**Some Interval Neutrosophic Linguistic Maclaurin Symmetric Mean Operators and Their Application in Multiple Attribute Decision Making**

#### **Yushui Geng 1,\*, Xingang Wang 2, Xuemei Li 2, Kun Yu 2 and Peide Liu 3,\***


Received: 10 April 2018; Accepted: 17 April 2018; Published: 22 April 2018

**Abstract:** 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.

**Keywords:** multiple attribute decision making (MADM); neutrosophic number; Maclaurin symmetric mean; linguistic variables
