## 6 Case Study  
The proposed decision-making model will be applied to a practical problem of Forex investment. **Example 5**. : _The Flagship Investment Company (FIC) is known for investment plans in different commodities in Forex. Investors hire FIC for profitable plans for investment. An investor is interested in investing in four commodities--oil, gold, wheat, and copee, denoted as \(x_{1}\), \(x_{2}\), \(x_{3}\) and \(x_{4}\), respectively. This investor approached the FIC to indicate which commodity is most profitable to invest in. The FIC summons a committee of four economic experts \(e_{1}\), \(e_{2}\), \(e_{3}\), and \(e_{4}\). Each expert will provide his preferences in terms of the HPMPR depending upon many factors, such as previous market rates, market trends, possible future decisions of different regulatory bodies, economic stability, and the global peace situation. The complex nature of the Forex requires tools that will model the vagueness and produce realistic results. The HPMPR will allow an economic experts to express their hesitancy and provide the probabilities of different preference degrees, which are bound to be different because of the factors discussed above. Based on the experience, the economic knowledge weight vector of experts is \(\omega=(0.1,0.4,0.2,0.3)^{T}\). The economic expert \(e_{k}\) provides his HPMPR \(H_{k}\)\((k=1,2,3,4)\) as follows._  
\[H_{1}=\left( \begin{array}{cccc}\{[11]&\{0.2|0.2979,8|0.7021\}&\{0.15|0.6622,7.5|0.3378\}&\{0.25|0.0636,5|0.9364\}\\ \{5|0.2979,0.125|0.7021\}&\{1|1\}&\{0.31|0.2236,5.09|0.7764\}&\{0.4|0.4313,8.88 |0.5687\}\\ \{6.6667|0.6622,0.1333|0.3378\}&\{3.225|0.2236,0.1965|0.7764\}&\{1|1\}&\{0. 22|0.7145,3.68|0.2855\}\\ \{4|0.0636,0.2|0.9364\}&\{2.5|0.4313,0.1126|0.5687\}&\{4.545|0.7145,0.2717|0.28 855\}&\{1|1\}\end{array} \right)\]  
\[H_{2}=\left(\begin{array}{cccc}\{[11]&\{0.15|0.5048,0.55|0.3816,418.018\}& \{0  
**Step 3:** The consistency tolerance value \(CI_{r}\) is decided to be 1.01, so all the HPMPRs \(H_{k}^{(0)}\)\((k=1,2,3,4)\) need to be adjusted. Therefore, we go to step 4 and then return to step 2.  
Steps 2-4 are repeated to obtain the following acceptably consistent HPMPRs:  
\[H_{k}^{(0)}=\left(\begin{array}{cccc}\{10.2200,10.2203,10.5414\}&\{0.3020.265,0.30206,27.2890,547\}&\{0.190227,37.5480,5840,584  
**Step 9:** By Equations (42) and (43), scores and deviations of \(h_{i,g}\)\((i=1,2,3,4)\) are calculated as follows:  
\[s\left(h_{1,g}\right) = 0.9742,s\left(h_{2,g}\right)=1.0013,s\left(h_{3,g}\right)=0.9646\text { and }s\left(h_{4,g}\right)=1.0563\] \[d\left(h_{1,g}\right) = 0.6118,d\left(h_{2,g}\right)=0.1299,d\left(h_{3,g}\right)=0.2142 \text{ and }d\left(h_{4,g}\right)=0.4881.\]  
**Step 10:** The comparison of scores and deviations computed in Step 9 provides us with the following final preference ranking:  
\[x_{4}>x_{2}>x_{1}>x_{3}.\]  
**Step 11:** End. **Remark 2**. : _The proposed decision support model is divided into three main parts, Steps 1-4 deals with the consistency issue of data provided by the economic experts, Steps 5-7 generate a reasonable consensus among them, and Steps 8-10 provide the final standings of all the commodities. Figures 8-11 present the comparison of area graphs of score values for normalized, acceptably consistent and consistent HPMPRs made from \(H_{1}\), \(H_{2}\), \(H_{3}\), and \(H_{4}\), respectively, by the end of Step 4._  
_The results of the case study point out copper as the best commodity for investment, whereas wheat is the least favorable. The Forex market is not fully predictable because of its complexities, and there are numerous factors that can alter the profit margin of any commodity. The HPMPR has a better chance of modeling and handling its vagueness with the help of probability theory._  
**Remark 3**. : _The inspection of Table 4 reveals why it is important to consider the probabilities of different preference degrees. Often, decision-makers are taking decisions related to future scenarios like our case study.