Application of Artificial Neural Networks to Predict Solonchaks Index Derived from Fuzzy Logic: A Case Study in North Algeria

Abstract

Soil salinization, particularly under irrigation in the arid regions of North Africa, represents a major constraint to sustainable agricultural development. This study investigates the Chott El Hodna region in Algeria, a Ramsar-classified wetland severely affected by salinization. Two representative soil profiles (P1 and P2) were initially characterized, revealing chemical properties dominated by calcium-chloride and calcium-sulfate types. Based on these findings, 26 additional profiles with moderate levels of gypsum, limestone, and soluble salts were analyzed. The limited number of profiles reflects the environmental homogeneity of the area, allowing the study site to be considered a pilot zone. Fuzzy logic was employed to classify soils, identify intergrade soils, and determine their degree of membership to Solonchaks within the Calcisol class, addressing the lack of precision in conventional classifications. Results indicate that 50% of soils are Solonchaks, 46.15% are Calcisols, and 3.85% are intergrades. Principal Component Analysis (PCA) revealed that soil solution chemistry is mainly governed by the dissolution of evaporite minerals (gypsum, halite, anhydrite) and the precipitation of carbonate phases (calcite, aragonite, dolomite). Statistical analyses using Artificial Neural Networks (ANN) and Multiple Linear Regression (MLR) demonstrated that ANN achieved superior predictive performance for the Solonchak index (Is), with R² = 0.70 and RMSE = 0.17, compared with R² = 0.41 for MLR. This study proposes a robust framework combining fuzzy logic and ANN to improve the classification of saline wetland soils, particularly by identifying intergrade soils, thus providing a more precise numerical classification than conventional approaches.

1. Introduction

Globally, soil salinization and secondary salinization due to intensive agriculture and irrigation inefficiencies are now significant obstacles to the sustainable development of agriculture. More than 100 countries in the world have saline and alkaline (sodic) soils. Saline-alkali land is estimated to cover 9.5 × 10⁹ hectares worldwide [1,2]. Arid regions are characterized by saline soils, which are formed and evolved by a variety of natural and agriculture induced processes [3]. In North Africa, a combination of a geological history favorable to salt accumulation, a hydrological system influenced by climatic recharge, and poorly managed irrigation makes soil salinity a persistent threat [4]. In Algeria, from east to west and from the coast to the desert, agricultural soils are increasingly threatened by the accumulation of soluble salts, making them vulnerable to salinization [5,6,7]. In arid regions, both natural and human induced conditions are responsible for high salt accumulation in surface and subsurface soils. The Boussaâda region, specifically the Hodna (or Hodna Basin in Algeria), is a prime example of a saline environment shaped by multiple salinization processes. In this regard, before any land rehabilitation projects can be started, the region’s soils must be thoroughly characterized to determine their salinity levels and the quality of the water that is available for irrigated agriculture [8].

Fuzzy (continuous) classification is particularly valuable for grouping different soil types into continuous classes with associated membership values [9]. However, according to the same author, the application of fuzzy logic remains complex and labor-intensive, as it requires a large number of inference rules, whose definition can be intricate. Additionally, defining membership functions, a crucial component of fuzzy logic, is often difficult to calibrate for certain soil parameters, such as texture [10] or the various diagnostic criteria of reference groups established by the Food and Agriculture Organization (FAO) [11].

To overcome these challenges, it would be beneficial to develop predictive models capable of estimating the Solonchak index (Is) derived from fuzzy logic, using the diagnostic criteria defined by the [11] for Solonchak classification. Such an approach would significantly reduce the time required for soil identification, thereby improving the efficiency of soil mapping and management.

The main objective of this study was to determine the salinity condition and salinization dynamics of the saline soils in the Hodna region, which is situated in Boussaâda Algeria (Wilaya of M’Sila). Determining the chemical makeup of soil solutions, mapping salt distribution profiles, and evaluating the soil solution were part of this process. This study has yielded 26 soil profiles that are high in soluble salts. The development of saline soils in the study area is hampered by their high limestone content. The different types of limestone accumulation represent a physical barrier to the development of crop root systems and also lead to a reduction in the plant available fraction of phosphorus in the soil [12]. The degree of the Solonchaks’ affiliation with the Calcisols was evaluated in order to address this primary concern of salinization of soils. This was accomplished by using fuzzy logic to analyze the 26 soil profiles found within the research area.

In this context, two types of saline soils (Solonchaks) with different salinization processes were examined. To date, fuzzy logic has never been applied to saline Solonchak soils in naturally occurring wetland areas in arid climates of North Africa. This approach makes it possible to assess the degree of membership of Solonchak soils relative to Calcisols and, as a result, to identify intergrade soils of the Solonchak-Calcisol type. However, the implementation of fuzzy logic is relatively complex. For this reason, it proved useful to develop a predictive model for the indices generated by the fuzzy logic method where several studies, including those by [13,14,15,16] have demonstrated that models based on artificial neural networks (ANN) represent an effective alternative for predicting complex variables. Accordingly, we constructed a multiple linear regression (MLR) model and compared its performance to that of an ANN model. This study is innovative, as to the best of our knowledge, no previous work has addressed the prediction of Solonchak index (Is) derived from fuzzy logic using ANN modeling. The main advantage of this model over MLR lies in its ability to capture non-linear and complex relationships, while offering robustness against multicollinearity and interactions among variables, phenomena that are very common in soil science. For example, electrical conductivity (EC) is strongly correlated with the concentration of certain cations and anions present in the soil solution. The ANN model has the ability to effectively handle collinearity among independent variables, thereby minimizing its impact on prediction accuracy.

Another major strength of modeling is its capacity to reduce the number of samples to be collected and the laboratory analyses to be performed, resulting in considerable time savings and better resource optimization, while providing reliable predictions that are directly applicable to soil management and classification.

Chott El Hodna

Chott el Hodna, which is part of the Hodna region (also known as the Hodna Basin), lies about 200 km southeast of Algiers (Figure 1) and has an arid environment. The annual rainfall average is 167 mm and fluctuates throughout the year. The area has recorded extreme temperatures ranging from a minimum of 9.4 °C to a maximum of 39.3 °C, with the average yearly temperature of 19.6 °C.

The Ramsar Convention’s [17] designation of this area as a wetland led to its selection as the research area. It is experiencing an advanced phenomena of soil salinization and is home to ecological populations (plants, birds, nesting areas, aquatic species, etc.) that are in danger of extinction. Thus, research on the Solonchaks in this area is crucial to maintaining the sustainable viability of this delicate environment.

2. Data Sources and Research Methodology

2.1. Soil Sampling

Two soil profiles (P1 and P2) (Figure 1) were selected based on the diagnostic criteria for the salic horizon of the Solonchak reference group, according to the FAO classification (2022) (

Table 1. Diagnostic criteria of soil groups recommended [11].

Soil Groups (Output Variables)	Variables Used (WRB) (Input Variables)
Solonchaks	− EC (dS m−1) − E (cm) − (EC × E)
Calcisols	− CE (%) − E (cm) − SC (%)

E (depth): thickness of diagnostic horizons, EC: electrical conductivity, SC: secondary carbonate, CE: Calcium carbonate equivalent.

). For each profile, soil samples were taken for every 30 cm depth to a depth of 1.5 m (

Table 2. Sample collection depth.

Levels	Depth (cm)
Level 1	0–30
Level 2	30–60
Level 3	60–90
Level 4	90–120
Level 5	120–150

), resulting in five soil samples per profile and with a total of ten samples.

Profile 1 is located in the upstream section of the toposequence, whereas Profile 2 is positioned in the downstream section (Figure 1). A depth interval of 30 cm was chosen due to the absence of significant variations in the morphological characteristics of the soils. Additionally, 26 Solonchak profiles were identified in the study area based on these two reference profiles (Figure 1). These Solonchaks, characterized by high limestone content (15% < CaCO₃ < 52%) and significant salinity levels (15 dS m⁻¹ < EC < 72 dS m⁻¹) in most horizons, were analyzed to assess their affiliation with Calcisols using fuzzy logic. The Mamdani Fuzzy Inference System (MFIS) was applied to these 26 profiles [18]. The profiles were selected to represent the spatial variability of Solonchak components along the topo sequence, from upstream to downstream. The slope of the wetland plays a crucial role in the spatial variability of soil characteristics, directly influencing the distribution of soil constituents, which is an important factor in the formation and behavior of Solonchaks.

2.2. Soil Analysis Methods

Electrical conductivity (EC) was measured using a diluted soil extract (1:5 ratio) By HANNA HI6321-02 benchtop conductivity meter due to the sandy texture of the soils, following the method of the USDA Salinity Laboratory [19]. The EC values obtained from the diluted extracts were then converted into EC values for the saturated paste extract using the formula proposed by [20], (Equation (1)).

$$\mathit{\text{PE (value of Past Extract)}}=7.98\times z(\mathit{\text{value of Extract}}({\displaystyle \frac{1}{5}}))$$

(1)

The volumetric approach was used to measure the overall amount of limestone, while sieving was used to estimate the quantities of sand Coarse sands were separated using a 2 mm to 0.2 mm sieve and fine sands were separated using a 0.2 mm to 0.05 mm sieve. By examining the cations and anions found in a 1:5 soil extract, the ionic balance was determined. Atomic absorption spectrometry (PerkinElmer Analyst 400) was used to measure the quantities of calcium and magnesium, while flame photometry (Flame Photometer M410, SHERWOOD) was used to estimate the concentrations of sodium and potassium. Sulfates were measured gravimetrically using barium chloride, whereas chlorides were quantified using the Mohr method by titrating with silver nitrate. This method is an argentometric titration technique used to determine the chloride ion (Cl⁻) concentration in a sample. It is based on the precipitation of chloride ions by silver ions (Ag⁺), forming insoluble silver chloride (AgCl): Ag⁺ + Cl⁻ → AgCl (The precipitation of chloride ions by silver ions).

• General Procedure:

  (a)

  Preparation of the soil extract: prepare an aqueous soil extract, typically using a 1:5 soil-to-water ratio.

  (b)

  Addition of the indicator: Add a few drops of potassium chromate (K₂CrO₄), which serves as the indicator.

  (c)

  Titration with silver nitrate (AgNO₃): Ag⁺ first reacts with Cl⁻ to form insoluble white AgCl.

  (d)

  Titration endpoint: Once all chloride ions are precipitated, the excess Ag⁺ reacts with the indicator to form brick-red silver chromate (Ag₂CrO₄), signaling the endpoint of the titration.

Principle: Silver ions first precipitate the chloride ions as white AgCl, when no free chloride ions remain, Ag⁺ reacts with chromate to form red Ag₂CrO₄, marking the endpoint.

• Calculation: The chloride concentration (Cl⁻) is calculated based on the volume of AgNO₃ consumed during titration and its normality.

Sulfuric acid titration was used to measure the carbonates and bicarbonates, while ammonium carbonate extraction was used to measure the amount of gypsum.

2.3. Decision-Making Using Fuzzy Logic

Three essential phases are involved in using fuzzy logic: fuzzification, inference, and defuzzification.

2.3.1. Fuzzification

The process of turning numerical values (or physical characteristics of diagnostic criteria) for every soil type (Table 1) into fuzzy variables is known as “fuzzification”. Fuzzy sets and Gaussian membership functions were used for this analysis (Figure 2).

Based on linguistic variables, the fuzzy (input) variables were separated into three subsets: Low (L), Medium (M), and High (H).

To account for Solonchak variability and improve classification, the linguistic variable limits for calcium carbonate equivalent (CE), electrical conductivity (EC), secondary carbonates (SC), and diagnostic horizon thickness were meticulously established.

The interaction between these classes and their degrees of membership, defined by the Gaussian function, is illustrated in Figure 2.

The same procedure was applied to the output variables, which were converted into Solonchaks index (Is) and Calcisols index (Ic) using the Gaussian membership function, as illustrated in Figure 3.

In fuzzy logic, these parameterizations are informed by human expertise and field observations [21,22], which helps capture the complex relationships between different soil parameters. The limits were carefully established to account for spatial variability while ensuring smooth and accurate representation in the modeling process. Similarly, the calibration of the membership functions was carried out based on the analytical data of the studied soils (EC, CaCO₃, etc.), field observations, and interpretation standards, such as those related to EC.

2.3.2. Inference Rules

Five input variables (diagnostic criteria or physical factors) (Table 1), each of which was split into three subgroups that corresponded to the Solonchak and Calcisol categories, served as the basis for the development of the inference rules.

A soil was classified as a Solonchak if all its diagnostic criteria were High (H), with the same logic applied for Calcisols. For instance:

IF EC is L and (EC × E) is L and E is L (Solonchak criteria) and Calcium Carbonate Equivalent is G and SC is H (Calcisol criteria) then Solonchak is L, and Calcisol is Higher. In this situation, the soil is classified as a Calcisol because its diagnostic criteria prevail over those of the Solonchaks. For example Rule 1: IF EC is H and (EC × E) is H and E is H and c. E is L and SC is L and is L then Solonchak is Higher, Calcisol is L. The consequence of this rule is that the soil is classified Solonchak, because the set of diagnostic criteria for Solonchaks is higher.

Inference rules are based on expert reasoning, which consists of logically combining information derived from diagnostic criteria to determine the corresponding soil class. Specifically, each criterion is first expressed as a linguistic variable (e.g., “low,” “medium,” or “high”) and then converted into a numerical value through a defuzzification process.

For example, if all diagnostic criteria for Solonchaks exhibit high values and, simultaneously, the criteria for Calcisols are also high, the soil will be classified as a Solonchak higher. This rule reflects the expert logic that the dominance of characteristics associated with a specific soil type takes precedence over the presence of secondary traits.

Similarly, when the diagnostic criteria for Solonchaks are low or medium, the classification considers the relative intensity of the other diagnostic criteria, particularly those of the Calcisols. Thus, the inference process relies on a series of logical combinations that allow the soil to be consistently assigned to the most representative class, effectively replicating the reasoning of an experienced pedologist.

In this study, soil classification was determined using five physical variables (two for each soil type) and three linguistic variables (Low, Medium, and High). A total of 45 inference rules (Equation (1)) were formulated to account for all possible combinations of diagnostic criteria determined by the following equation:

$$\left(3\times {\complement }_2^1+3\times {\complement }_2^2\right)\times 5=45$$

(2)

where ∁ is combination

However, only 21 inference rules were selected based on their high statistical significance p < 0.05) in correlating the Solonchak Index (Is) and Calcisol Index (Ic) with World Reference Base (WRB) diagnostic criteria (except for diagnostic horizon thickness) [6,7]. As a result, the other inference rules were excluded. Furthermore, the validation of the 21 selected rules was confirmed through field verification. The observation of Solonchaks thus corresponded to the classification obtained by fuzzy logic after applying these 21 rules. Fuzzy logic relies on field expertise, where the expert assesses the relevance of rules based on their knowledge of the studied soils. The 21 applied inference rules showed concordance both with field observations and with the diagnostic criteria adopted by the WRB. In other words, the discarded rules held no logical significance from a pedological perspective.

2.3.3. Defuzzification

Defuzzification is the process of converting fuzzy information into precise, measurable values. In this study, the centroid method (Z) was applied [23]. The expression for Z is given by the following equation:

$$\mathit{Z}={\displaystyle \frac{{\int }_{\mathrm{D}}\mathrm{y}\times {\mathsf{\mu }}_{\mathrm{r}\mathrm{e}\mathrm{s}}\left(\mathrm{y}\right)\times \mathrm{d}\mathrm{y}}{{\int }_{\mathrm{D}}{\mathsf{\mu }}_{\mathrm{r}\mathrm{e}\mathrm{s}}\left(\mathrm{y}\right)\times \mathrm{d}\mathrm{y}}}$$

(3)

2.4. Membership Function (μres(y))

Inference methods generate a membership function for the output variable “y”, which corresponds to Solonchak and Calcisol classifications.

In this study, Z represents the Solonchak index (Is) or Calcisol index (Ic) obtained using the Mamdani Fuzzy Inference System (Figure 3) [18]. The Is and Ic indexes were computed using MATLAB software.

2.5. Modeling

Two models were developed to predict Is:

−

The first model was built using Multiple Linear Regression (MLR).

−

The second model was developed using an Artificial Neural Network (ANN).

Solonchak Index (Is) modeling using ANN. The artificial neural network (ANN) model consists of four independent variables E (Depth), pH, CaCO₃, EC and a dependent variable (Is). This results in four input variables, one output variable (Is), and four neurons, together with a bias neuron, arranged in a single hidden layer (Figure 4). The number of neurons in the hidden layer is determined by a trade-off between learning capacity and generalization ability. Too few neurons may lead to underfitting, whereas too many can result in overfitting, particularly when the dataset is limited, as in our study. Similarly, the choice of a single hidden layer is justified by the small dataset size, since adding additional layers would increase the risk of overfitting.

Conversely, larger and more diverse datasets allow for the training of deeper networks while maintaining strong generalization performance.

In our study, the first trial allowed us to evaluate the chosen configuration, and the second trial confirmed its stability with a low and consistent error rate, indicating that the model achieved satisfactory convergence.

The relative error was (RE) calculated using Equation (4).

$$\mathit{RE}=\left(\right(\left|X\mathit{\text{measured}}-X\mathit{\text{predicted}}\right|)/(X\mathit{\text{measured}})\times 100$$

(4)

-

X measured = measured value

-

X predicted = predicted value

For training and validation: 18 samples (69.23%) were used for training and 8 samples (30.76%) were used for validation (testing). The relative error rates were found to be low at both the training and validation stages (0.01) (

Table 3. Observation processing summary of model.

Parameters	N	(%)	Relative Error
Training	18	69.23	0.21
Testing	8	30.76	0.01

N: Number of samples.

). The same percentage was used for the training and validation of the MLR model.

The primary model used was an ANN based on Multi-Layer Perceptron (MLP). To optimize the learning process, we applied the conjugate gradient optimization algorithm. The activation function used was a hyperbolic tangent function (Equation (5)).

$$f\left(x\right)=(e^{2x}-1)/(e^{2x}+1)$$

(5)

The conjugate gradient optimization algorithm was introduced to provide more efficient optimization by improving convergence, finding the minimum in fewer iterations, and avoiding redundancy in search directions.

The training of the Artificial Neural Network (ANN) model parameters was conducted using the error backpropagation algorithm [24,25]. The error backpropagation algorithm is a supervised learning method widely used to train multilayer neural networks. Its goal is to adjust the synaptic weights in order to minimize the prediction error between the network output and the target (expected) values. It relies on the gradient descent optimization technique to iteratively reduce the overall error. The steps of the Backpropagation Algorithm are as follows: initialize weights and biases, perform forward propagation, calculate the output error, carry out backward propagation, update the weights, and repeat the process until convergence.

2.6. Modeling of Is Using Multiple Linear Regression (MLR)

Multiple Linear Regression was used to create the second model for predicting Is (MLR). One dependent variable and four independent variables make up this model. The MLR model employed the same set of variables as the ANN model.

2.7. Cross Validation Tests

The coefficient of determination (R²) and the root mean square error (RMSE) (Equation (6)) were computed to validate the model. Similarly, to assess the validity of regression models, we conducted an ANOVA statistical test.

$$\text{RMSE}=\sqrt{{\sum }_{n=1}^n\left({{\text{Value Predicte}}_{\mathrm{i}}-{\text{Value Measured}}_{\mathrm{i}})}^2\right)/\mathrm{n}}$$

(6)

n = number of observations

The Is values predicted by the two models and those determined using fuzzy logic were compared using Student’s t-test to determine whether there was a significant difference.

To further guarantee the reliability of the findings, tests for normality and homogeneity of variances were conducted.

A collinearity test was also conducted, as strong correlations between predictor variables can pose problems in the modeling process [26]. The test findings demonstrated that there was no multicollinearity among the variables Is, lime content, EC, pH, and E, with variance inflation factors (VIF) (Equation (7)) ranging from 1.73 to 2. These independent variables were therefore thought to be suitable for building the ANN model.

$$\mathit{\text{VIFi}}=1/(1-R_i^2)$$

(7)

-

VIFi = Variance Inflation Factor for variable Xi

-

$R_i^2$ = Coefficient of determination obtained by regressing Xi on all other independent variables

The autocorrelation of residuals was confirmed using the Durbin-Watson test.

MATLAB, SPSS, and Excel-Stat were used for all analyses. The determination of the chemical facies was carried out using the Diagramme software.

3. Results and Discussions

3.1. Analysis of Soil Constituents

The descriptive statistical results for the soil constituents analyzed are presented in

Table 4. Descriptive statistics of soil constituents.

Parameters	Fine Sands	Coarse Sands	Total Limestone	Gypsum
	%	%	%	%
Maximum	59.12	54	5	35
Minimum	22.59	27	0	5
SD	9.38	10.24	1.61	8.84
Mean	38.98	38.95	1.95	20.2
CV (%)	24.06	26.29	82.56	43.76

SD: Standard deviation; CV: Coefficient of variation.

. These results show that the soil texture in the study area consists primarily of fine sand (59.12% > fine sand > 22.59%) and coarse sand (54% > coarse sand > 27%), indicating a predominantly sandy texture. Additionally, gypsum content is significant, with an average of 20.2%, and exhibits a highly heterogeneous distribution (CV = 43.76%). In contrast, the total limestone content is relatively low, averaging only 1.95%.

Figure 5 and Figure 6 display the findings of the analysis of the soil solution for Profile 1 regarding the ionic composition and salinity of the four soil solutions.

The salt distribution with depth (Figure 5) reveals high salinity in the deepest horizon (ECps = 19.32 dS m⁻¹). The relatively lower surface salinity is attributed to leaching caused by recent irrigation, with salts accumulating in the lower horizons. Notably, the highest salinity corresponds to the horizon richest in fine sand, indicating that fine sands are more susceptible to salinization than coarse sands. This suggests a descending salt profile (Figure 5). According to the U.S. Salinity Laboratory (USSL) classification [19], all soil levels are saline, with the first horizon classified as only slightly saline.

The cations in the soil solution (Figure 6) classified according to their predominance are: Ca²⁺ > Na⁺ > Mg²⁺ > K⁺.

For the anions present in Profile 1 (Figure 6), SO₄²⁻ is the dominant ion, accounting for 40.42%. The classification of anions by predominance is: SO₄²⁻ > Cl⁻ > HCO₃⁻.

The analysis of the soil solution for Profile 2 (Figure 7 and Figure 8) displays the findings for the ionic composition and salinity of the four soil solutions for Profile 2.

The salt distribution with depth (Figure 7) shows high surface salinity (EC = 50.22 dS m⁻¹). Leaching from irrigation water has lowered the salinity in the deeper horizons, with electrical conductivity varying between 35.42 dS m⁻¹ and 50.22 dS m⁻¹. Salinity decreases in the third horizon but increases again in the fourth horizon, indicating salt accumulation. Fine sands are more affected by salinization compared to coarse sands. The salinity profile follows a concave pattern, as shown in Figure 7. According to [19], the soil exhibits salinity from the first to the fifth horizon.

The cations present in the soil solution (Figure 8), show Ca²⁺ is the most abundant, with an average concentration of 33.61%. The classification of cations by predominance is Ca²⁺ > Mg²⁺ > Na⁺ > K⁺. Amongst the anions in Profile 2 (Figure 8), the anion Cl⁻ is the most prevalent, with the following classification predominance: Cl⁻ > SO₄²⁻ > HCO₃⁻.

The determination of the chemical facies of the soil solutions studied was based on the Piper diagram (Figure 9), which revealed the following findings:

Regarding the cations (left triangle, Figure 9), the points are primarily clustered toward the calcium (Ca⁺⁺) apex, with a moderate contribution from magnesium (Mg⁺⁺) and a very low proportion of sodium and potassium (Na⁺ + K⁺). This indicates that most of the samples exhibit a calcium-type facies.

For the anions (right triangle), the points are located between the chloride (Cl⁻) and sulfate (SO₄⁻) poles, far from the bicarbonate + carbonate (HCO₃⁻ + CO₃⁻) pole. This distribution reflects a chloride- to sulfate-type chemical facies, which is characteristic of mineralized waters, typically influenced by evaporation and salt dissolution. In the central diamond-shaped field, the points are concentrated in the SO₄ + Cl/Ca + Mg sector, confirming the predominance of calcium–chloride and calcium–sulfate facies. These facies are generally associated with salinization processes and the dissolution of evaporitic minerals, such as gypsum and halite, in the studied soils.

The Piper diagram analysis (Figure 10) highlighted the following key observations:

For the cations (left triangle), the points are mainly clustered toward the calcium (Ca⁺⁺) pole, with a moderate contribution from magnesium (Mg⁺⁺) and a very low proportion of sodium and potassium (Na⁺ + K⁺). This indicates a dominant calcium-type facies.

Regarding the soil solution anions (right triangle), the points are mostly located between the sulfate (SO₄⁻) and chloride (Cl⁻) poles, far from the bicarbonate + carbonate (HCO₃⁻ + CO₃⁻) pole. The samples thus exhibit a sulfate to chloride facies, which is typical of mineralized waters, generally influenced by evaporation and salt dissolution.

The central diamond field of the diagram shows a concentration of points in the SO₄ + Cl⁺/Ca⁺ Mg sector, confirming the predominance of calcium–sulfate and calcium–chloride facies. These facies are commonly associated with salinization processes and the dissolution of evaporitic minerals, such as gypsum and halite, in the soils of the studied area.

The pH values in the soil solutions range from 7.99 to 8.47, showing minimal variation. Overall, the soil reaction is alkaline. These two chemical facies suggest that the soils studied follow a neutral saline pathway, consistent with findings from previous studies [27].

The gypsum content (calcium sulfate) significantly influences the chemical composition of the soil solution. The solutions from the studied soils show considerable sulfate content and very high calcium concentrations. Chlorides are the dominant anion in the soil solution of Profile 2, while sulfates are predominant in Profile 1. In both profiles, calcium is the dominant cation, followed by magnesium. This distribution explains the two chemical facies observed: calcium chloride and calcium sulfate, both of which indicate a neutral saline pathway. These findings align with previous studies on Algerian soils [28] in regions such as Bas Cheliff and Ouargla.

3.2. Principal Component Analysis (PCA) of EC, Cations, and Soil Solution

We applied principal component analysis (PCA) to identify which elements of the soil solution most influence the variation in electrical conductivity (EC) (Figure 11). The PCA results (Figure 10) show that the first principal axis is driven by the contribution of Cl⁻ (r = 0.96), SO₄⁻ (r = 0.82), EC (r = 0.99), Na⁺ (r = 0.92), and Mg⁺⁺ (r = 0.79). The second axis is influenced by HCO₃⁻ (r = 0.55), Ca⁺⁺ (r = 0.85), K⁺ (r = 0.43), and pH (r = −0.56) (p > 0.05). Additionally, pH also contributes to the first axis, indicating that Cl⁻ (20.4%), Na⁺ (18.7%), Mg⁺⁺ (13.81%), and SO₄⁻ (14.91%) have a stronger effect on the variation in EC than other variables (K+, Ca⁺⁺, pH, and HCO₃⁻).

However, Cl⁻ and SO₄⁻ are strongly correlated with EC and load similarly on Factor 1, while Na⁺ is also aligned but slightly less dominant than initially suggested. These three ions contribute significantly to the variability of EC.

The PCA results highlight that the more soluble ions have a greater influence on EC variation. This observation is consistent with the fact that Na⁺ is the dominant cation in the soil solution and does not participate in mineral precipitation until EC values are very high [29]. The behavior of Mg⁺⁺ and Ca⁺⁺, however, may be partially influenced by the precipitation of magnesite and calcite [29]. Yet, this control appears insufficient to prevent their continued increase with rising salinity. Similarly, while sulfate ions can be controlled by precipitation of sulfate minerals, their increase remains insufficient to fully limit their accumulation in the presence of elevated salinity [19]. The soil’s CaCO₃ content is generally supersaturated with respect to pure calcite, which explains its relatively low variation and persistence at the soil surface [30,31]. The chemical composition of soil solutions is mainly controlled by the dissolution of evaporite minerals (gypsum, halite, anhydrite) and the precipitation of carbonate phases such as calcite, aragonite, and dolomite [32].

3.3. Soil Classification Using Fuzzy Logic

Table 5. Descriptive statistics of the Is and Ic.

Parameters	Is	Ic
Maximum	0.52	0.49
Minimum	0.15	0.16
SD	0.14	0.07
Mean	0.29	0.24
CV (%)	0.47	0.3

SD: Standard deviation; CV: Coefficient of variation.

displays the statistical findings for the Calcisol (Ic) and Solonchak (Is) indices. The extreme values of the Is and Ic indices for the profiles under study are somewhat close together, as Table 5 demonstrates, indicating that the soils are comparable. This suggests that some Solonchaks might actually be categorized as Calcisols, or at the very least, resemble them. For Solonchaks and Calcisols, the typical indices are roughly 0.29 and 0.24, respectively. The soils under study are mostly Solonchaks, despite the fact that they also show a notable degree of resemblance to Calcisols, as the fuzzy classification tends to prefer soils with higher indices. Similarly, the mean Is indices are higher than the Ic indices, indicating that fuzzy logic classification predominantly favors Solonchaks. However, some soils are classified as Calcisols by fuzzy logic due to their high CaCO₃ content. In contrast, the WRB classifies all of these soils as Solonchaks, because this classification system prioritizes this reference group: a soil is identified as a Solonchak as soon as it meets the diagnostic criteria for Solonchaks, even if the diagnostic features of Calcisols are also present. The indices obtained through fuzzy logic for the 26 profiles are shown in Figure 12.

Figure 12 illustrates that of the 26 profiles classified as Solonchaks according to the FAO criteria [11], 13 profiles (50%) were also classified as Solonchaks by fuzzy logic (Is > Ic), due to their high soluble salt content (61.9 > EC (dS m⁻¹) > 15.5). Conversely, 12 profiles (46.15%) were classified as Calcisols (Ic > Is), likely because they are rich in limestone (52 > CaCO₃ (%) > 18). Additionally, for one profile (Profile 2) (Is = Ic = 0.24), which represents 3.84% of the profiles examined, fuzzy logic generated similar indices. This suggests that Profile 2 was categorized as a Solonchak-Calcisol intergrade using fuzzy logic. The profile’s equilibrium of soluble salts (EC = 23.5 dS m⁻¹) and limestone concentration (CaCO₃ = 20.5%) is responsible for this outcome. These results are in agreement with [6].

Fuzzy logic analysis showed that Solonchaks, which were previously categorized by the WRB, are significantly comparable to Calcisols, with Solonchaks belonging to the Calcisol category to a greater extent. Although the WRB designated all 26 profiles as Solonchaks, the distinctions between the two classification schemes might be due to the WRB’s threshold values, which might not be appropriate for every soil situation. The priority order that WRB used to define soil groups may also be to blame for this, as taxonomic fragmentation may cause crucial information to be lost in soil mapping.

In contrast, fuzzy logic, which is a continuous and numerical classification system [7], relies on linguistic variables and Gaussian-type membership functions for each criterion. This allows for a more nuanced representation of soils, accounting for overlaps between soil groups [33].

Fuzzy logic offers a significant advantage over traditional soil classification methods because it can manage uncertainty and ambiguity in data. Unlike rigid approaches, fuzzy logic allows soils to be assigned degrees of membership to multiple categories [34,35,36], making it especially useful for classifying soils with mixed characteristics, such as limestone-rich Solonchaks that may intergrade with Calcisols. Flexibility, adaptability, increased accuracy, and better uncertainty management are some of its advantages. The management of agricultural land impacted by salinization benefits greatly from this increased accuracy in soil classification.

3.4. Modeling of Is Carried out by ANN

The contribution of each independent variable ranges from 32.6% to 100% (

Table 6. Importance of independent variables for prediction of Is.

Independent Variables	Importance	Normalized Importance (%)
E (cm)	0.16	32.6
pH	0.17	34.2
CaCO3 (%)	0.16	34
EC (dS m−1)	0.49	100

). Among these, electrical conductivity (EC) exerts the strongest influence (100%) in predicting the salinization index (Is), followed by the thickness of the diagnostic horizon (E, 32.6%), pH (34.2%), and calcium carbonate (CaCO₃, 34%), with the latter two variables showing an equivalent contribution to Is prediction. Conversely, the ANN model exhibits low sensitivity to the thickness of the diagnostic horizon (E) and high sensitivity to variations in EC.

The analysis of the relative importance of the input variables with respect to salinization highlights EC as the most determinant factor, as its increase directly leads to a rise in Is. This result is scientifically consistent since EC directly reflects the total concentration of soluble salts in the soil, which is the primary indicator of salinization. CaCO₃ also has a positive influence, due to its presence in the studied Solonchaks. This observation is confirmed by the results of fuzzy logic, which reveal that these Solonchaks exhibit a certain degree of affiliation with Calcisols. Moreover, the existence of intergrade soils of the Solonchak-Calcisol and the analysis of the ANN model highlights that carbonate-rich soils promote the formation of secondary salts and establish an environment conducive to salinization, particularly through their interactions with calcium sulfates or chlorides. The pH also exerts a positive effect, indicating that a slight alkalinization accompanies the increase in Is, which is expected in saline soils where the accumulation of alkaline salts and carbonate precipitation tend to raise pH. Finally, the positive effect of the diagnostic horizon thickness is more moderate, reflecting a secondary contribution to the development of salinization, likely linked to the role of horizon depth in salt migration and accumulation.

Overall, the ANN model identifies EC as the dominant factor, followed by CaCO₃ and pH, while E has a weaker but still coherent effect, aligning with the known mechanisms of soil salinization leading to Solonchak formation. This agreement between the model’s variable importance and the scientific understanding of pedological processes strengthens both the credibility of the model and its scientific utility.

Furthermore, fuzzy logic was employed to validate the ANN model’s ability to predict Is. This finding is consistent with previous studies [13,14,15,16], which also demonstrated the effectiveness of ANN in predicting various soil parameters. The predictive performance of ANN arises from its use of complex algorithms that integrate both regression and classification for multiple applications, including Solonchak classification. Its capacity to capture intricate, non-linear relationships are inspired by the functioning of the human neurological system [37].

In comparison, the MLR model produced less accurate predictions. Finally, the awarding of the Nobel Prize in Physics to the pioneers of neural networks underscores their profound impact across diverse scientific fields, including soil science [16].

3.5. Modeling of Is Using (MLR)

The modeling of Is using MLR (Equation (8)), the regression coefficient parameters of the MLR model are presented in

$$\text{Is}=-0.042\cdot \text{pH}+0.0001\cdot {\text{CaCO}}_3+0.001\cdot \mathrm{E}+0.005\cdot \text{EC}+0.421$$

(8)

Among all the predictors (E, pH, CaCO₃, and EC), none showed a significant effect on the prediction of Is (p < 0.05), except for EC, which exhibited a significant effect (

Table 7. The coefficients of the multiple linear regression (MLR) model for Is prediction.

Model (Is)	Unstandardized Coefficients		Standardized Coefficients	t	Sig.
	B	Std. Error	Beta
Constant	0.421	0.66	—	0.63	0.53
pH	−0.042	0.09	−0.093	−0.43	0.66
CaCO3 (%)	0.000	0.004	0.008	0.034	0.96
E (cm)	0.001	0.000	0.235	1.287	0.21
EC (dS/m)	0.005	0.002	0.599	3.196	0.004

Predictors: EC (dS m⁻¹), E: Depth (cm), CaCO₃ (%), pH; Dependent Variable: index of Solonchak, Statistically significant (p < 0.05).

).

Modeling of Is produced a relatively weak model (R² = 0.41), indicating that the predictive variables explain only 41% of the variability in the dependent variable (Is). Additionally, the Durbin-Watson test [38] did not provide conclusive evidence of autocorrelation between the residuals (E, pH, CaCO₃, EC) (

Table 8. Model summary and DurbinWaston test of MLR model.

Model	R2	Ajusted R2	SEE	Durbin-Watson
MLR	0.41	0.3	0.11	1.55

Predictors: EC (dS m⁻¹), E: Depth (cm), CaCO₃ (%), pH; Dependent Variable: index of Solonchak, SEE: Standard Error of Estimation, Statistically significant (p < 0.05).

).

The analysis of variance (ANOVA) (

Table 9. ANOVA test of MLR.

Parameters	Sum of Squares	df	Mean Square	F	Significant
Regression	0.2	4	0.05	3.74	0.19
Residual	0.28	21	0.01
Total	0.49	25

Dependent variable “Is” independent variable EC, Depth (E), CaCO₃ and pH. Statistically significant (p < 0.05).

) indicates that the MLR model explains only a fraction of the total variance (0.20 out of 0.49). However, the F-test value (p = 0.19) shows that this contribution is not statistically significant. In other words, the independent variables (E, pH, CaCO₃, EC), considered jointly, do not significantly improve the prediction of the dependent variable.

Cross validation tests further reveal that the model derived from artificial neural networks (R² = 0.7; RMSE = 0.17) provides a better prediction of Is compared to the MLR model (R² = 0.41; RMSE = 0.91) (

Table 10. Comparison between the two models ANN and MLR.

Models	R2	RMSE	Student’s Test (p Value)
MLR	0.41	0.91	0.01
ANN	0.70	0.17	0.057

Statistically significant (p < 0.05).

). Likewise, Student’s t-test indicated that the difference between Is predicted by the ANN model and Is calculated by fuzzy logic is not significant at the 0.05 probability level (p-value = 0.057 > 0.05). In contrast, Student’s t-test showed a significant difference between Is predicted by MLR and Is calculated by fuzzy logic (p-value = 0.01 < 0.05) (Table 10).

As a result, we can reject the MLR model and confidently verify the ANN model for predicting Is. MLR is a simple method for predicting soil properties [39]. However, due to its lack of flexibility, MLR does not produce reliable forecasts. As a result, machine learning methods have become increasingly popular for predicting soil properties. Many authors [13,14,15,16] have emphasized the accuracy of ANN-derived models. Consequently, we can confidently validate the ANN model for predicting Is, while rejecting the MLR model, as confirmed by [40].

4. Conclusions

Data analysis of this study reveals that the three soils investigated are primarily characterized by very high salinity levels (0.7 < ECps (dS m⁻¹) < 50). Only the soil from borehole 1 exhibits relatively low salinity (0.7 < ECps (dS m⁻¹) < 5.5). As a result, three distinct salt profiles were identified for Profiles 1 and 2 descending and concave, respectively.

The chemical facies observed were classified as calcium-sulfate and calcium-chloride types, indicating that the soils have evolved along a neutral saline pathway. Additionally, the data showed that 50% of the soils were classified as Solonchaks, 46% as Calcisols, and 3.84% as intergrades between Solonchak and Calcisol.

Fuzzy logic analysis demonstrated a high degree of accuracy in calculating the membership values between soils and their intergrades. These results suggest that fuzzy logic could effectively enhance conventional saline soil classification methods and may be applicable to other global soil classification systems. Furthermore, statistical analysis revealed that the artificial neural network (ANN) model outperformed the multiple linear regression (MLR) model in predicting the Is index, as validated through fuzzy logic.

Based on these results, we recommend the adoption of ANN models, particularly for the prediction of complex parameters that are difficult to measure or compute in soil classification.

Overall, the findings of this study provide promising prospects for improving the classification and management of saline soils, contributing to a better understanding of Solonchaks and, in particular, their intergrade soils in wetlands of arid regions such as those in North Africa. Fuzzy logic provides highly accurate numerical classification through the derived indices, which can be readily integrated into emerging precision agriculture technologies. The integration of fuzzy logic and artificial neural network (ANN) modeling provides a robust framework capable of enhancing both scientific understanding and practical approaches for the sustainable management of saline landscapes. Through the generation of digital soil maps (Is), thereby promoting optimized soil management.