## 3 Material and Methods
### HMP-Coffee Model
#### 3.2.2 Hierarchical-Multicriteria Phase
The utility functions \(f\) define decision-making rules by combining scale values of basic attributes \(\text{X}_{1},\text{X}_{2},\ldots,\text{X}_{n}\) to obtain the qualitative value of the aggregate attributes (See Equation (2)). The weights \(\text{w}_{1}\), \(\text{w}_{2}\),..., \(\text{w}_{n}\) (i.e., from the weight definition step allow defining the value of the utility functions f by setting the corresponding attribute's contribution to the final result f (See Equation (3)). \[\text{f}:\text{X}_{1}=\text{value}_{1}\text{ and }\text{X}_{2}=\text{value}_{2} \text{ and }\ldots\text{and }\text{X}_{n}=\text{Value}_{n}\text{ then }\text{Y}=\text{Value}_{n} \tag{2}\] \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{4}{c}{**Weight-Based La Sultana Farm’s Operation**} \\ \cline{2-5}
**Attribute** & **Weight 1** & **Weight 2** & **Weight 3** & **Weight 4** & **Weight 5** \\ \hline
**vo: Crop’s final profitability level** & & & & =100\% \\
**gv1: Production Costs** & & & & 40\% \\ t19: Labor of the crop & & & & 42.60\% \\ t23: Investment in crop care activities & & & 56\% & \\ t18: Execution time in crop activities & & 70\% & & \\ t1: Time spent on fertilization & 25\% & & & \\ t2: Time spent on renovation & 56\% & & & \\ t3: Time spent on weed/pest and diseases control & 18\% & & & \\ t4: Price of workforce & & 30\% & & \\ t20: Investment on Supplies & & & 44\% & \\ t24: Investment in fertilization activities & & 79.83\% & & \\ t5: Chemical fertilizers & 21\% & & & \\ t6: Organic fertilizers & 79\% & & & \\ t7: Weeds supplies & & 13\% & & \\ t8: Renovation supplies & & 7.13\% & & \\ t22: Management expenses & & & 15.80\% & \\ t9: Maintenance & & & 71\% & \\ t10: Transportation expenses & & & 29\% & \\ t22: Investment in harvest time & & & 32.84\% & \\ t11: Payment for coffee harvesting & & & 99\% & \\ t12: Implements for coffee pickers & & 1\% & & \\ t13: Benefice coffee process & & & 5.03\% & \\ t14: Thresh coffee process & & & 3.05\% & \\
**gv2: Production Volume** & & & & **40\%** \\ t17: Coffee volume production & & & **20\%** \\
**gv3: International Market** & & & **20\%** \\ t15: USD price & & & 50\% & \\ t16: The coffee price in the New York Stock Exchange & & 50\% & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Weights defined for the set of HPM-Coffee attributes. The Attribute column contains the basic attributes, aggregate attributes, and output variable. The Weight column includes five weights levels for attributes of the HMP-coffee model. \[\text{f}(\text{X}_{1},\text{X}_{2},\dots,\text{ X}_{n})=(\text{w}_{1}\text{X}_{1})\text{ and }(\text{w}_{2}\text{X}_{2})\text{ and }(\text{w}_{1}\text{X}_{n}) \tag{3}\]  
DEXI represents utility functions in an attribute table where each row indicates a function f for one combination of the scale values of basic attributes [36]. In the generation of rules for the HMP-Coffee model, we obtained 10 attribute tables and 93 IF-THEN rules. As an example, for the \"labor of the crop\" rule, the basic attribute X1 = \"Execution time in crop activities\" must be filled in the corresponding attribute table as **High**, **Average**, or **Low** and **X2 = \"Price of workforce\" as **Expensive**, **Average**, or **Cheap**. In turn, the aggregate attribute Y = \"labor of the crop\" must be recorded as **High**, **Normal**, or **Low**. Once the decision-maker fills up all attributes, the model can estimate the level of profitability. All tables developed for HPM-Coffee are in Supplementary Materials available our GitHub repository [41].