The materials used in this research are HCl 37% Sigma-Aldrich Merck KGaA Brand (Mr 36.5 g/mol), Commercial Gelatin Gelita Brand (Mr 90000 g/mol), Pluronic P123 Sigma-Aldrich Merck KGaG Brand (Mr 5800 g/mol), Methylene Blue Sigma-Aldrick Merck KGaA Brand (Mr 319.85 g/mol), and Iron (III) Nitrate Nonahydrate Sigma-Aldrick Merck KGaA Brand (Mr 241.86 g/mol).

Mesoporous iron oxide-carbon (MIC) nanocomposite was prepared by mixing ferric nitrate with P123 and gelatin. 19.5 mL of HCl 37% was diluted in 127 mL of water. Subsequently 4 grams of P123 were added to the HCl mixture using a magnetic stirrer and burette, stirred at 550 rpm at 40°C in a closed Erlenmeyer flask. Ferric nitrate nonahydrate (Fe(NO₃)₃.9H₂O) was weighed 16.83 grams and added to the mixture, followed by stirring at the same speed for 24 hours. This mixture was homogenized using an autoclave and then heated in an oven for 24 hours at 90°C an autoclave and then heated in an oven for 24 hours at 90°C. To obtain the precipitation, the mixture was neutralized with 20 mL of NaOH 5 M and filtered through filter paper. This precipitate obtained was dried in the oven for 24 hours at 100°C then calcined for 5 hours at 550°C. Samples were labelled as MIC-x, where x represents the gelatin:P123 weight ratio 0%, 1%, 5%, 10%, and 20% (w/w).

The synthesized samples were characterized using X-ray diffraction (XRD) Pananalytical (version PW3050/60), Shimadzu 21 Fourier-transform infrared spectroscopy (FT-IR) with 0.5–1 cm resolution. Scanning electron microscopy-Energy dispersive x-ray (SEM-EDX) with the JEOL JSM-700 capturing picture microscope on 15.0 kV voltage speed, Transmission electron microscopy (TEM), and Thermal gravimetric analysis (TGA).

250 mL of MB solution 20 ppm was prepared. Each samples was weighed 10 mg and added to MB solution. This mixture then homogenized using shaker in dark adsorption for 60 minutes then followed by photocatalytic for 90 minutes under the UV light. in photocatalytic process, the solution was taken 10 mL every 10 minutes. At the beginning, 10 mL of MB solution was taken and labelled as the initiate concentration (Co). Absorbance measurement conducted using UV-Vis spectrophotometer in 664 cm⁻¹ wavenumber. Degradation percentage has calculated using the followed equation (1) below:

After the 1^st degradation process, then the methylene blue loaded with iron oxide photocatalyst dried in a dessicator for 24 h. Then the membrane was dip into the 50 mL methanol solution for 48 h. Then the cycle repeated upon the iron oxide recovery. After the specific amount of experiment, the amount of dye absorbed for every cycle was measured using the UV-Visible Spectrophotometer then repeated these steps using ethanol.

A fuzzy graph was constructed to explore the relationship between the physicochemical properties of MIC and its photocatalytic activity under visible light. To start, a crisp graph was created based on the experimental data describing the physicochemical properties. Next, a fuzzy inference system (FIS) model was built in MATLAB with four input variables and one output variable. The input variables included surface area, porosity, particle size, and amount of carbon, while the output variable was photocatalytic activity. Triangular membership functions (MFs) were applied to all input variables, and the output variable. In the process of fuzzification, membership functions (MFs) were defined for all input and output variables in the fuzzy inference system. A membership function maps each crisp input value into a degree of membership ranging from 0 to 1, representing the extent to which the input belongs to a fuzzy set (e.g., low, medium, high).

Several types of membership functions are commonly used in fuzzy systems, including triangular, trapezoidal, Gaussian, sigmoidal, and bell-shaped functions. In this study, triangular membership functions were chosen due to their simplicity, computational efficiency, and suitability for systems with limited data. Compared to Gaussian or bell-shaped functions, which require more parameters and can lead to overfitting, triangular functions offer a clear central tendency and are easier to interpret and tune. This makes them particularly advantageous in experimental models involving a small number of observations [22, 23].

Each triangular membership function is defined by three parameters: a (lower limit), b (peak or center), and c (upper limit). These parameters determine the support and the shape of the function. The triangular function f(x) for a variable x is mathematically represented as follows:

The compact versions of the previously described functions are as shown in equation 4.2, with parameters a and c at the triangle’s base and parameter b at the top.

This study utilized the Mamdani fuzzy inference system, employing a standard three-step process: fuzzification of input variables, rule evaluation and aggregation of rule outputs, and defuzzification. In the first step, the membership functions assigned degrees to the crisp (numerical) input data, determining the appropriate fuzzy sets. In the second step, the fuzzy inputs acted as antecedents in the fuzzy rules. When a rule contained multiple antecedents, fuzzy operators (AND, OR, and NOT) processed them to generate a single output value for each variable. In the third step, aggregation combined all the rules to produce a single fuzzy output set. Various inferencing techniques, such as max-min, max-product, and sum-product, were tested, with max-min proving to be the most effective for maintaining suitable constraint propagation. Finally, during defuzzification, the aggregated output was converted into a crisp value, using the center of gravity (COG) method in this study. Following the development of the fuzzy inference system model, a sensitivity analysis was conducted to determine the membership value based on the proposed model. The membership value represented the dominant properties influencing the photocatalytic activity of the synthesized materials under visible light. Finally, a fuzzy graph was created to illustrate the relationship between the input and output variables in the physicochemical properties-photocatalytic activity relationship of the MIC nanocomposites. Details Equation for MSE, RMSE, ARE, AARE, SD and R² (Eqs. 4–9) were computed to confirm the fuzzy model’s acceptable performance

Mean squared normalized error, MSE.

Root mean squared error (RMSE).

Average relative error (ARE).

Absolute average relative error (AARE).

Standard deviation (SD).

Correlation coefficient (R²).

The results of observations using Fourier Transform Infra Red (FT-IR) can be seen in Fig. 1 with detailed data provided in the Table 1 for reference. The absorption bands at wavenumber range 3200 – 3720 cm⁻¹ and 1640 cm⁻¹ are a vibrational mode of stretching and flexing O-H in absorbed water and may be bound to the surface of iron atoms [26]. From each sample it can be seen that the wide peaks are formed, thus the amount of water absorbed is still in the range of sufficient volume. Along with the addition of gelatin variations, it produces samples with an increasing oxygen content. This was also confirmed using EDX characterization with the composition of element mapping on samples in one spot which showed that samples with high gelatin variations (ranging from 10 – 20%) showed an increase in the mapping composition of oxygen element.

The absorption of iron oxide (iron oxide-carbon nanocomposite) formed can be observed at peaks of 431 – 519 cm⁻¹. It was stated that the peaks formed were at 459.23 cm⁻¹ and 518.54 cm⁻¹ in samples without gelatin.. IR absorption bands in the range of 550 – 630 cm⁻¹ correspond to Fe – O bond vibrations at tetrahedral and octahedral sites, indicating the formation of spinel structures [26]. The aromatic C-O stretching was observed at 1060 and 1241 cm⁻¹, CH₂ symmetric and asymmetric stretching show at 2875 and 2925 cm⁻¹, respectively. This has also been confirmed using TEM characterization which shows that molecules with a spinel shape are formed. But as the variety of gelatin increases, the absorption formed shifts to 500 – 850 cm⁻¹. The peaks that form on the spectrum are getting sharper along with the gelatin addition. It can be concluded that, iron oxide is formed increasingly pure.

Fig. 1 (below) illustrates the x-ray diffractogram of each sample with a range 2θ from 5 – 90°. The entire sample shows sharp peaks on 2θ which is located between 30° to 40°. This main peak indicates the presence of iron oxide-carbon nanocomposite peaks (a-Fe₂O₃) which is crystalline (not amorphous). Based on ICDD Card number 33-0664) the peak of iron oxide-carbon nanocomposite peaks will be visible on 24.16°, 33.12°, 35.63°, 40.64°, 49.47°, 54.08°, 57.42° correspond to (012), (104), (110), (113), (024), (116), and (018) [33]. However some linear peaks with the peaks of maghemite crystals appear, according to JCPDS numbers 39-1346 peaks on maghemite appeared on 2θ = 18.3°, 30.2°, 35.45°, 43.32°, 53.81°, 57.22°, 62.98°, 74.54° correspond to (111), (220), (311), (400), (422), (511), (440), (533) [34]. The main peak of each sample is located not far from the peak of iron oxide-carbon nanocomposite at 2θ = approximately 31.6°. The transformation of maghemite to iron oxide-carbon nanocomposite occurs due to the oxidation of Fe²⁺. Fe²⁺ reacts with oxygen at high temperatures, producing more Fe³⁺ ions [35]. Thus, it can be concluded that the formation of half maghemite occured due to the imperfection of oxidizing Fe²⁺ ions to form iron oxide-carbon nanocomposite crystals. Based on Table 2, the percentage of crystallinity is in the range of 60 – 95%. The sample with the lowest crystallinity is the MIC5% sample which is 62.5% and the highest is MIC1% which is 95%. The formation of iron oxide crystals becomes better and more regular with the addition of gelatin. This has been supported and confirmed by SEM data. The sample histogram with the gelatin addition can be seen more regularly.

The morphology of the sample is seen in the form of irregular agglomerates (Fig. 2 (left)). This irregular pattern can be caused by the annealing process in the sol-gel method [36]. The particles in the sample are spinel shaped, the size distribution of particles formed ranges from 1 – 50 mm. The smallest particle size is no gelatin addition sample, which is 1.851 mm while the largest is a sample with the addition of 10% gelatin, which is 5.4745 mm. The sample morphology formed is an agglomerate because an agglomeration occurred along with the addition of gelatin. There are many active groups such as carboxyl functional groups, amino, and hydroxyl groups in gelatin. The OH functional groups in Pluronic P123 and NH in gelatin have a tendency to interact electrostatically with iron precursors due to their affinity [31, 32]. Therefore, both molecules can direct the structure of the material. In making templates, gelatin will interact with P123 to form micelles [39]. These micelles are then used as templates for the formation of porous materials.

The samples’ surface elemental composition was studied using energy dispersive X-ray spectroscopy shown in Table 2. Fe and C peaks can be observed in the spectra of MIC1%, b. MIC5% and MIC 10%. These results support the production of the iron oxides carbon composite. N as side product of undecomposed gelatin was not detected in any sample and carbon content increased from 4.68% to 22.03% as increasing gelatin content, implying that carbon from gelatin was incorporated into the iron oxide during heat temperature treatment. The carbon peak is attributed to mesoporous iron oxide covered by carbon. The presence of Fe, C, and O peaks verified the effective synthesis of iron oxide carbon composites. The spectra also indicated Fe and C peaks, which are crucial criteria for photocatalysis.

Iron oxide synthesized using gelatin has a larger particle size. This is due to the formation of stable micelles between P123, gelatin, and iron. When dissolved in water, ferric nitrate will be hydrolyzed and form iron oxide. Pluronic P123 plays a role in preventing iron oxide from hydrolyzing by replacing nitrate ions in ferric nitrate with PEO. Gelatin as a natural template then forms an ester bond between the gelatin carbonyl group (−COO−) with the hydroxyl group (−OH) in PEO to stabilize PEO. During synthesis, the NH₂ group on the gelatin will be protonated then forms an anionic surfactant with a positive charge. This positive charge can increase the size of the micelle which causes an increase in particle size [38]. Based on Fig. 2 (left), there are two possible way to explain this research. According to EDX results, samples with no gelatin,1% gelatin and 5% gelatin addition contain 12–14% oxygen composisition. In addition, this data supported by SEM results which indicates the large form of Fe in spinel shape. Due to the raise of Fe atoms, it forms the larger shape. For the fewer gelatin addition samples, the hydrophobic properties of P123 and Gelatin will form micelles and it would attract the Fe atoms to bond with another Fe atoms. So it will form a larger shape after the hydrothermal process. After the calcination, it would remove the template so the iron oxide remains. But as the gelatin addition raised, the reaction mechanism illustration would follow the second way, the hydrophilic properties of P123 and gelatin would form micelles and trapping the oxygen atoms to bond with iron atom in a small shape after hyrothermal process. After the calcination, the template removed and the smaller iron oxide particles remains. It was supported by the SEM results which indicates the smaller shape of iron oxide particle.

Based on the TEM result on Fig. 2 (center), the structure formed is a spinel shape. The resulting image has a dark and light effect. After measuring the particle size using ImageJ software, it can be determined that the diameter of the surface formed is 23 nm. It is in the range of 13 – 23 nm. Due to limitations in measuring other samples, it is considered that the morphology of MIC1% can represent the entire sample. This has been confirmed by the characterization of N₂ Adsorption-Desorption which the diameter range is 13 to 19 nm. Fig. 3 also clarifies the correlation between the SEM, TEM, and N₂ adsorption–desorption data, thereby supporting the development of the flowchart depicting the structure–activity relationship of the MIC composites using a fuzzy logic graph.

The sample with gelatin addition adheres to type IV isotherm. Based on Fig. 3 (above), this mesoporous Fe₂O₃ material has a radius range of 0 – 170 nm. IUPAC classified type IV isotherm as a characteristic of porous materials characterized by the appearance of hysteresis loop. This loop indicates the amount of volume of N₂ gas adsorbed and desorbed differently. This loop hysteresis can be observed in the relative pressure (P/Po) range of 0.8 – 1.0. In Table 3, each iron oxide sample has a pore diameter in the range of 3 – 18 nm. Along with the gelatin addition, the surface area of the sample will increase. This is proven where the surface area of MIC0% smaller than samples with gelatin addition. The surface area of MIC0% is 1.707 m²/g while samples using gelatin have a surface area with a range of 16 – 27 m²/g. The addition of gelatin has a great influence in pore formation based on Fig. 3 (below). As gelatin is added, the total pore volume will tend to increase, the difference between MIC0% sample is 0.004379 cc/g while samples with 1% gelatin has a total pore volume of 0.07232 cc/g. Pore diameter in materials without gelatin is in the range of 3 nm while materials with gelatin have pore diameters in the range of 3 – 18 nm. The gelatin addition forms more amine groups (−NH₂) which pull the pore outward until it is wider and deeper. Based on Table 3, material with no gelatin have a mesoporous volume of 0.004 cc/g while materials with gelatin have a mesoporous volume in the range of 0 – 0.2 cc/g. The material with 10% gelatin has a larger surface area, pore diameter, and pore volume. Sample with 10% gelatin have catalyst characteristics with wider and deeper pore diameters. Thus, sample with 10% gelatin are expected to provide more optimal MB adsorption performance.

The TGA analysis curve formed looks similar. The TGA curve of the MIC1% is similar to MIC5%. The TGA curve of the MIC10% is similar to MIC20% while the TGA curve of MIC0% has only a slight resemblance to other samples. TGA analysis shown in Table 2, showed that the first weight loss begins in the range of 50° – 100°C, at this temperature the entire sample begins to lose weight, this weight loss is related to water bound to the surface of the material, and also the remaining solvent that has not been maximally lost [34, 35]. Furthermore, at temperatures of 120° – 420°C, MIC1% and MIC5% samples experienced weight loss of 1.024% and 0.433% respectively. This loss occurs due to the formation of (γ-Fe₂O₃) to (α-Fe₂O₃) and the transformation of goethite to iron oxide-carbon nanocomposite [41]. Continued at a temperature of 700°C there was a weight loss in the entire sample in the range of 4–8%. This weight loss occurs due to the formation of iron oxide-carbon nanocomposite to wüstite (FeO) [42]. There is an anomaly in the TGA curve of the MIC0% sample. Where the curve shows in the range of 100° – 700°C seen to have an increase in mass. This can occur possibly due to the formation of oxide layers [43].

The heating process of the MIC materials resulted in varying degrees of mass loss across the samples, as indicated by the thermogravimetric data. The initial mass loss in the low-t mperature range (0–100°C) corresponds mainly to the evaporation of physically adsorbed water, while the medium-temperature range (120–420°C) reflects the decomposition of organic residues such as gelatin and the P123 template. At higher temperatures (>700°C), the mass reduction is associated with the degradation of remaining functional groups and partial restructuring of the silica framework. These variations in thermal decomposition behavior influence the surface area and pore distribution of the materials, which subsequently affect their photocatalytic performance. The sample with moderate mass loss, MIC10%, exhibits an optimal balance between thermal stability and the presence of active surface sites, and is therefore predicted to show the highest methylene blue photodegradation efficiency among the tested catalysts.

The gelatin addition leads to more weight loss. Sample without gelatin tended to lose less weight compared to other sample. Gelatin plays a role in donating oxygen atoms which later bind more water. The remaining oxygen atoms present in iron oxide will also be released at temperatures above 700°C to form wüstite (FeO), as a result of high pressure resulting in a rearrangement of iron oxide-carbon nanocomposite compounds to wüstite (FeO). In the context of this study, exploration was carried out on the effectiveness of MB photodegradation using Mesoporous Fe₂O₃ on variations of gelatin. This study aims to identify the most optimal variation of gelatin photocatalyst in producing hydroxyl radicals (·OH). Hydroxyl radicals (·OH) have the potential to degrade certain organic compounds. The interesting process is the photodegradation of MB from waters into materials that are considered low toxic, namely CO₂ and H₂O [44]. Hydroxyl radicals act as oxidizing agents in degrading MB [45]. Based on Fig. 11, it can be seen that the degradation process of methylene blue is relatively increasing at 0 to 90 min. At 0 – 90 minis a photocatalysis process that uses UV irradiation. UV light has active role in the process of degradation of methylene blue. Because the longer the irradiation time, the color of the methylene blue solution becomes more faded, so it can be assumed that the concentration of methylene blue dye in the solution is decreasing and UV light becomes easier to reach the photocatalyst.

The reaction mechanism of methylene blue degradation is that electrons in the Fe₂O₃ photocatalyst will be excited from the valence band to the conduction band when exposed to UV light. These electrons then make holes (h⁺). Then the oxygen adsorbed on the surface of the photocatalyst traps these electrons and converts them into super oxide radicals. This super oxide radical then interacts with H₂O to create radical hydroperoxide (HO₂^·) and radical hydroxide (OH^·). Simultaneously, holes formed from previous UV light will react with H₂O which also produces hydroxide radicals (OH^·). These hydroxide radicals act as strong oxidizing agents to degrade methylene blue in the following mechanism [46].

(degradation products)

In the dark adsorption process, for samples MIC1% – MIC20% degradation remains contant without sudden increases. However, in MIC0% sample, the adsorption process can produce a methylene blue degradation percentage of up to 30% for the first time. This is due to technical issue where the dark adsorption step should be performed without light. However, in this process, external light entering compromises the effectiveness of the dark adsorption process. The dark adsorption process homogenizes the soltion and achieve equilibrium, enabling faster degradation of methylene blue during photocatalysis. The degradation process become faster because some of these methylene blue molecules are trapped in the pores of Fe₂O₃, making it easier for UV light to pass to the hole in the photocatalyst. In addition, as the irradiation time increases, the Fe₂O₃ photocatalyst absorbs higher photon energy so it will be easier to degrade methylene blue.

Based on Fig. 4 which shows the highest degradation efficiency is the MIC10% sample, which reaches 96.23%. This is indeed predicted from the characteristics of a good material. In the EDX characterization, the oxygen composition in the MIC10% sample is more than other samples, this is also confirmed by FTIR characterization which detects the presence of O-H groups in the wide range of 3300 cm⁻¹. The presence of the O-H group plays important role to produce hydroxyl radicals which are strong oxidizing agents that are able to reduce organic pollutants such as methylene blue to become products with low toxicity, namely CO₂ and H₂O [44]. The most effective sample in degrading methylene blue dye is Fe-G with a ratio 1:0.1 w/w of P123 and Gelatin or MIC10%. This is supported by good characterization data, starting from the results of FTIR, MIC10% is proven to have a iron oxide-carbon nanocomposite group, the XRD MIC10% results show the crystallinity formed still can maintain its crystal shape so this MIC10% crystal still has crystallinity of 89%, this material has a good crystallinity. In addition, on the SEM histogram, the MIC10% sample shows that the diameter of the MIC10% particle is 5.47 mm. This size is larger than other materials that are only in range 1 – 4.6 mm. Moreover, the particles are well distributed, which is apparent from the consistent pattern displayed in the histogram. The BET results also shows the largest sample pore surface area is MIC10%, which reached 26.922 m²/g followed by deep pore. The TGA results, the MIC10% sample still has good thermal stability. And in photocatalytic test, MIC10% sample is able to work effectively in providing a source of electrons that can convert oxygen into oxide radicals which play a role in increasing hydroxide radicals in degrading methylene blue dyes. Thus it can be concluded that the better photocatalytic activity sample is MIC10%. This conclusion can be based on the results of the characterization of MIC10% samples and their good photocatalytic activity to degrade methylene blue dye

The mesoporous iron-carbon nanocomposite using P123-Gelatin as a template for photodegradation of methylene blue has shown significant efficiency, which can be attributed to three primary factors: surface area, particle size, and porosity. Each of these factors plays a vital role in the degradation process, and their interdependence creates a synergistic effect that enhances the overall performance of the nanocomposite. Surface area is crucial in determining the number of active sites available for methylene blue molecules to adsorb and undergo degradation [15, 41]. A larger surface area provides more interaction points between the dye and the catalytic material, facilitating a more efficient photodegradation process [42, 43]. The high surface area of mesoporous materials allows for greater exposure to light and better adsorption of methylene blue molecules, resulting in higher degradation rates [44, 45]. Particle size is directly related to surface area [15]. Smaller particles not only increase the available surface area but also improve the efficiency of photogenerated charge carriers by reducing the recombination of electrons and holes. In our study, reducing particle size led to a substantial increase in photocatalytic activity. Smaller particles expose more catalytic sites, enabling faster reaction rates and more efficient degradation of methylene blue molecules. Porosity, on the other hand, enhances the material’s ability to transport methylene blue molecules to the active sites within the nanocomposite. A highly porous structure allows for better diffusion of the dye molecules into the internal regions of the material, maximizing the utilization of the catalytic surface [52]. Higher porosity facilitates mass transfer, which can enhance surface reactions and effectively reduce charge recombination, hence increased the photocatalytic activity [53]. The synergy between surface area, particle size, and porosity plays a critical role in optimizing the performance of the nanocomposite. The relationship between surface area and particle size ensures that smaller particles with larger surface areas provide more active sites for photodegradation [53]. Meanwhile, the combination of surface area and porosity allows methylene blue molecules to diffuse more efficiently through the material, reaching deeper into the nanocomposite. This ensures that the photocatalytic process occurs throughout the entire structure, not just on the outer surface. Additionally, the interplay between particle size and porosity ensures that smaller particles allow for better diffusion and access to the inner catalytic sites, resulting in a more effective degradation process [46, 47]. In conclusion, the interaction between surface area, particle size, and porosity creates a powerful synergy that significantly enhances the photocatalytic degradation of methylene blue using mesoporous iron-carbon nanocomposites. These factors work together to maximize adsorption, improve diffusion, and optimize the reaction kinetics, making the nanocomposite an efficient material for environmental remediation. The results of this study suggest that further tuning of these factors could lead to even more effective materials for industrial and environmental applications [46].

Regeneration process conducted using the methanol and the ethanol. Based on the graph above, using methanol has an effective way to regenerate the system. The percentage of removal efficiency using methanol decreased gradually. On the 1^st cycle, the percentage or methylene blue removal is 92.65%. It is considered high enough after regeneration process. Then start to decrease more to 90.74% on the 2^nd cycle, then 85.33% on the 3^rd cycle, and 82.14% on the 4^th cycle. On the 4^th cycle, the percentage of removal efficiency still in 80% range. On the other side, the percentage of removal efficiency using ethanol also decreased gradually. On the 1^st cycle, the percentage of removal efficiency of methylene blue is 91.38%. It has considered high however not as high as methanol result. Then start to decrease more to 87.56% on the 2^nd cycle. It has different result from methanol, since methanol solution still defend the percentage of removal efficiency in a range of 90%. Then it decreased more to 82.14% on the 3^rd cycle and 78.64% on the 4^th cycle. These results has low effectivity compared with methanol.

As shown in Fig. 4, the photocatalyst regenerated with ethanol maintained higher removal efficiency (82.14% after four cycles) compared to methanol (78.64%). This difference is attributed to the stronger polarity and hydrogen-bonding ability of ethanol, which enhances desorption of adsorbed dye molecules and intermediate species from the catalyst surface without excessively altering the surface hydroxyl groups. In contrast, methanol’s smaller molecular size and higher volatility may lead to partial surface dehydration and weaker solvation effects, resulting in less effective regeneration and slightly lower catalytic activity. Therefore, the superior regeneration performance of ethanol suggests more efficient surface reactivation and preservation of the mesoporous structure, consistent with its moderate solvent–catalyst interaction strength.

To highlight the novelty of this work, Table 3 summarizes recent studies on common photocatalytic systems. Compared with TiO₂, ZnO, and Fe₂O₃-based composites, the MIC10% nanocomposite exhibited the highest degradation efficiency (96%) under visible light, indicating enhanced surface reactivity and charge transfer due to the synergistic Fe–SiO₂ interface. This comparison emphasizes the competitiveness of the MIC system in both performance and stability.

In order to construct a fuzzy logic Mamdani system, logical thinking related to photocatalysis is carried out by the experts. The inputs of physicochemical properties that have a significant impact on the photocatalytic activity were selected. A crisp graph that represents the relationship between the 4 physicochemical properties of MIC and the photodegradation of MB was constructed, as shown in Fig. 5.a For fuzzy logic analysis, 5 photocatalysts were synthesized by varying P123 and gelatin composition to correlate physicochemical properties with photocatalytic activity. The physicochemical properties are represented as graph vertices, and the input-output relationship variables are used as graph linkages (e_i). The links were referred to as edges for each of the variables studied.

Fig. 5b illustrates the fuzzy inference model of the input variables and photocatalytic activity. The membership functions for input variables (surface area, porosity volume, amount of C and particle size) and output variable photocatalytic activity were low, medium, and high. All input and output variables were given triangular membership functions (MFs). The max-min inference approach was the most effective method in this study because it presented a suitable and expressive setting for constraint propagation. The defuzzification process continued in the last stage using the aggregated outputs. The defuzzifier then converted them to a crisp integer. In this study, the center of gravity approach (COG) was implemented in the defuzzification methods. A total of 8 rules were developed to show the relationship between the input and output variables. The rules were constructed using experimental data from the physicochemical properties and photocatalytic activity. The number of fuzzy rules was limited to eight to maintain model simplicity and avoid overfitting, given the small number of experimental samples. These rules were selected based on observed trends in the data and expert knowledge. The correlation coefficient (R²) of 0.9135 demonstrated an acceptable agreement between the fuzzy data and experimental data (Fig. 5c) Furthermore, several important parameters such as mean squared normalised error (MSE), root mean squared error (RMSE), average relative error (ARE), absolute average relative error (AARE), standard deviation (SD), and correlation coefficient (R²) were computed to confirm the fuzzy model’s acceptable performance. The values of MSE, RMSE, ARE (in%), AARE (in%), SD (in%), and R² derived from the fuzzy model of input-output variables are shown in Table 8. The results validated the fuzzy model’s ability for predicting MB photodegradation using mesoporous Fe₂O₃/TiO₂ heterostructures. Table 3 presents the list of all experimental and predicted fuzzy data with the full information of four input variables in each run. It summarizes the surface area (v₁), porosity (v₂), particle size (v₃), and carbon content (v₄), and the photocatalytic activity (v₅).

Fig.5d-5e illustrates the relative importance of each factor of physicochemical properties to photocatalytic activity. It is clearly observed that the amount of Fe influenced the photocatalytic activity by 35 % in comparison to the other three assessed input variables. A sensitivity analysis was performed in the fuzzy model to predict the dominant factors of physicochemical properties in predicting MB’s photocatalytic activity. This sensitivity analysis was performed for each input variable individually, while keeping the other input variables constant. This was done using a One-Variable-At-a-Time (OVAT) method, where each variable was varied across its full fuzzy membership range (low–medium–high), while others were fixed at their medium values. The relative change in the output was normalized to determine percentage influence. In this study, each input variable has a distinctive impact on the output variables. Fig. 5d–5e illustrates the relative importance of each physicochemical factor contributing to photocatalytic activity. It is clearly evident that both particle size and porosity exerted the greatest influence, accounting for approximately 35% of the overall effect compared to the other two evaluated input variables. As demonstrated in Fig. 5d–5e, the surface area had the lowest sensitivity to photocatalytic activity (8 %) compared to the other variables affecting photocatalytic activity.

The fuzzy graph was constructed to represent the relationship between the physicochemical properties and photocatalytic activity, as shown in Fig. 5d–5e The membership values calculated using the sensitivity analysis results. A sensitivity analysis was determined in the fuzzy model to predict the dominant factor of physicochemical parameters that affect the efficiency of photocatalytic activity. This sensitivity analysis was conducted separately for each input variable, while the other input variables remained constant. In this analysis, each input variable had a significant effect on the output variables. Fuzzy graph type III is utilized in the fuzzy graph illustration.

The fuzzy inference model, based on Mamdani logic and triangular membership functions, effectively captured the nonlinear relationships between structural properties and photocatalytic activity. Beyond providing accurate predictions (R² = 0.91), the model offered valuable insights into the relative contributions of individual physicochemical parameters. In particular, the sensitivity analysis revealed that carbon content and particle size were the most influential factors affecting performance, offering practical guidance for future optimization of photocatalyst design. These findings highlight the utility of fuzzy logic as a powerful decision-support tool in materials research, especially when conventional linear models fall short in handling uncertainty and complexity.