# Decision-Making Approach Based on Neutrosophic Rough Information
## 3 Applications to Decision-Making
### Context of Recruitment  
Choosing the right candidate for the position available is not something that should be left to chance or guesswork. **How to choose the right candidate? **  
In any recruitment process the ability of the candidate is weighed against the suitability of the candidate. Pakistan Telecommunication Company Limited (PTCL) wants to recruit a person for the post of administrator. To keep the procedure simple, the company wants to appoint their employee on the basis of education (Edu) and experience (Exp). Let \(X^{*}=\{(C1,Edu),(C1,Exp),(C2,Edu),(C2,Exp),(C3,Edu),(C3,Exp)\}\) be the set of candidates who applied for the post and their corresponding attributes. Let \(R\) be a neutrosophic tolerance on \(X^{*}\) given as follows: \begin{tabular}{c|c c c c c c} \hline \hline \(R\) & (C1,Edu) & (C1,Exp) & (C2,Edu) & (C2,Exp) & (C3,Edu) & (C3,Exp) \\ \hline (C1,Edu) & (1,1,0) & (0.3,0.6,0.1) & (0.6,0.7,0.2) & (0.6,0.5,0.8) & (0.3,0.2,0.1) & (0.9,0.1,0.1) \\ (C1,Exp) & (0.3,0.6,0.1) & (1,1,0) & (0.9,0.9,0.3) & (0.8,0.7,0.6) & (0.4,0.5,0.9) & (0.3,0.1,0.1) \\ (C2,Edu) & (0.6,0.7,0.2) & (0.9,0.9,0.3) & (1,1,0) & (0.6,0.5,0.1) & (0.3,0.2,0.1) & (0.4,0.8,0.7) \\ (C2,Exp) & (0.6,0.5,0.8) & (0.8,0.7,0.6) & (0.6,0.5,0.1) & (1,1,0) & (0.1,0.1,0.2) & (0.5,0.6,0.7) \\ (C3,Edu) & (0.3,0.2,0.1) & (0.4,0.5,0.9) & (0.3,0.2,0.1) & (0.1,0.1,0.2) & (1,1,0) & (0.2,0.1,0.2) \\ (C3,Exp) & (0.9,0.1,0.1) & (0.3,0.1,0.1) & (0.4,0.8,0.7) & (0.5,0.6,0.7) & (0.2,0.1,0.2) & (1,1,0) \\ \hline \hline \end{tabular}   
Let \(X=\{((C1,Edu),0.9,0.1,0.5),((C1,Exp),0.2,0.6,0.5),((C2,Edu),0.7,0.2,0.3),((C2, Exp),0.1,\)\(0.3,0.9),((C3,Edu),0.4,0.6,0.8),((C3,Exp),0.8,0.1,0.2)\}\) be a neutrosophic set define on \(X^{*}\). Then the lower and upper approximations of \(X\) are given as:  
\[\underline{R}X=\{((C1,Edu),0.2,0.1,0.6),((C1,Exp),0.2,0.2,0.8),((C2, Edu),0.1,0.2,0.6),\] \[((C2,Exp),0.1,0.3,0.9),((C3,Edu),0.2,0.6,0.8),((C3,Exp),0.2,0.1,0.5 )\},\] \[\overline{R}X=\{((C1,Edu),0.9,0.6,0.2),((C1,Exp),0.7,0.6,0.2),((C2, Edu),0.7,0.6,0.3),\] \[((C2,Exp),0.6,0.6,0.3),((C3,Edu),0.4,0.6,0.2),((C3,Exp,0.9,0.3,0.2)\}.\]  
Let \(Y^{*}=\{(C1,Edu)(C1,Exp),(C1,Exp)(C2,Edu),(C1,Edu)(C3,Exp),(C3,Exp)(C1,Exp),\)\((C1,Exp)(C2,Exp),(C2,Edu),(C3,Exp)(C3,Edu),(C2,Exp),\)\((C3,Exp)(C2,Exp)\}\subseteq X^{*}\times X^{*}\) and \(S\) be a neutrosophic tolerance relation on \(Y^{*}\) given as follows: \begin{tabular}{c|c c c c c} \hline \(S\) & (C2,Exp)(C2,Edu) & (C3,Exp)(C2,Exp) & (C3,Exp)(C3,Edu) & (C3,Edu)(C2,Exp) \\ \hline (C1,Edu)(C1,Exp) & (0.6,0.5,0.8) & (0.8,0.1,0.6) & (0.4,0.1,0.9) & (0.3,0.2,0.6) \\ (C1,Exp)(C2,Edu) & (0.8,0.7,0.6) & (0.3,0.1,0.1) & (0.3,0.1,0.1) & (0.4,0.5,0.9) \\ (C1,Edu)(C3,Exp) & (0.4,0.5,0.8) & (0.5,0.1,0.7) & (0.2,0.1,0.2) & (0.3,0.2,0.7) \\ (C3,Exp)(C1,Exp) & (0.5,0.6,0.7) & (0.8,0.7,0.6) & (0.4,0.5,0.9) & (0.2,0.1,0.6) \\ (C1,Exp)(C2,Exp) & (0.6,0.5,0.6) & (0.3,0.1,0.1) & (0.1,0.1,0.2) & (0.4,0.5,0.9) \\ (C2,Exp)(C2,Edu) & (1,1,0) & (0.5,0.5,0.7) & (0.3,0.2,0.7) & (0.1,0.1,0.2) \\ (C3,Exp)(C2,Exp) & (0.5,0.5,0.7) & (1,1,0) & (0.1,0.1,0.2) & (0.2,0.1,0.2) \\ (C3,Exp)(C3,Edu) & (0.3,0.2,0.7) & (0.1,0.1,0.2) & (1,1,0) & (0.1,0.1,0.2) \\ (C3,Edu)(C2,Exp) & (0.1,0.1,0.2) & (0.2,0.1,0.2) & (0.1,0.1,0.2) & (1,1,0) \\ \end{tabular}   
Let \(Y=\{((C1,Edu)(C1,Exp),0.2,0.1,0.1),((C1,Exp)(C2,Edu),0.1,0.1,0.3),((C1, Edu)(C3,Exp),\)\(0.2,0.1,0.2),((C3,Exp)(C1,Exp),0.2,0.1,0.2),((C3,Exp)(C1,Exp),0.2,0.1,0.2),((C1, Exp)(C2,Exp),0.1,0.2,0.3),((C2,Exp)(C2,Edu),\)\((C3,Exp)(C2,Edu),\)\((C3,Edu),0.2,0.1,0.3)\}\) be neutrosophic rough set on \(Y^{*}\).