According to the previous studies that have been conducted in this plain using the deterministic method [32], 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 [33], 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.
The fuzzy results were compared with the standard of the World Health Organization (Table 6) to analyze the fuzzy method. 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 1, 6 with 75–76% 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, sample No 1 and 3 are exactly the same in terms of the position of the parameters in the desirable, acceptable and unacceptable classes, but based on the fuzzy method, the percentage of drinking confidence in samples 1 and 3 is 75% and, 50%, respectively (Table 6). While, in fact, in samples NO3-, most of the evaluated parameters, including nitrate, sulfate, hardness, etc., are more concentrated than sample No.1 (Table 1), and this indicates the accuracy of the fuzzy 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 [20, 23], 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 32–70%. 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 [34], but fortunately, no unexpected results were obtained in the current research and the possible defect of the fuzzy method was ineffective.