedure and effectiveness of the proposed method. Compared with the existing methods, the proposed method is more convenient to express the complex and unclear information. At the same time, it is more scientific and flexible in solving the MADM problems by considering the interrelationships among multi-attributes.