1 Introduction

Groundwater is a precious source of freshwater storage for human survival worldwide. It is considered a pure source of freshwater and other surface water storage [1, 2]. In the globe, almost 65% of groundwater is taken for drinking, 20% for livestock and irrigation, and 15% for industry and mining from whole extracted groundwater [3, 4]. According to WHO, almost 80% of the health risks are related to impure drinkable water use [5].

Iran’s climatic and geographical characteristics, precipitation with the Mediterranean regime, and its different topographical position provide the environment for water infiltration to the ground. These agents, in addition to the leakage of surface water, have underlined the matter of groundwater in Iran. About the fact that the volume of the groundwater is minimal and inadequate, protection and management of these resources are very important. Also, in recent years, industrial and agricultural development has led to groundwater pollution and reduced the quality of this precious resource [6].

In addition, failure to check the quality of groundwater sources may cause their contamination to remain hidden and lead to the occurrence of diseases in humans, such that high nitrate concentrations in drinking water cause cyanosis in infants, respiratory disorders, digestive diseases, and cancer types [7]. A high concentration of chloride gives the water a salty taste [8] or may cause cancer, abortion, eye, brain, and nerve diseases, or a high concentration of sodium may lead to heart problems in adults, neuroglial damage in young children [9] or high water hardness causes high blood pressure, Arteriosclerosis and Sudden death of the Kidney and Bladder Stones in Susceptible individuals, as temporary or permanent atopic eczema [8].

Therefore, due to the lack of groundwater resources and the importance of maintaining the health of the residents of the region, the investigation of the drinking quality and the classification of groundwater resources in the Northern Dezful Andimeshk has become doubly important and has been addressed in this research. Water field researchers have conducted extensive studies in the field of assessing the quality [10, 11] and vulnerability of groundwater [12, 13]. Some researchers have used deterministic methods such as the Schoeller diagram [14,15,16,17,18,19], and the Water Quality Index (WQI) [5, 20,21,22,23], and each has reached considerable and valuable results.

Assessing the quality of groundwater is a difficult task due to inherent uncertainties in the sampling and analysis stages. Artificial intelligence methods, especially fuzzy inference systems, have proven effective in evaluating groundwater quality in uncertain and intricate hydrogeological systems, which, in addition to reducing uncertainties, combine the advantages of traditional methods [24]. Due to the ability of the fuzzy method to reduce uncertainties and its other advantages, some other researchers have tried to combine or compare the traditional methods with the fuzzy inference system so that a group of researchers have used both the drinking water quality index and the fuzzy inference system to compare or combine the results and have better and acceptable results. They have achieved more than the previous obedience [5, 24,25,26,27,28,29,30].Groundwater quality evaluation has been studied extensively using deterministic and fuzzy methods, or a combination of both. However, there have been few studies comparing the Schoeller and fuzzy methods when assessing drinking water quality. This research aims to address this gap by conducting a comparative evaluation of these two methods for assessing drinking water quality in Northern Dezful-Andimeshk. Notably, this is also the first time the fuzzy method has been used to evaluate drinking water quality in this region.

2 Materials and methods

2.1 Sampling and laboratory analysis

On 30th October 2020, 16 samples of groundwater were taken from different parts of the plain. For sampling, polyethylene plastic bottles were used to check groundwater quality in the Northern Dezful-Andimeshk Plain. The Electrical Conductivity (EC) and pH were measured using digital conductivity meters. So the samples were transferred to the Khorramabad hydrology laboratory and concentration of Calcium (Ca2+), Magnesium (Mg2+), Bicarbonate (HCO3−), Chloride (Cl−), Sodium (Na+), Sulfate (SO42−), Nitrate (NO3−), Total Hardness (TH), and Total Dissolved Solids (TDS) based on standard methods American Public Health Association (APHA) [31] were measured. The Ca2+, HCO3−, Cl− and TH were analyzed by volumetric methods. Mg2+ was calculated from TH and Ca2+ contents. Na+ was determined by flame photometer, SO42− was estimated using the colorimetric technique. NO3− was determined by spectrophotometer. To check the accuracy and precision of the results, spiked and duplicate samples were used, and finally, to check the overall accuracy of the obtained data, the ion balance calculation method was used, and samples with a balance error of more than 5% were reanalyzed until their error be reduced to less than 5%. The results of the laboratory analysis are given in Table 1.

Table 1 Results of laboratory analysis for groundwater samples of Northern Dezful- Andimeshk plain
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After these steps, to evaluate and zone the groundwater in the region in terms of drinking water quality, the standard and logarithmic Schoeller diagram in the GWW software environment then was used Mamdani Fuzzy system in the MATLAB software environment, and finally, the results of both methods were used for the zoning of the area from the opinion drinking of view was done using Arc GIS 10.5 software.

2.2 Study area

Northern Dezful Andimeshk study area, with a total area of 475 km2, is located between Dezful and Andimeshk cities, and hydrogeological, it is considered one of the large Karun sub-basins. In this plain, the primary source of drinking water is groundwater sources. Field operations were carried out in October 2020, and 16 samples were taken from the groundwater sources of the understudied area to investigate the region geology. The concentration of Calcium (Ca2+), Chloride (Cl−), Magnesium (Mg2+), Carbonate (CO32−) and Bicarbonate (HCO3−), Sodium (Na+), Nitrate (NO3−), and Sulfate (SO42−) ions, TH (Total Hardness), and TDS (Total Dissolved Solids) were then determined. After visiting and getting to know the geological phenomena, the geological map of the Northern Dezful-Andimshek Plain was prepared based on the 1/250000 map of Khuzestan. In terms of stratigraphy, the sediments of this plain include Quaternary alluviums, which are mainly created from the erosion of the Bakhtiari formation conglomerate (Paleocene) and, anhydrite and marl Aghajari formations (Pliocene and Miocene) are located around the aquifer to a small extent and interlayered with the Bakhtiari formation. The base map and sampling locations are shown in Fig. 1.

Fig. 1
figure 1

Base map and sampling points of Northern Dezful—Andimeshk Plain

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3 Theory

3.1 Schoeller deterministic method

In water studies, a method that classifies water quality based on the concentration of some desired element is called a deterministic method, such as a Schoeller diagram. In this diagram, the concentrations of ions are plotted on logarithmic axes with the same scale, then the points on the axes are connected by straight lines. This diagram works well in terms of speed of operation, ease of comparison and showing a large number of samples in one sheet and is widely used in Iran [32]. The basis of this diagram is Schoeller standard [33], which classifies drinking water quality into six groups based on the concentration of Na+, Cl− and SO42− parameters, TDS and TH. These six groups are classified as good, acceptable, inappropriate, bad, can be consumed in situation emergency, and non-drinkable, and are given in Table 2.

Table 2 Classification of drinking water quality based on Schoeller standard
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Parameters HCO3−, Cl−, Ca2+, Mg2+, SO42−, Na+, TH and TDS are given to GWW software (Ground Water software for Windows) as inputs, and the software also generates the evaluation of the quality of water as output of Schoeller diagram to draw the Schoeller diagram. GWW is a comprehensive software program in the Excel environment and can draw hydrochemical diagrams, including the Schoeller diagram. The advantages of using this software are reducing manual calculations, increasing the accuracy and precision of calculations, organizing large volumes, high information, and quality graphic.

3.2 Fuzzy method

Fuzzy Inference Systems are applicable in three types: Mamdani Fuzzy Logic (MFL), Larsen Fuzzy Logic (LFL), and Sugeno Fuzzy Logic (SFL). Their main difference is in their output type. In SFL, the outputs are linear, but in the other two types, they are non-linear. Also, in terms of efficiency, two kinds of Sugeno and Larsen are mostly used for complex mathematical calculations and control systems, but Mamdani system is mostly used for processing and estimation of parameters and has high interpretation power [34]. Therefore, the Mamdani Fuzzy Logic system was used in this research.The fuzzy inference system transforms human reasoning into mathematical functions using fuzzy rules (If–Then). This system generally consists of four main parts: fuzzification, fuzzy rules, fuzzy inference engine, and defuzzification. Fuzzification is a process that converts the desired parameter values for inputs and outputs into linguistic variables required for the fuzzy rules stage by defining a membership function for inputs and outputs. Fuzzy rules: in fuzzy systems, a series of fuzzy rules creates a connection between model inputs and outputs. Each rule includes two parts: condition (If) and result (Then) [35]. Fuzzy inference engine: in this section, the operation of inferring and combining fuzzy rules is performed based on the type of applied operator. In other words, this part controls the method of combining rules [36]. Defuzzification is a process that converts the fuzzy output into nonfuzzy values and displays it as a numerical value. In this research, the following steps were carried out in order. 1- Fuzzifying the actual values obtained from the laboratory analysis by determining the inputs and outputs and their membership function values. 2- Defining fuzzy if–then rules for the inputs and outputs. 3- Applying fuzzy operators for the fuzzy inference engine so the model can make decisions based on them. 4- Defuzzification of fuzzy values to get the final result quantitatively. These quantitative values extracted from the fuzzy system are the same confidence percentage of water potability for the samples.

4 Results

4.1 Schoeller deterministic method evaluation

Drinking water should be free of color, smell, and taste, and in terms of elements and substances, it should be within the standard range determined by health organization [8]. According to Schoeller standard (Table 2), groundwater quality is divided into six groups classified as good, acceptable, inappropriate, bad, can be consumed in situation emergency, and non drinkable. The drawn Schoeller diagram of Northern Dezful-Andimeshk Plain also shows that the quality of groundwater varies from good to bad, so samples No. 1, 2, 3, 4, 5, 6, 7, 8, 10, and 16 are good for drinking, samples No. 9 and 15 are acceptable, samples 11, 12 inappropriate and samples 13 and 14 have bad quality. These results are shown in Fig. 2.

Fig. 2
figure 2

Schoeller diagram of groundwater samples of Northern Dezful—Andimeshk Plain

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Next, for zoning the plain, a category or class between the numbers 1 to 4 was assigned to each sample, the results shown in Table 3. Then, the categories obtained in both water quality zoning methods were used in the Arc GIS environment.It is worth mentioning that due to the low Root Means Square Error (RMSE) caused by IDW (Inverse Distance Weighting) method, this method was used for water quality zoning, the results of which are shown in Fig. 3.

Table 3 Schoeller classification for drinking water wells in the Dezful-Andimeshk Plain
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Fig. 3
figure 3

Zoning map of groundwater quality of Northern Dezful—Andimeshk plain by Schoeller diagram

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The Schoeller method zoning map (Fig. 3) has four water quality ranges: good, acceptable, inappropriate, and bad. So 270.36 km2 of the area has good quality, 99.14 km2 has acceptable quality, 89.37 km2 has inappropriate quality, and 17 km2 has bad quality. According to this zoning, the process of changes in water quality can be justified to a large extent from the point of view of hydrogeology and geology so that the water quality at the entrances of the plain (northeast and eastern edge) has the good and acceptable quality and towards the output of the plain (western and southwestern margins) has inappropriate to bad quality. In addition, in the southwest of the plain, due to the presence of interlayers of gypsum and marl of the Aghajari formation with the conglomerate of the Bakhtiari formation, the amount of Na+, Cl− and SO42− exceeded the permissible limit of Schoeller and caused bad quality in samples 13 and 14.

4.2 Fuzzy method evaluation

Nine parameters affecting water quality, including Na+, Cl−, HCO3−, Ca2+, Mg 2+, SO42−, NO3−, TDS, and TH were selected to assess the drinking water by fuzzy method. To reduce the error and complexity of the model, these nine parameters were classified into three groups, and a number of inputs and one output were determined for each group, as follows: First group: Ca2+, Mg2+, HCO3−, SO42−. Second group: Na+, Cl−, TDS, and TH. Third group: NO3−, the output from the first group and the output from the second group were defined. In these groupings, to make the final decision based on a single and final group, the outputs of the first and second groups have been used as input for the third group. In fuzzy systems, each fuzzy rule includes linguistic variables and linguistic characteristics, so based on the WHO standard and expert opinion, linguistic characteristics (desirable, acceptable, and non-acceptable) and linguistic variables (parameters affecting water quality, including Na+ and Ca2+ are defined for each group, and the linguistic characteristics and linguistic variables of the parameters of all three groups are listed in the Table 4. In this table, the unit of all ions and TDS is in mg/L, and the unit of TH is in mg/L of calcium carbonate. After determining the standards, linguistic characteristics, and linguistic variables and determining equations based on the opinion of the expert, a trapezoidal fuzzifier was used to fuzzification the actual values of the inputs. To determine each input membership function, enter the parameters actual values in a special place in the software and consider the membership function between 0 and 1 for them. For example Fig. 4 shows the type of fuzzifier and the shape of the membership function of the parameters of the second group.

Table 4 Fuzzy values and linguistic characteristics of the first, second, and third groups
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Fig. 4
figure 4

The type of fuzzifier and the membership function of the parameters of the second group (Na, Cl, TH, and TDS)

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Decision-making in the fuzzy inference engine is based on the rules applied by the expert. This model uses the “and” operator and “if–then” rules to create a relationship between inputs and outputs. So, in the “if” section, the model inputs are defined, and in the “then” section, the model’s output is defined. For the first, second and third groups, respectively, 16, 81, and 27 rules are determined. Table 5 shows rules 1 to 10 of the second group, for example, rule number 3 means that if Na level; Cl level; TH level, and TDS level, respectively are desirable, desirable, acceptable and acceptable (inputs of the model), then the groundwater quality (output of the model) is acceptable in terms of drinking.

Table 5 The number of rules (rules 1 to 10) used in the second group
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For defuzzification, the weight of each law was considered equal to one, and the center of gravity deffuzzifier was used as the most common defuzzifier [37]. Then, to get the final output from the model, the actual values of the parameters of the groundwater samples are entered in the display section of MATLAB rules, and the drinking water quality and confidence levels of all samples are determined, the results of which are shown in Table 6. In this Table, columns 5 and 6 show decision-making by the fuzzy method, and columns 2, 3, and 4 show decision-making based on the WHO standard. Based on the results obtained from the fuzzy method, 12.5% of the samples have a confidence percentage lower than 25%, which were placed in the unacceptable group for drinking, and 43.75% of the samples with a confidence percentage of 30 to 70 are in the acceptable group for drinking, and another 43.75% with a percentage of confidence of 70 to 81 were placed in the desired category (Table 6).

Table 6 The results of the fuzzy method based on the standard of the World Health Organization for drinking
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Finally, for the region zoning, the potability confidence percentage data obtained from the fuzzy inference system was used, and its zoning map was drawn in the GIS environment using the IDW method, which is shown in Fig. 5.

Fig. 5
figure 5

Zoning map of the qualitative distribution of groundwater resources of Northern Dezful—Andimeshk Plain by the fuzzy method

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Based on the zoning map by fuzzy method, there are three desirable, acceptable, and nonacceptable ranges. Samples No. 1, 5, 6, 7, 8, 10, and 16 are in the range of desirable quality, samples No. 3, 9, 11, 12, 13, 14, and 15 are in the acceptable range, and samples No. 2 and 4 are in the nonacceptable range. It was also found that the groundwater in 100.34 km2 of the total area of the plain has desirable quality, in 358.28 km2 has acceptable quality, and in 17.62 km2 of the area of the plain has nonacceptable quality. In this map, the best water quality is in the east and northeast, and towards the west of the plain, it tends to an acceptable state with a downward trend, but in the middle of the plain, this trend is disrupted and changed to nonacceptable quality. This issue is due to excessive amounts of nitrate (caused by agricultural activity and wastes from Dokuohe town) in the middle of the plain [38].

5 Discussion

According to the previous studies that have been conducted in this plain using the deterministic method [38], the quality of groundwater for drinking has been mostly good to acceptable, and only in a small part of the region, they have had inappropriate quality, in the deterministic method of the current research, the quality of water is mostly good and acceptable and only in a small part of the south and southwest of the region, it has shown inappropriate to bad quality. In other words, the results of the present study, using the deterministic method, confirm the previous study to a large extent. On the other hand, in another study [39], nitrate anomalies were detected at some points, so in this study, in addition to the deterministic method, the fuzzy method was also used to involve both the concentration of the main elements and the concentration of nitrates and make a more comprehensive assessment of water quality.

Considering that the results of the Schoeler method are qualitatively in accordance with the standard of the WHO [8] and this standard has considered qualitative limits for all parameters affecting water quality, therefore, for the analysis of the fuzzy method, the results of the fuzzy method with WHO made a comparison, the results of which are shown in (Table 6).

According to the WHO standard, samples No. 1, 6 and, 2 are almost similar in terms of the actual value of the parameters in the desirable, acceptable and non-acceptable classes and they differ only in the amount of nitrate, but sample No. 2, with the level 20% confidence is non-drinkable and samples 1and 6 with 75% to 76% are desirable, of quality. This difference is due to the high concentration of nitrate in sample number 2, which was not included in the evaluation by Schoeller method and, this means that the fuzzy method has high accuracy and comprehensiveness, and according to the concentration of the parameters in the samples, it has provided different confidence percentages, but the deterministic method does not have this efficiency.

The superiority of the fuzzy method over the deterministic method is better determined by comparing the confidence level in groundwater samples, which confirms the high efficiency of the fuzzy method in evaluating the quality of drinking water. For example, in Table 6, the ions in samples No. 1 and 3 are similar in terms of desirable, acceptable, and unacceptable quality categories, and in the Schoeller diagram, both samples have acceptable quality, but based on the fuzzy method, the higher concentration of ions in sample 3 compared to sample 1 has shown its potability percentage, so that the percentage of potability in samples 1 and 3 is 75 and 50%, respectively. This issue shows the high accuracy of the fuzzy method compared to the deterministic method.

In the deterministic method, water is evaluated qualitatively, while in the fuzzy method, it is evaluated both qualitatively and quantitatively with the drinking confidence percentage.

According to the studies of some researchers [24, 28], the fuzzy method is a suitable tool compared to the deterministic methods in reducing uncertainties, and if there are threshold values of some parameters and deterministic classifications resulting from them, the fuzzy method shows more flexibility and provides a more logical evaluation, because the linguistic characteristics of each parameter are taken out of the absolute 0 or 1 state and for each, the membership function is considered between 0 and 1, but in the deterministic method, the threshold concentration of each parameter in each class has only 0 or 1. In this study, this superiority of the fuzzy method was also proven, so that, according to Schoeller standard, in samples No. 13 and 14, the amount of Cl− and Na+ are slightly beyond the threshold of the inappropriate class, and this caused these samples to be placed in the bad class of Schoeller diagram (Fig. 3). However, in the fuzzy method, because the membership function between 0 and 1 is considered for the linguistic characteristics of the inputs the partial transgression of Na+ and Cl− from the boundary of Schoeller inappropriate class are not considered and are considered as acceptable (Fig. 5).

There is also a difference between the zoned maps with the fuzzy and the deterministic method. According to the deterministic method, 56.2% of the total area of the plain has good quality, but in the fuzzy method, 21% of the plain has desirable quality. In the deterministic method, 20.85% of the total area is of acceptable quality, but in the fuzzy method, 75.29% of the total area with a confidence percentage varies from 32 to 70%. In the deterministic method, it covers 18.77% of the plain area with inappropriate quality, but in the fuzzy method, this quality class does not exist at all. Also, in the deterministic method, it is 3.57%, and in the fuzzy method, it is 3.71% of the region. In the deterministic method, the bad water quality is located in the southwest of the plain, while in the fuzzy method, the waters with unacceptable quality are located in the north to the middle of the plain, especially in samples 2 and 4. This issue is probably due to the high nitrate concentration in this area, while in the deterministic method, nitrate is not included in the evaluation.

The samples that were determined to be unsuitable for drinking in the deterministic method also have a low confidence level of 32–38% in the fuzzy method, and this issue is very consistent with the zoning caused by Schoeller method and confirms the accuracy and precision of the fuzzy method over the deterministic method.

Due to the ability of the fuzzy method to involve different parameters in water quality, it also has a high potential for change in zoning, so that, if any parameter affecting water quality increases or decreases, the decision of the fuzzy inference system and map of the resulting zoning will also change. In other words, using the fuzzy method, zoning is more flexible in displaying environmental pollution than the deterministic method. The fuzzy method removes the limitations of the deterministic method to perform a comprehensive evaluation and reduces the uncertainties of different stages, but it may also reduce the accuracy of the evaluation compared to the deterministic method. One of the possible disadvantages of the fuzzy method is that increasing parameters affecting water quality may reduce the accuracy of the fuzzy model [40], but fortunately, no unexpected results were obtained in the current research and the possible defect of the fuzzy method was ineffective.

6 Conclusion

The drinking water quality in the Northern Dezful-Andimeshk Plain was assessed and categorized using the Schoeller diagram and the Mamdani Fuzzy Inference System. The results showed that according to the Schoeller method, groundwater sources in 270.36 km2 of the plain area have good quality, 99.14 km2 have acceptable quality, 89.37 km2 have inappropriate quality, and 17 km2 have bad quality. In the evaluation by fuzzy method, it was found that the groundwater sources in 100.34 km2 of the plain area, with a confidence level of 70% to 81%, have desirable quality, and 358.28 km2, with a confidence level of 30% to 50%, have acceptable quality and, 17.62 km2 of the plain with a drinking confidence level of 20% to 22% have an unacceptable quality. Based on the results of this research, it was determined that while both methods are acceptable, one method is better for evaluating the quality of drinking water. The Schoeller method is a fast and efficient method to assess the quality of a large number of water samples simultaneously and display the results graphically. However, it may not be comprehensive enough. In contrast, the fuzzy method provides a more comprehensive assessment of water quality, reduces uncertainties, and expresses results in both quantitative and qualitative terms. It also offers greater flexibility in matching local conditions. However, the fuzzy methods complexity may sometimes produce unexpected results, but this was not the case in this research.The study suggests that in the future, the fuzzy method should be used to evaluate the quality of drinking water, taking into account microbial parameters and heavy metals to achieve a more complete and comprehensive evaluation. It also proposes using the fuzzy method in combination with other definitive graphical methods such as Stiff and Piper.