## 2 Materials and Methods
### Fuzzy Logic Model (FLM)
#### 2.3.2 Outputs  
The fuzzy model produces three distinct outputs: SQ, PQ, and MC. To determine SQ, the model requires the calculation of PQ and MC, which are then fed back into the fuzzy system, as discussed in detail in the rules section. It is important to emphasize that SQ is not solely determined by either PQ or MC individually, but rather by the integration and combination of both factors.  
Physicochemical quality represents the physical and chemical characteristics of the soil that influence its suitability for plant growth. Parameters such as pH, temperature, humidity, and electric conductivity are taken into account [41]. By evaluating the input values and their corresponding linguistic variables, the fuzzy model assigns a degree of PQ to the soil. This assessment includes linguistic terms such as low, medium, and high, allowing for the classification of the soil's PQ based on the input parameters.  
On the other hand, MC focuses on the levels of essential macronutrients, namely nitrogen, phosphorus, and potassium, in the soil. These nutrients are crucial for plant growth and development [42]. The fuzzy model assesses the input values of these nutrients and assigns a degree of MC, utilizing linguistic terms such as low, medium, and high.  
The outputs of the FLM utilize triangular MFs for each linguistic term. This choice was made based on [43], which suggests that using triangular MFs is more appropriate for fuzzy numbers, which is the case for estimating each output.  
The details of these MFs, including their linguistic terms and parameters, can be found in Table 2. This comprehensive table enhances the reproducibility of the fuzzy model, allowing others to accurately replicate and understand the implementation of the MFs for each output.  
It is worth mentioning that the scale used for SQ and PQ ranges from 0 to 10. Both SQ and PQ employ a five-membership-function approach, including linguistic terms such as low, medium-low, medium, medium-high, and high. However, MC does not implement the medium linguistic term.  
The determination of the number of MFs for each output variable is based on the combinations of the related input variables. In order to assign equal importance to each input, a binary simplification approach is applied. For example, in the case of PQ, which depends on four input variables, the resulting combinations are represented using zeros and ones. Although there are sixteen possible combinations, they can be grouped based on the number of ones in each row and then ordered into five groups. These groups represent the different levels of PQ, ranging from none being good to all being good. Similarly, for MC, which depends on three input variables, the same principle is applied. The combinations are grouped into four required groups, representing the different levels of MC. SQ, unlike  
Figure 8: Visual representation of each linguistic term of (**a**) input pH MFs; (**b**) input temperature’s MFs.  
MC and PQ, follows a different approach to determining the number of MFs. While MC and PQ have four and five MFs, respectively, resulting in 20 possible combinations, the assignment of MFs for SQ is based on expert knowledge.  
The plotted MFs in Figure 9 demonstrate overlapping triangular shapes, enabling a smooth transition between linguistic terms. This design ensures a comprehensive assessment of SQ and MC, accounting for the gradual changes in input parameter values. The well-defined MFs play a crucial role in capturing the inherent uncertainty and providing accurate evaluations within the FIS [25; 31].