**Multiple-Attribute Decision-Making Method Using Similarity Measures of Hesitant Linguistic Neutrosophic Numbers Regarding Least Common Multiple Cardinality**

#### **Wenhua Cui and Jun Ye \***

Department of Electrical Engineering and Automation, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, Zhejiang, China; wenhuacui@usx.edu.cn

**\*** Correspondence: yejun@usx.edu.cn; Tel.: +86-575-8832-7323

Received: 10 July 2018; Accepted: 7 August 2018; Published: 9 August 2018

**Abstract:** Linguistic neutrosophic numbers (LNNs) are a powerful tool for describing fuzzy information with three independent linguistic variables (LVs), which express the degrees of truth, uncertainty, and falsity, respectively. However, existing LNNs cannot depict the hesitancy of the decision-maker (DM). To solve this issue, this paper first defines a hesitant linguistic neutrosophic number (HLNN), which consists of a few LNNs regarding an evaluated object due to DMs' hesitancy to represent their hesitant and uncertain information in the decision-making process. Then, based on the least common multiple cardinality (LCMC), we present generalized distance and similarity measures of HLNNs, and then develop a similarity measure-based multiple-attribute decision-making (MADM) method to handle the MADM problem in the HLNN setting. Finally, the feasibility of the proposed approach is verified by an investment decision case.

**Keywords:** hesitant linguistic neutrosophic number (HLNN); decision-making; similarity measure; distance measure; least common multiple cardinality (LCMC)
