# Modelling and Analysis of Neuro Fuzzy Employee Ranking System in the Public Sector +
## 3 Methodology
### Defining the Tasks in Public Organisations  
Although there is no specific list of assignments that are deployed in the public sector, nevertheless, each department processes tasks related to its field. For the purposes of the current research, the following primary tasks in the areas of interest were identified. These are shown in Table 1. \begin{table}
\begin{tabular}{l l} \hline \hline
**Financial Request** & **Technical Opinion** \\ \hline Suggestion of new technical document & Draft tender design \\ Committee minutes & Design of a national tender \\ Primary expense claim & Design of an international tender \\ Contract deployment & Implementation of a proposal for inclusion in the NSRF \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Public body tasks. As can be clearly identified from the list above, the empirical observation identified tasks that produce value. Time-limited procedures such as the signing of documents by a unit manager do not fit in the structure above since, no matter the profile of each user, in many cases, there is no need for special skills in order to accomplish such an action, which could lead to misleading results. Therefore, in our case, designing a non-electronic draft tender led to a time-factor \(TF_{p/Tk}\), while the electronic national tender to \(TF_{p/Tk+1}\) for each profile \(P_{j}\). \(TF_{p/T1}\) indicates the task with the minimum time duration, which is the completion of a financial request. The following table indicates the time (in minutes) for a non-electronic (\(T_{k}\)) and electronic tender (\(T_{k+1}\)), respectively, based on 15 different samples of profiles. It must be noted that, for our case above, a tender cannot be deployed by non-related profiles. \(P\) = Set of all profiles in the public sector. \(A\) = Set of all areas of interest (e.g., procurements, finance, informatics, logistics, tourism) in the public sector. Therefore, \(A_{procurement}\subseteq A\), and the corresponding profiles specialised for procurement jobs follow the same pattern: \(P_{procurement}\subseteq P\). As seen in Table 2, the mean time for \(TF_{p/Tk}\) is 180 min and for \(TF_{p/Tk+1}\) is 816 min, thus resulting in the ratio:  
\[\frac{TF_{p/Tk}}{TF_{p/Tk+1}}=4.52 \tag{7}\] \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c} \hline \hline
**Sample No** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** & **14** & **15** \\ \hline \(TF_{p/Tk}\) (min) & 149 & 106 & 81 & 319 & 209 & 157 & 208 & 171 & 129 & 138 & 180 & 338 & 197 & 208 & 115 \\ \(TF_{p/Tk+1}\) (min) & 1049 & 1185 & 1090 & 739 & 900 & 946 & 1047 & 396 & 909 & 571 & 771 & 734 & 460 & 823 & 623 \\ \(TF_{p/T1}\) (min) & 53 & 74 & 47 & 25 & 21 & 29 & 31 & 44 & 66 & 46 & 54 & 86 & 43 & 63 & 42 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Time-factor table. Figure 3: Measuring time. The standard deviation of \(TF_{P/Tk}\) is 69.4 compared to 226 for \(TF_{P/Tk+1}\), respectively. For the simplest task, which is a financial request, the mean time for \(TF_{P/T1}\) is 48 min with a standard deviation of 17.6 min. In order to establish a correlation among the list of tasks, a task weight \(TW_{x}\) is assigned to each and every \"job\" undertaken by the employees. Following the general rule of [1], for every task \(TID_{i}\) and \(TID_{j}\), there is always a dependency between them, which follows the rule:  
\[TWi=f(TWj)i,j>0 \tag{8}\]  
\(TW_{1}\) is the minimum task weight upon which the tasks will be related. Therefore, \(TW_{1}\) and \(TW_{i}\) also follow the same relation:  
\[TWi=f(TW1)i>0 \tag{9}\]  
As discussed in Section 3.4, statistical information is extracted through the electronic protocol of each public body. The average time-factor for all profiles \(P_{j}\), per \(TID_{i}\), was calculated and recorded through the system. Even at this stage, the expert's intervention could provide an inaccurate correlation among the \(TID_{s}\).