Fuzzy Logic-Based Assessment of Treated Wastewater Quality in Treatment Plant of Tlemcen, Algeria

Abstract

This study evaluates the performance of the Ain El Houtz wastewater treatment plant (WWTP) in Tlemcen, Algeria, by applying a fuzzy logic-based framework to multi-scale temporal data. A total of 2192 effluent samples collected between 2020 and 2022 were analyzed for Biochemical Oxygen Demand over five days (BOD₅), Chemical Oxygen Demand (COD), dissolved oxygen (O₂), pH, nitrate (NO₃⁻), phosphate (PO₄³⁻), and temperature. Expert-derived parameter weights were integrated into a Mamdani fuzzy inference system to compute a Fuzzy Water Quality Index (FWQI). Sensitivity analysis was conducted to assess the robustness of the model to variations in weights and membership functions. Results revealed satisfactory performance in 2020 and 2022 (FWQI > 85%), while 2021 showed critical degradation (FWQI ≈ 50%), unrelated to seasonal climate variability. Comparison with raw parameters and regulatory thresholds validated the FWQI’s ability to capture operational fluctuations. This work represents the first multi-scale fuzzy logic application to wastewater treatment monitoring in Algeria, highlighting both the potential and limitations of fuzzy indices in semi-arid contexts. The approach provides a transferable decision-support tool for improving effluent quality management and guiding corrective actions in WWTPs.

1. Introduction

Wastewater treatment plants (WWTPs) are essential for protecting aquatic ecosystems and ensuring sustainable water management, particularly in semi-arid regions such as Algeria, where population growth and urbanization exert increasing pressure on water resources. In such water-scarce contexts, the reuse of treated wastewater for irrigation represents a promising strategy to alleviate water stress and support sustainable agricultural practices. Assessing the quality of treated effluent remains challenging due to the complexity of physico-chemical parameters, measurement uncertainties, and the limitations of conventional indices.

Classical water quality indices, such as Horton’s WQI [1] and the NSF-WQI [2], have provided simplified tools for integrating multiple parameters. However, these models often oversimplify system dynamics, rely on fixed thresholds, and fail to account for nonlinear interactions or uncertainties in environmental data [3,4]. Recent reviews emphasize the need for more flexible approaches capable of capturing variability in wastewater treatment performance [5,6].

Fuzzy logic, introduced by [7], offers a robust alternative by modeling imprecise or uncertain situations through linguistic rules and continuous quality scores. Several international studies have demonstrated its relevance: Ref. [8] applied a fuzzy water quality index in Brazil; ref. [9] showed stricter classifications in Moroccan basins compared to conventional indices; ref. [10] assessed river water quality in Colombia using fuzzy inference; ref. [11] highlighted its consistency in Nigeria; and ref. [12] proposed hybrid fuzzy–AI frameworks for estuarine monitoring. These contributions confirm that fuzzy logic can integrate heterogeneous variables and provide more realistic classifications than traditional indices.

Despite this growing international use, fuzzy logic has rarely been applied to wastewater treatment monitoring in Algeria [13]. This study addresses the gap by applying a fuzzy-logic-based framework to evaluate the performance of the Ain El Houtz WWTP in Tlemcen. Unlike previous works, the analysis is conducted at three temporal scales (annual, seasonal, and monthly), enabling a more comprehensive understanding of operational variability. Recent advances in fuzzy-based environmental monitoring have further demonstrated the relevance of integrating fuzzy logic with modern data-driven approaches. For instance, Alotaibi and Nassif (2024) [14] highlighted the rapid growth of artificial intelligence applications in environmental monitoring through a bibliometric analysis of more than 4700 publications. Theisen et al. (2025) [15] proposed a graph-aware neural network (EGAN) for multi-modal environmental data analysis, showing the potential of combining fuzzy reasoning with deep learning. Similarly, a recent study [16] developed a hybrid model combining a BiLSTM network with an adaptive neuro-fuzzy inference system (ANFIS) to achieve highly accurate predictions for water quality assessment. The inclusion of these references reflects the current state of the art and situates the FWQI approach within the broader context of recent methodological developments. The objectives of this study are to (i) construct a fuzzy inference system incorporating expert-derived parameter weights, (ii) validate the model through sensitivity analysis and comparison with regulatory thresholds, and (iii) identify critical periods of performance degradation. This work represents the first multi-scale application of fuzzy logic to wastewater treatment monitoring in Algeria and contributes to the development of adaptive decision-support tools for semi-arid contexts. In addition, the originality of this study lies in the calibration of membership functions specifically adapted to the effluents of a wastewater treatment plant in a semi-arid climate (Tlemcen), the structuring of fuzzy rules to explicitly integrate operational parameters such as aeration failures, and the comparative validation of the FWQI against the classical WQI within the same dataset.

2. Materials and Methods

2.1. Study Area

The subject of the study is the wastewater treatment plant (WWTP) of Ain El Houtz, which plays a crucial role in managing wastewater and domestic water for the Tlemcen region in Algeria. Operational since 2005, it is designed to treat up to 30,000 m³ of wastewater per day, serving a population equivalent of 150,000 [17]. This facility is a key component of the national sanitation system, contributing to the protection of water resources and the reduction in pollution in the area.

The WWTP is located approximately 6 km north of the city of Tlemcen, on the right bank of the watercourse Ain El Houtz, at the foot of the Jebel Touma (Figure 1). It extends over an area of 13 hectares, in a peri-urban area subject to increasing pressures related to urbanization [17].

The Ain El Houtz WWTP operates using a biologically activated sludge process with extended aeration. This system relies on the oxidation of organic matter by aerobic microorganisms, facilitated by low-speed surface aerators. Treatment begins with a mechanical stage comprising screening, grit removal, and oil extraction, aimed at eliminating coarse particles. The wastewater is then directed to aeration basins, where nitrification and denitrification phases take place. Secondary sedimentation ensures the separation of biological sludge, while final chlorination provides disinfection prior to discharge. The extracted sludge is thickened and subsequently dried on open-air beds. This process ensures high purification efficiency and compliance with regulatory discharge standards [17].

2.2. Data Used

Seven physicochemical parameters were selected as input variables due to their essential role in evaluating the performance of the wastewater treatment plant. These parameters, including biological oxygen demand (BOD₅) over five days, chemical oxygen demand (COD), dissolved oxygen concentration (O₂), hydrogen potential (pH), nitrate (NO₃⁻), phosphate (PO₄³⁻), and temperature, were measured from both influent and treated effluent samples. This dual sampling ensured a representative evaluation of the plant’s efficiency.

During each campaign, samples were collected simultaneously at the influent and effluent of the plant, with an average of 20 to 25 samples per campaign, depending on seasonal and operational conditions. Temperature, electrical conductivity, and pH were measured immediately after collection using HQ40D Portable Multi-Parameter Meters (Hach Company, Loveland, CO, USA), while other parameters, including BOD₅, COD, and nutrients, were analyzed according to the Standard Methods for the Examination of Water and Wastewater [18]. Samples were preserved at 4 °C and transported to the laboratory within six hours to minimize degradation. Quality assurance procedures included duplicate samples, blanks, and regular calibration of instruments, ensuring rigorous and reliable evaluation of the WWTP’s performance.

To determine the relative importance of each parameter in assessing water quality, a structured questionnaire was submitted in March 2025 to a panel of 14 experts (university researchers, engineers from the National Sanitation Office, and water treatment specialists). Each expert assigned a percentage weight to the seven parameters, ensuring that the total sum equaled 100%. The values were aggregated and normalized to obtain final weights according to the formula:

$$wi={\displaystyle \frac{\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l} \mathrm{s}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r} i}{\mathrm{S}\mathrm{u}\mathrm{m} \mathrm{o}\mathrm{f} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{s}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{s}}}\times 100$$

(1)

where

• i = index of the parameter under consideration.

2.3. Methodology

2.3.1. Fuzzy Logic Algorithm for Water Quality Evaluation

Assessing water quality is inherently complex due to the variability of physico-chemical parameters and the uncertainties associated with environmental data. Conventional indices often rely on fixed thresholds, which may oversimplify the gradual transitions observed in real systems. To overcome these limitations, a fuzzy logic–based algorithm was developed. This approach integrates expert knowledge with fuzzy set theory to provide a more flexible and nuanced evaluation of water quality. By considering parameters such as BOD₅, COD, pH, dissolved oxygen, and nutrients, the algorithm is capable of handling imprecision and variability, thereby producing a synthetic indicator that better reflects the actual state of the effluent. The overall structure of the fuzzy logic algorithm is illustrated in Figure 2.

2.3.2. Selection of the Software Used

To evaluate the quality of treated wastewater using fuzzy logic, MATLAB (Matrix Laboratory) software (The MathWorks, Inc., Natick, MA, USA) version R2024a was selected. This choice is justified by its ability to process complex information, model non-linear systems, and integrate specialized tools for fuzzy-logic applications [19].

MATLAB is widely recognized for its robustness and flexibility in engineering, environmental sciences, and applied research. Among its features, the Fuzzy Logic Toolbox^TM enables the design, simulation, and optimization of fuzzy systems based on linguistic rules, membership functions, and inference matrices [20]. This toolbox provides both computational efficiency and visual tools that are essential for interpretation and decision-making.

Several studies have confirmed the relevance of MATLAB for wastewater treatment applications. For example, ref. [19] developed a fuzzy logic controller in MATLAB to regulate a wastewater treatment plant, achieving improved purification performance and operational stability. Similarly, ref. [8] applied fuzzy logic models to evaluate water quality, demonstrating the robustness of MATLAB in handling complex environmental data. Such evidence supports the suitability of MATLAB for implementing the fuzzy inference system in this study [8,19,20]. All simulations in this study were performed using MATLAB R2024a with the Fuzzy Logic Toolbox.

2.3.3. Construction of the Fuzzy System

The evaluation of treated wastewater quality was carried out using a Mamdani-type fuzzy inference system, developed in MATLAB with the Fuzzy Logic Toolbox^TM. This system is based on three fundamental steps:

• Fuzzification of input parameters: transformation of numerical values (BOD₅, COD, dissolved O₂, pH, NO₃⁻, PO₄³⁻, temperature) into degrees of membership to linguistic categories (“Good,” “Average,” “Bad”).
• Application of linguistic rules: construction of a set of IF… THEN… rules that translate the interactions between parameters and overall water quality. Example: If BOD₅ is bad AND O₂ is low → Water quality is bad.
• Defuzzification of the output: conversion of fuzzy results into a single numerical value of the FWQI, obtained using the centroid method, recognized for its robustness in environmental applications [21,22].

This approach effectively manages the uncertainties inherent in environmental data while producing a synthetic water quality index (FWQI) that is more flexible and interpretable than conventional methods [23,24]. Similar applications have demonstrated the relevance of fuzzy logic in complex and variable environments, notably in the field of industrial water treatment [25].

2.3.4. Triangular Membership Functions

Traditional water quality indices, while useful, present limitations in terms of flexibility and uncertainty management [5,26]. To address this, the present model adopts triangular membership functions, which allow the gradual transitions between quality classes (“Good,” “Average,” “Bad”) to be represented [7].

Each function is defined by three points:

• a: minimum value (μ = 0),
• b: central value (μ = 1),
• c: maximum value (μ = 0).

This structure avoids abrupt breaks between classes and enables a more realistic assessment of environmental parameters. The thresholds were defined by combining Algerian and international standards for wastewater reuse with calibration based on the actual dataset distribution (mean, standard deviation, and range). This dual approach ensures that the fuzzy sets remain aligned with regulatory requirements while accurately reflecting the empirical variability observed at the Ain El Houtz WWTP.

The parameters a, b, and c of the triangular membership functions for the input variables are presented in

Table 1. Triangular membership function parameters (a, b, c) for input variables, based on Algerian wastewater reuse standards.

Variable	Unit	Term Language	a	b	c
BOD5	mg/L	Good	0	10	20
		Average	15	25	35
		Bad	30	40	50
COD	mg/L	Good	0	50	100
		Average	80	125	170
		Bad	150	200	250
O2 dissolved	mg/L	Good	2	6	10
		Average	1	2	4
		Bad	0	0.5	2
pH	-	Acidic	5	6	6.5
		Neutral	6.5	7.5	8.5
		Basic	8.5	9	10
NO3−	mg/L	Good	0	10	20
		Average	15	30	45
		Bad	40	50	60
PO43−	mg/L	Good	0	1	2
		Average	1.5	5	8
		Bad	7	10	15
Temperature	°C	Good	0	15	25
		Average	20	30	35
		Bad	30	35	40

, while those for the output variable (FWQI) are shown in

Table 2. Triangular membership function parameters (a, b, c) for the FWQI, based on fuzzy logic conventions in environmental applications.

Variable	Unit	Term Language	a	b	c
FWQI	%	Bad	0	30	50
		Average	40	60	80
		Good	70	90	100

(values adapted from fuzzy logic conventions in water quality assessment [21,22,27].

The corresponding curves have been generated in MATLAB for ease of interpretation. They express each measured value as a degree of membership in the relevant fuzzy set.

The data in Table 1 and Table 2 are operated according to the following formula to plot these functions:

$$\mathsf{\mu }\left(x\right)=\left\{\begin{array}{cc}0,& if x<a or x>c\\ {\displaystyle \frac{x-a}{b-a}}& if a\le x\le b\\ {\displaystyle \frac{c-x}{c-b}}& if b\le x\le c\end{array}\right.$$

(2)

where:

• a, b, c = Category thresholds
• μ(x) = Degree of membership in a category (0 to 1)

This step prepares the data for fuzzification by converting the measured digital values into fuzzy values that are usable by the inference system [28,29].

2.3.5. Sensitivity Analysis

The sensitivity analysis was carried out to test the robustness of the fuzzy model. Two aspects were evaluated:

• Variation in weights

The weights assigned to the parameters were modified by ±10% to account for expert uncertainty in parameter weighting, following common practice in fuzzy water quality index studies [20]. This tolerance margin reflects the typical range of variability observed in expert-based assessments and ensures robustness of the FWQI model.

• Baseline (BOD₅ = 25%) → FWQI = 72.8
• BOD₅ increased (+10%, i.e., 27.5%) → FWQI = 72.1
• BOD₅ decreased (–10%, i.e., 22.5%) → FWQI = 73.4

The maximum deviation observed was ±0.7 points (≈±1%), confirming that the FWQI is stable with respect to weight variations.

• Membership function shapes

Triangular membership functions were compared with trapezoidal and Gaussian forms. Example for COD = 64 mg/L and O₂ = 4.78 mg/L:

• Triangular → FWQI = 72.8
• Trapezoidal → FWQI = 73.2
• Gaussian → FWQI = 73.5

The differences remained below 1%, with no change in the final classification of water quality.

2.3.6. Fuzzification of Data

Fuzzification is a key step in the system of fuzzy inference. It is to transform the numerical values measured for each parameter into degrees of belonging to linguistic categories that are predefined, such as “Good”, “Average”, or “Bad”. This operation enables the representation of the environmental data in a form that is fuzzy, more adapted to the natural variability and uncertainty of real-world systems.

The conversion is done with the help of the previously defined triangular membership functions. These functions are characterized by three points:

• a and c define the boundaries of the category (where μ = 0)
• b is the vertex of the function (where μ = 1)

The degree of membership μ(x) of a value x in a category is calculated according to the following formulas:

If x ∈ [a, b] (a branch growing):

$$\mathsf{\mu }={\displaystyle \frac{\mathrm{x}-\mathrm{a}}{\mathrm{b}-\mathrm{a}}}$$

(3)

If x ∈ [b, c] (a branch descending):

$$\mathsf{\mu }={\displaystyle \frac{\mathrm{c}-\mathrm{x}}{\mathrm{c}-\mathrm{b}}}$$

(4)

If x ∉ [a, c], then:

μ(x) = 0

This method is applied to each of the seven input parameters of the model (BOD₅, COD, O₂, pH, NO₃⁻, PO₄³⁻, Temperature). It allows for converting each measured value representation, fuzzy, which will then be used in the inference engine to evaluate the overall quality of the water.

2.3.7. Inference Rules

The fuzzy system is based on a set of linguistic rules of the type “If... Then...”, constructed from the technical expertise and known interactions between the parameters of water quality. These rules are used to connect the input fuzzy output fuzzy representing the global state of the resource.

The following rules were used in the fuzzy inference system:

Rule 1—Health Hazard (Critical Organic Pollution)

• If BOD₅ is Bad AND COD is Bad
• Then Water Quality (WQ) is Bad

Rule 2—Proper Operation of the Treatment Plant

• If BOD₅ is Good AND COD is Good AND O₂ is Good AND NO₃⁻ is Good
• Then WQ is Good

Rule 3—Oxygenation Problem

• If O₂ is Very Low (bad)
• Then WQ is Bad

Rule 4—Intermediate Situation

• If all parameters are Average
• Then WQ is Average

Rule 5—Good Organic Load but Average Oxygenation

• If BOD₅ and COD are Good AND O₂ is Average
• Then WQ is Average

Rule 6—Average Organic Load but Good Oxygen and Nitrates

• If BOD₅ and COD are Average AND O₂ and NO₃⁻ are Good
• Then WQ is Average

Rule 7—Good Basic Conditions (other parameters ignored)

• If BOD₅, COD, O₂, and NO₃⁻ are Good, Then WQ is Good (even if pH, PO₄³⁻, or Temperature are bad)

Rule 8—Acidic condition with oxygen deficiency

• If pH is Acidic AND O₂ is Bad
• Then WQ is Bad

Rule 9—Alkaline imbalance with moderate organic load

• If pH is Basic AND COD is Average
• Then WQ is Average

Rule 10—Phosphate overload with bad organic removal

• If PO₄³⁻ is High AND COD is Bad
• Then WQ is Bad

Rule 11—Moderate nitrate with average organic load

• If NO₃⁻ is Average AND BOD₅ is Average
• Then WQ is Average

Rule 12—Temperature stress with oxygen deficiency

• If Temperature is High AND O₂ is Bad
• Then WQ is Bad

Rule 13—Balanced nutrients with average organic load

• If NO₃⁻ is Good AND O₂ is Good AND BOD₅ is Average
• Then WQ is Average

Rule 14—Acceptable phosphate with good organic removal

• If PO₄³⁻ is Average AND BOD₅ is Good AND COD is Good
• Then WQ is Good

Rule 15—Combined stress condition

• If Temperature is High AND PO₄³⁻ is High AND O₂ is Bad
• Then WQ is Bad

The activation of the rules is based on the logical operator of the minimum (min), consistent with the approach of Mamdani, widely used to model complex and uncertain systems [30]. The aggregation of active rules is then given by the superposition of the outputs blurred, allowing a coherent synthesis of the results.

This method has been validated in several studies, including [27], who proposed a model for evaluating fuzzy on the quality of surface waters, and [23], who demonstrated the effectiveness of a system of fuzzy inference for the assessment of groundwater resources.

The fuzzy rule base incorporates uncertainty by allowing gradual transitions between classes rather than rigid thresholds. This design reduces the impact of measurement variability and parameter fluctuations, ensuring that borderline values are treated more consistently.

2.3.8. Defuzzification

Defuzzification is the last step in the fuzzy system. It allows for converting the output fuzzy aggregated into a single, easily interpretable numeric value. The method used is that of the center of gravity (centroid), recognized for its robustness in environmental applications [21,22].

The formula used is:

$$\mathrm{F}\mathrm{W}\mathrm{Q}\mathrm{I}={\displaystyle \frac{{\sum }_{i=1}^{n}yi\times \mu \left(yi\right)}{{\sum }_{i=1}^n\mu \left(yi\right)}}$$

(5)

where:

• yi: discrete value of the output variable
• μ(yi): degree of membership of yi
• n: number of points considered

This method allows for obtaining a final index (FWQI) between 0 and 100, reflecting the overall quality of the treated water.

• Calculation of the Classical Water Quality Index (WQI)

For comparative validation purposes, the classical Water Quality Index (WQI) was calculated using the weighted arithmetic method. Each parameter Pi (BOD₅, COD, O₂, pH, NO₃⁻, PO₄³⁻, temperature) was normalized against its standard value Si, then multiplied by a relative weight Wi reflecting its environmental importance. The WQI was obtained by aggregation according to the formula:

$$\mathrm{W}\mathrm{Q}\mathrm{I}={\displaystyle \frac{\sum Wi\times Qi}{\sum Wi}}$$

(6)

where Qi is the relative quality of parameter i, calculated as:

$$Qi={\displaystyle \frac{Ci}{Si}}\times 100$$

(7)

• WQI → Water Quality Index (final score, 0–100).
• i → Index representing each parameter included in the calculation (e.g., BOD₅, COD, O₂, pH, NO₃⁻, PO₄³⁻, temperature).
• Wi → Weight assigned to parameter i (reflects its relative importance in water quality assessment).
• Qi → Quality rating of parameter i, expressed as a percentage relative to its standard.
• Ci → Measured concentration of parameter i in the effluent.
• Si → Standard permissible value (regulatory or guideline threshold) for parameter i.
• ∑(Wi·Qi) → Weighted sum of all parameter quality ratings.
• ∑Wi → Sum of all weights (normally equal to 1 or 100%).

The conventional classification categories are: Excellent (90–100), Good (70–90), Fair (50–70), and Bad (<50). As an illustration, for the year 2021, the measured values yielded a WQI ≈ 55, classifying the effluent as ‘Fair.’ This result allows a direct comparison with the FWQI, which gave ≈ 50% (class ‘Average’), but with increased sensitivity to borderline conditions. The detailed comparative results are presented in Section 3.5.

2.3.9. Temporal and Seasonal Assessment Methodology

In addition to the overall FWQI calculation, analyses were conducted at three time intervals: annual, seasonal, and monthly. For the seasonal evaluation, FWQI values were calculated separately for the dry season (May–October) and the wet season (November–April) in order to capture the influence of climatic variations, such as rainfall, dilution, and temperature, on the performance of the WWTP. This methodological distinction ensures coherence with the subsequent results in Section 3.4, where annual, seasonal, and monthly FWQI values are analyzed.

Furthermore, the methodology explicitly considered the need to separate environmental variability from systemic malfunction. Climatic factors (temperature, rainfall, dilution) were assessed through seasonal FWQI comparisons, while persistent deviations across consecutive months, independent of seasonal trends, were interpreted as indicators of operational malfunction. Since the Ain El Houtz WWTP does not receive significant industrial discharges, influent variability is primarily linked to stormwater inflows, which dilute and alter wastewater composition during rainfall events. This framework ensures that, when performance degradation is observed, it can be attributed to either external environmental drivers or to internal technical failures of the WWTP, providing a coherent basis for interpretation in the results and discussion sections.

3. Results

The application of the fuzzy logic algorithm produced FWQI values that summarize effluent quality. In the following subsections, detailed results are presented through tables and figures, including membership functions, weighting parameters, and the final FWQI scores. These outputs allow temporal and comparative evaluation of treatment performance.

3.1. Determination and Final Weights of Physico-Chemical Parameters for FWQI Calculation

Before analyzing the temporal dynamics (annual, seasonal, and monthly), it is essential to present the final weights assigned to the physico-chemical parameters (

Table 3. Final weighting parameters for the assessment of water quality.

Parameters	Importance (Weight %)
BOD5 (Biochemical Oxygen Demand over five days)	25%
COD (Chemical Oxygen Demand)	20%
O2 (dissolved Oxygen)	15%
pH	10%
NO3− (Nitrates)	10%
PO43− (Phosphate)	10%
Temperature	10%

). These weights constitute the basis of the FWQI calculation and provide justification for the methodological choices adopted.

The final weights assigned to the physico-chemical parameters (Table 3) reveal clear differences in their relative influence on the FWQI. Biochemical Oxygen Demand over five days (BOD₅) and Chemical Oxygen Demand (COD) emerged as the most dominant parameters, with respective weights of 25% and 20%. This predominance reflects their direct role in characterizing the organic load of the effluent and the efficiency of biological treatment processes. High BOD₅ and COD values indicate insufficient degradation of organic matter, which has immediate consequences for both agronomic reuse and environmental safety.

Dissolved oxygen (15%) also plays a critical role, acting as a key indicator of the balance between microbial activity and aeration efficiency. Its intermediate weight highlights its importance in sustaining biological processes while confirming that oxygen deficiency can rapidly compromise treatment performance.

Other parameters, such as pH, nitrates, phosphates, and temperature, each contributed around 10% to the complementary information. Their lower weights do not diminish their relevance; rather, they reflect their secondary but supportive role in the overall evaluation.

For instance, pH stability ensures optimal microbial activity, while nutrients (NO₃⁻, PO₄³⁻) provide insights into eutrophication risks and compliance with reuse standards.

Overall, the weighting scheme confirms that the FWQI is primarily driven by indicators of organic pollution (BOD₅ and COD), supported by oxygen availability, while ancillary parameters refine the diagnosis and contextualize the effluent’s suitability for irrigation.

3.2. Justification of Choice of Triangular Functions

After comparing the different membership function shapes, the deviations observed on the FWQI remained very small (<1%). This confirms the robustness of the model and justifies the choice of triangular functions, selected for their simplicity of definition (only three parameters), intuitive interpretability, and wide use in scientific literature. This simplicity ensures efficient implementation while maintaining consistency with regulatory thresholds.

Figure 3 illustrates the membership functions of the triangular input and output. It enables one to visualize the distribution of values and their degree of membership in the studied system.

3.3. Descriptive Statistics of Water Quality Parameters

Before presenting the results obtained from the fuzzy inference system, it is essential to characterize the raw water quality data collected at the Tlemcen plant. This step provides a transparent overview of the variability of the measured parameters and sets the initial context of the treatment.

Table 4. Descriptive statistics of raw influent water quality parameters.

Parameter	Min	Max	Mean	Standard Deviation	Range
Temperature (°C)	7.39	25.75	16.27	4.72	18.36
COD (mg/L)	16.00	68.00	38.94	12.38	52.00
BOD5 (mg/L)	7.50	35.00	18.74	6.46	27.50
O2 (mg/L)	4.12	4.89	4.70	0.16	0.77
pH	7.39	7.73	7.53	0.09	0.34
NO3− (mg/L)	0.29	14.40	7.18	4.33	14.11
PO43− (mg/L)	1.90	10.30	5.36	2.06	8.40

summarizes the descriptive statistics (minimum, maximum, mean, standard deviation, quartiles, and range) for the main pollution indicators (BOD₅, COD, O₂, pH, NO₃⁻, PO₄³⁻, and Temperature). These values serve as a baseline prior to applying the FWQI and facilitate a clearer understanding of the actual influent conditions.

Descriptive statistics of the raw parameters (Table 4) reveal a high and variable organic load (mean BOD₅ = 195.77 mg/L; mean COD = 378.56 mg/L), with a COD/BOD₅ ratio ≈ of 1.93 indicating good biodegradability. Dissolved oxygen remains very low (mean = 0.84 mg/L), confirming the anoxic nature of the influent. Nutrients show contrasting behavior: nitrates are highly skewed with occasional peaks, while phosphates are relatively stable. pH remains constant around 7.8, and temperature reflects seasonal variations. These raw data highlight a polluted but biodegradable effluent, which justifies the use of a fuzzy index for a more robust assessment of water quality.

3.4. Temporal Analysis of FWQI Values (Annual, Seasonal, and Monthly)

In order to obtain an in-depth assessment and detailed explanation of the quality of the water at the level of the WWTP of Ain El Houtz, we opted for analyses at three time intervals: annual, seasonal, and monthly. This method promotes a comprehensive understanding of the fluctuations and trends, considering environmental elements and operational issues.

The annual review provides a consolidated view of the performance over an extended period of time, highlighting the significant changes in the quality of the water. The analysis of seasonal periods examines the impact of climatic factors such as temperature and precipitation on the effectiveness of the treatment, identifying the periods of vulnerability or the optimality of the system. Finally, the monthly assessment provides a more detailed and responsive assessment, revealing the short-term variations that can be related to one-off events such as accidental pollution, increases in hydraulic load, or technical malfunctions. This blanking time also allows for ensuring a rigorous, sensitive, and contextualized evaluation of the actual performance of the WWTP over the entire period studied.

3.4.1. Annual Evaluation

The annual FWQI values (

Table 5. Annual fuzzy water quality index (2020–2022).

Year	FWQI (%)	Class	Optimal Threshold (70%)	Critical Threshold (50%)
2020	85.6	Good	Higher	Higher
2021	50.0	Average	Less than	Equal
2022	86.1	Good	Top	Top

) highlight the contrasting performance of the Ain El Houtz WWTP between 2020 and 2022.

• 2020 and 2022: FWQI scores of 85.6% and 86.1%, classified as Good, demonstrate the plant’s ability to consistently produce effluent suitable for irrigation. These values exceed the optimal threshold (70%), confirming the robustness of the treatment process.
• 2021: In contrast, the FWQI dropped to 50%, exactly at the critical threshold. This indicates a systemic malfunction rather than isolated incidents. Effluent quality during this year was insufficient for safe reuse, exposing potential agronomic and health risks.

This sharp decline, framed by two optimal years, suggests a prolonged malfunction linked to a major technical failure.

3.4.2. Seasonal Assessment

Seasonal FWQI values (

Table 6. Seasonal assessment of the quality of the water by FWQI.

Year	Dry Season FWQI (%)	Wet Season FWQI (%)	Class	Optimal Threshold (70%)	Critical Threshold (50%)
2020	85.6	85.5	Good	Higher	Higher
2021	50.0	50.0	Average	Less than	Equal
2022	86.2	85.9	Good	Top	Top

) provide insights into the resilience of the WWTP under climatic variations, applying the framework for distinguishing environmental from systemic factors established in Section 2.3.7.

• 2020 and 2022: Both dry and wet seasons showed stable FWQI values above 85%, with minimal variation (<0.3%). Following the methodological framework, this seasonal stability indicates that the treatment process was resilient to climatic fluctuations (temperature, rainfall, dilution), ruling out environmental factors as primary drivers of performance variation during these years.
• 2021: FWQI remained fixed at 50% across both seasons. According to the criteria defined in the methodology, this uniform degradation, persisting through both dry and wet periods, points to internal and structural failures rather than to climatic causes.

3.4.3. Monthly Assessment

The monthly FWQI analysis (

Table 7. Monthly evolution of the fuzzy quality index (2020–2022).

Month	2020 FWQI (%)	2021 FWQI (%)	2022 FWQI (%)	Class of 2020	Class of 2021	Class of 2022
January	85.2	50.0	-	Good	Average	-
February	85.0	50.0	-	Good	Average	-
March	85.4	50.0	-	Good	Average	-
April	85.5	50.0	85.2	Good	Average	Good
May	-	-	-	-	-	-
June	85.6	-	85.0	Good	-	Good
July	85.3	-	-	Good	-	-
August	85.4	-	-	Good	-	-
September	-	-	-	-	-	-
October	-	-	86.3	-	-	Good
November	50.0	-	86.1	Average	-	Good
December	50.0	-	86.2	Average	-	Good

Note: “-” indicates unavailable data due to missing or excluded samples.

) provides a granular view of performance fluctuations.

• Late 2020: A sudden drop in November–December (FWQI = 50%) marked the onset of dysfunction.
• 2021: FWQI remained at the critical threshold from January to April, confirming a chronic failure.
• 2022: From April onwards, FWQI values returned to >85%, indicating successful corrective intervention and lasting recovery.

This monthly analysis reveals a clear three-phase trajectory: stable performance in early–mid 2020, followed by the onset of systemic malfunction in late 2020 (November–December), its persistence throughout 2021 (January–April, and beyond where data are available), and recovery from April 2022 onwards. This pattern satisfies the methodological criteria for identifying systemic failure: persistent deviation across consecutive months, independent of seasonal trends (Section 2.3.7). The timing aligns with operational reports indicating prolonged aeration system failure during this period. While the operators’ perspective and contextual explanations are examined in detail in Section 4.2, the present results establish the temporal continuity of the malfunction. During certain months, the FWQI classified the effluent quality as “Average.” These fluctuations can be explained by seasonal temperature variations, which likely affected bacterial activity and treatment efficiency, as well as occasional organic shock loads that temporarily increased influent COD and BOD₅ concentrations. Such operational and environmental factors contributed to short-term performance degradation and are reflected in the monthly FWQI outcomes.

3.5. Validation of FWQI by Comparison with WQI

The comparative results between FWQI and WQI (

Table 8. Comparative Table FWQI vs. WQI.

Year	FWQI (%)	FWQI Class	WQI	WQI Class
2020	85.6	Good	82	Good
2021	50.0	Average	55	Average
2022	86.1	Good	83	Good

) show overall consistency in effluent classification. In 2021, for instance, both indices classified the effluent as “Average.” This class corresponds to water quality that is acceptable but unstable: it does not meet the standards of “Good” quality and indicates an intermediate zone where fluctuations or occasional exceedances may compromise system reliability.

Nevertheless, the fuzzy approach (FWQI) proved more sensitive in detecting borderline conditions. FWQI yielded a value exactly at the critical threshold (≈50%), signaling a borderline situation, whereas WQI was slightly higher (≈55), which tends to smooth the perception of risk. This difference in sensitivity illustrates the methodological advantage of FWQI, which can highlight borderline conditions that the classical WQI does not distinguish as clearly.

3.6. Numerical Validation of FWQI Using RMSE

In addition to the qualitative comparison between FWQI and WQI, a numerical validation was performed to quantify deviations between the two indices. The root mean square error (RMSE) was calculated over the 2020–2022 period, providing an assessment of FWQI accuracy relative to the classical WQI.

$$\mathit{R}\mathit{M}\mathit{S}\mathit{E}=\sqrt{{\displaystyle \frac{\mathbf{1}}{\mathit{n}}}{{\sum }_{\mathit{i}=\mathbf{1}}^{\mathit{n}}({\mathit{y}\mathit{i}}^{\mathit{F}\mathit{W}\mathit{Q}\mathit{I}}-{\mathit{y}\mathit{i}}^{\mathit{W}\mathit{Q}\mathit{I}})}^{\mathbf{2}}}$$

(8)

• yi^FWQI = value estimated by the FWQI
• yi^WQI = reference value from the classical WQI
• n = total number of observations (here, 3 years: 2020, 2021, 2022)
• Application to the data (2020–2022):

  $$RMSE=\sqrt{{\displaystyle \frac{{(85.6-82)}^2+{(50.0-55)}^2+{(86.1-83)}^2}{3}}}\approx 3.98$$

The results show that FWQI and WQI lead to similar classifications (Good, Average, Good). However, the RMSE calculation (≈3.98) confirms that numerical deviations between FWQI and WQI remain low, validating the robustness of FWQI. Moreover, the fuzzy logic approach demonstrates enhanced sensitivity in borderline situations, further supporting its relevance for water quality monitoring.

4. Discussion

4.1. Robustness of the FWQI

As detailed in the sensitivity analysis (Section 2.3.4), FWQI values remained stable under variations in parameter weights and membership function shapes. This finding is consistent with [10,24], who demonstrated that fuzzy logic is particularly effective in handling uncertainty and continuous environmental data, unlike conventional indices based on rigid thresholds. The coherence of our results with classifications established in other contexts (rivers, groundwater) confirms the transferability and reliability of the methodology.

4.2. Diagnosis of the 2021 Malfunction and Comparison with Literature

Applying the distinction between environmental variability and systemic malfunction established in the methodology (Section 2.3.7), the 2021 performance degradation can be definitively classified as a systemic failure.

The FWQI clearly identified this prolonged malfunction in 2021. Data and observations indicate that the major failure was due to the prolonged shutdown of the aeration system. The main aerators were out of service for several months, leading to a critical drop in dissolved oxygen in the biological basins. This oxygen deficiency inhibited microbial activity responsible for organic matter degradation, causing an accumulation of BOD₅ and COD in the effluent. Consequently, the FWQI remained fixed at the critical threshold (≈50%) throughout 2021, confirming that the aeration system failure was the decisive factor behind treatment degradation. Nevertheless, this decline cannot be solely attributed to the technical malfunction, but was likely amplified by seasonal temperature variations, enhancing bacterial kinetics and intensified biological activity linked to organic loading. This combination of technical and environmental factors further explains the severity of the FWQI decrease in 2021.

The diagnosis of aeration failure in 2021 is supported by operational records documenting prolonged aerator shutdowns, combined with monitoring data showing persistent oxygen depletion and elevated BOD₅/COD levels. While no formal statistical correlation was applied, the convergence of operational evidence and FWQI classification provides a robust diagnostic framework.

This diagnosis satisfies both criteria established in Section 2.3.7: (i) the absence of seasonal variation in FWQI values ruled out climatic factors, and (ii) the persistence of degradation across consecutive months confirmed systemic malfunction rather than episodic disturbance.

This diagnosis is consistent with [23], who showed that fuzzy indices applied to groundwater more effectively detect systemic degradations than isolated parameter monitoring. Similarly, ref. [8] demonstrated that fuzzy logic indices provide stricter and more realistic classifications of river water quality, while [6] emphasized their relevance in overcoming the limitations of conventional indices and addressing systemic issues in complex water systems.

Recent work on the Maghnia WWTP [31] applied a statistical approach combining the Weighted Arithmetic Water Quality Index (WAWQI) and the Water Pollution Index (WPI), validated using Bland–Altman analysis. Their study revealed significant exceedances of standards at the outlet, particularly for ammonium and phosphates, indicating chronic system overload. The complementarity of WAWQI and WPI confirmed the low quality of treated water and the need for targeted optimization, especially for nutrient removal. Our fuzzy logic approach converges with these findings, emphasizing the ability of synthetic indices to detect structural failures and provide robust operational diagnostics.

Thus, the comparison between FWQI and WAWQI/WPI demonstrates that, despite methodological differences (fuzzy logic vs. weighted statistical indices), both approaches converge on the same conclusion: the necessity of integrated tools to identify malfunctions and guide optimization strategies for Algerian wastewater treatment plants.

4.3. Positioning Within Recent AI-Based Environmental Monitoring Advances

Recent advances in AI-based environmental monitoring have highlighted the potential of hybrid approaches combining fuzzy reasoning with machine learning and deep learning models. For instance, ref. [14] demonstrated the rapid growth of AI applications in environmental monitoring, while [15] proposed a graph-aware neural network integrating fuzzy reasoning for multi-modal data analysis. Similarly, ref. [16] demonstrated that integrating fuzzy logic with a BiLSTM network significantly improves prediction accuracy for water quality monitoring.

Within this context, our study contributes by applying a fuzzy water quality index (FWQI) specifically calibrated for wastewater treatment monitoring in Algeria. Unlike previous works, the FWQI was validated at multiple temporal scales (annual, seasonal, monthly) and compared with the classical WQI, providing both methodological novelty and practical insights for semi-arid wastewater management. This positioning situates our contribution within the broader trend of AI-enhanced environmental monitoring, while emphasizing the originality of applying fuzzy logic to wastewater treatment plants in Algeria.

4.4. Limitations and Perspectives

Several limitations must be acknowledged:

• Missing monthly data, reducing temporal resolution.
• Absence of microbiological parameters (fecal coliforms, E. coli, streptococci, etc.), which are critical indicators of effluent sanitary safety. Their exclusion limits the scope of the FWQI, as effluent classified as “Good” in physicochemical terms may remain unsuitable for agricultural reuse if microbial loads are high.

These limitations echo the concerns raised by [11] regarding both conventional and fuzzy indices, which may overestimate or mask failures when data are insufficient.

Future improvements should include:

• Integration of operational parameters (flow rate, sludge age, aeration efficiency) to develop a Fuzzy Performance Index, combining causes and effects.
• Addition of microbiological parameters to provide a more comprehensive evaluation aligned with international standards for wastewater reuse.
• Development of a predictive tool inspired by [32], enabling real-time management and anticipation of failures.

5. Conclusions and Recommendations

The evaluation of treated wastewater quality at the Ain El Houtz WWTP over the period 2020–2022, conducted through a fuzzy inference system, provided a clear characterization of temporal dynamics and enabled the detection of critical performance phases.

The multi-scale approach (annual, seasonal, and monthly) revealed stable effectiveness of the treatment process in 2020 and 2022, with FWQI values well above the optimal threshold. In contrast, 2021 represented a distinct disruption, with FWQI fixed at the critical limit, directly linked to the prolonged shutdown of the aeration system and the resulting drop in dissolved oxygen in the biological basins.

Comparison with other studies on the Maghnia WWTP confirms the relevance of fuzzy indices and integrated approaches in detecting structural failures and improving operational diagnostics. Beyond these findings, the study demonstrates the practical feasibility of applying FWQI to other wastewater treatment plants in Algeria and similar semi-arid climates. The methodology, based on expert-derived weights and calibrated membership functions, can be readily adapted to different operational contexts and regulatory frameworks, making FWQI a transferable and reliable tool for environmental monitoring and decision support. In practical terms, the findings underline the importance of integrating fuzzy-based indices into the routine monitoring of wastewater treatment plants. FWQI provides operators with a proactive diagnostic tool that facilitates early detection of malfunctions, supports informed decision-making, and contributes to sustainable management of water resources in semi-arid regions.

It is recommended to:

• expand the model to include operational parameters (flow rate, sludge age, aeration efficiency);
• strengthen automation in qualitative monitoring;
• train operators in interpreting fuzzy outputs for proactive management;
• generalize this approach to other treatment plants to develop predictive and intelligent tools for sustainable water resource management.