# Multiple Attribute Decision-Making Method Using Linguistic Cubic Hesitant Variables
## 5 Illustrative Example  
An illustrative example is presented in this section to indicate the application of the proposed MADM approach in a LCHV setting. A computer company wants to hire a software engineer. Though the human resources department preliminarily selects four potential candidates (alternatives)--\(Z_{1}\), \(Z_{2}\), \(Z_{3}\), and \(Z_{4}\)--from all the applicants, they need to be further assessed based on the requirements (attributes) of innovation capability (\(R_{1}\)), work experience (\(R_{2}\)), and self-confidence (\(R_{3}\)). Then, five experts (decision makers) are invited to choose the most suitable candidate among them in the interview. Here, the importance of the three attributes is indicated by the weight vector \(\mathbf{\omega}\) = (0.45, 0.35, 0.2). Thus, the five experts will assess each potential candidate \(Z_{1}\) (\(i\) = 1, 2, 3, 4) over the three attributes \(R_{1}\) (\(j\) = 1, 2, 3) using the hybrid information of uncertain and hesitant linguistic terms so as to express the assessment values of LCHVs from the predefined LTS \(Y\) = {\(y_{0}\) (extremely poor), \(y_{1}\) (very poor), \(y_{2}\) (poor), \(y_{3}\) (slightly poor), \(y_{4}\) (moderate), \(y_{5}\) (goodish), \(y_{6}\) (good), \(y_{7}\) (very good), and \(y_{8}\) (extremely good)} with \(q\) = 8. For example, in the assessment process of \(R_{1}\) for \(Z_{1}\), the interval linguistic value \([y_{4},y_{6}]\) is assigned by two of the five experts corresponding to the two uncertain ranges \([y_{4},y_{5}]\) and \([y_{4},y_{6}]\), and then the HLS \(\{y_{4},y_{6}\}\) is assigned by three of the five experts corresponding to the three linguistic evaluation values \(y_{4},y_{4}\), and \(y_{6}\), which can be expressed as the LCHN (\([y_{4},y_{6}]\), \([y_{4},y_{6}]\)). Using a similar evaluation method, all the LCHNs assessed by the five experts can be constructed as the following LCHN decision matrix:  
\[M=(z_{ij})_{4\times 3}= \begin{array}{l}Z_{1}\\ Z_{2}\\ Z_{3}\\ Z_{4}\end{array} \left[ \begin{array}{l}([y_{4},y_{6}],\{y_{5},y_{6}\})\\ ([y_{3},y_{5}],\{y_{4},y_{5},y_{6}\})\\ ([y_{5},y_{7}],\{y_{6},y_{7}\})\\ ([y_{5},y_{7}],\{y_{5},y_{6}\})\\ ([y_{6},y_{7}],\{y_{4},y_{5},y_{6}\})\\ ([y_{5},y_{7}],\{y_{5},y_{6}\})\\ ([y_{5},y_{7}],\{y_{5},y_{7}\})\\ ([y_{4},y_{6}],\{y_{6},y_{7}\})\\ \end{array} \right]\]  
Thus, the MADM approach presented, based on the WAA or WGA operator of the LCHVs, can be utilized for the MADM problem with LCHN information. For the application, the MADM approach relating to the WAA operator of LCHVs is used for the illustrative example and depicted using the following decision steps:  
**Step 1. ** The LCMNs of \((r_{i1},r_{i2},\ldots,r_{in})\) (\(i=1,2,\ldots,m\)) in \(M=(z_{ij})_{m\times n}\) can be obtained as \(c_{i}=6\) for \(i=1,2,3,4\). After that, the decision matrix \(M\) can be extended into the extension decision matrix below:  
\[M^{e}=(z_{ij}^{e})_{4\times 3}= \begin{array}{l}Z_{1}\\ Z_{2}\\ Z_{3}\\ Z_{4}\end{array} \left[ \begin{array}{l}(y_{4},y_{5}),\{y_{5},y_{5},y_{5},y_{6 },y_{6},y_{6}\})\\ (y_{5},y_{5}),\{y_{4},y_{5},y_{5},y_{6},y_{6}\})\\ (y_{5},y_{7}),\{y_{5},y_{7},y_{7},y_{7},y_{7}\})\\ (y_{5},y_{7}),\{y_{5},y_{5},y_{6},y_{6},y_{6}\})\\ (y_{5},y_{7}),\{y_{5},y_{5},y_{5},y_{6},y_{6}\})\\ (y_{5},y_{7}),\{y_{5},y_{5},y_{5},y_{6},y_{6},y_{6}\})\\ (y_{5},y_{7}),\{y_{5},y_{5},y_{5},y_{6},y_{6},y_{6}\})\\ (y_{5},y_{7}),\{y_{5},y_{5},y_{5},y_{5},y_{6},y_{6},y_{6}\})\\ (y_{5},y_{7}),\{y_{5},y_{5},y_{5},y_{5},y_{7},y_{7}\})\\ (y_{5},y_{7}),\{y_{5},y_{5},y_{5},y_{5},y_{7},y_{7},y_{7}\})\\ \end{array} \right]\]  
**Step 2. ** Based on Equation (13), the aggregated LCHN \(z_{1}\) for \(Z_{1}\) can be obtained as follows:  
\[z_{1}=f_{LCHV}(z_{11}^{e},z_{12}^{e},z_{13}^{e})=\sum_{j=1}^{3} \omega_{j}^{2}\] \[=\left(