Abstract

The demand for water has been increasing dramatically recently in domestic, industrial and agricultural sectors, due to economic development and population growth. Therefore, wastewater may be considered as a valuable water resource for some of the mentioned sectors. The main aim of this paper is to introduce a new method to determine the best applications of effluents. In order to achieve this goal, 60 monthly effluent water quality data, sample data fields which were collected and analyzed during the years 2013–2017 by the wastewater treatment plant of Arak city, Iran, were used. Two indices are developed and applied, which involved the entropy and fuzzy logic-based approaches. Six possible effluent applications were considered including industrial, artificial groundwater recharges, environmental purposes, irrigation usages for green spaces, oilseed and fodder production. The results showed that the quality of studied effluents has been improved during the five mentioned years. As in the last year, according to the indices, the effluents could be used for industrial, environmental, fodder production, oilseed production, and artificial groundwater recharge applications. Also, the fuzzy effluent quality index has produced larger values than the entropy index, such that their largest difference is equal to 32.9, and under similar conditions offered fewer possible applications.

INTRODUCTION

Urban population growth, industrial development and the sharp increase in water intake as well as water shortages, especially in hot and dry countries, caused the reuse of treated wastewater to be considered as an alternative source of water supply (Jing et al. 2017). On the other hand, it is well known that the effluents discharged from wastewater treatment plants (WWTPs) may constitute the most important point source of priority pollutants reaching the water bodies (Cabanillas et al. 2012), so the quality of the effluent, management and also the protection must be considered (Mourhir et al. 2014). So far, various indices in water resources assessment have widely been used. Moreover, indicators should be able to provide acceptable changes and values of the index in different regions. Most water quality indices have complexity and logic certainty (Mourhir et al. 2014). Therefore, the determination of effluent quality indices is essential owing to the fact that it has a simple calculation, can be monitored, and the wastewater quality will continuously rise with time and its utilization will cost less. The classic water quality indicators (WQIs) are definite and inflexible and the categories do not represent uncertainty in the data and general information (Lermontov et al. 2009). In order to compensate for this shortage, usage of fuzzy logic in water resources and all related problems is highly recommended (Araghinejad 2013).

Falah Nezhad et al. (2016) used an artificial neural network (ANN) for the design of a feed-forward, three-layer perceptron neural network model for computing the effluent quality index (EQI) for a municipal wastewater treatment plant in the south of Tehran. Their results showed that EQI predictions of this model had significant and very high correlation (R = 0.96, MSE = 0.1) with the measured EQI values. Das & Kumar (2009) assessed the effluents of various industries and developed approaches for their use in farming for a particular region. The results of their study indicated that options of industrial effluent (prospective) reuse in agriculture provide ways to combat the freshwater crisis without degrading environmental quality. It may be applied for assessing effluent before its reuse in several water-starved countries. Fang et al. (2017) evaluated the characteristics of activated sludge granules and flocs using a fuzzy entropy-based approach. Evaluation results show a higher overall score of granules, indicating that granules had more favorable characteristics than flocs. This new integrated approach is effective to quantify and differentiate the characteristics of activated sludge granules and flocs. The evaluation results also provide useful information for the application of activated sludge granules in full-scale wastewater treatment plants. Gorgij et al. (2017) estimated the groundwater quality for drinking purposes using an entropy theory, and compared results with the spatial autocorrelation of effective parameters of water quality. Using the entropy weighted WQI, they classified the groundwater quality into five categories: excellent, good, moderate, poor and extremely poor. According to the entropy weighted WQI, the groundwater quality of the study area can be classified into ‘good’ to ‘poor’ domains. Sahoo et al. (2017) investigated the changing trends in the water quality of the Brahmani River using the entropy weight and Bayes' rule. Comprehensive evaluation indicates that the water is acceptable for second grade surface source protection zones for centralized drinking water. Li et al. (2016) proposed a fuzzy improved water pollution index based on a fuzzy inference system and water pollution index. Their results show that Qu River water quality presents a downward trend and the overall water quality in 2010 was the worst. For the sake of comparison, fuzzy comprehensive evaluation and a grey relational method were also employed to assess the water quality of Qu River. The comparisons of these three approaches assessment results show that the proposed method is reliable. Hosseini-Moghari et al. (2015) developed fuzzy index monitoring water quality (FWQI (fuzzy water quality index)) to assess the quality of groundwater resources in Saveh city. Compared to the conventional WQI, their results showed that the elimination of some needed parameters in development of FWQI did not decrease the accuracy of water quality classification. Jianhua et al. (2011) analyzed the groundwater quality in Jingyan area in China using entropy water quality index (EWQI). Their research showed that the tested samples for drinking have good qualities. Usually, in the water quality index, the weight of each parameter is determined experimentally and based on the expert's opinion (Amiri et al. 2014). Misaghi et al. (2017) recommended consistent monitoring of the water quality and the establishment of a long term management plan for the use of this valuable water resource. Information due to water quality changes to be collected for effective management in the many regions of the world (Behmel et al. 2016).

The main aim of this paper is to present a new method to specify the best applications for effluents and compare and contrast the two new indices. The two indices used in this article are named fuzzy effluent quality index (FEQI) and entropy effluent quality index (EEQI). This paper is an improved and developed version of Rahimi et al. (2017).

MATERIALS AND METHODS

As mentioned above, the main aim of this paper is to determine the best application for the use of effluent. To achieve this goal, the usual application was investigated and initially six different types of the most common effluent applications including industrial, environmental, fodder production, oilseed production, irrigation of green spaces and artificial groundwater recharge purposes were considered as the possible effluent applications. The applications selected in this research are not for direct use of humans, such as drinking or washing. Also, 16 parameters were applied based on water quality indicators which are used widely in the agricultural, drinking and environmental water consumption sectors such as Wilcox diagram, Schuler diagram, FAO and WQIs. The 16 selected parameters are calcium (Ca), magnesium (Mg), nitrate (NO3), phosphate (PO4), pH, biochemical oxygen demand (BOD5), total dissolved solids (TDS), total suspended solids (TSS), fecal coliform, intestinal nematodes, arsenic (As), chromium (Cr), lead (Pb), mercury (Hg), cadmium (Cd) and aluminum (Al). The above-mentioned parameters were selected as the most significant parameters that can be used as inputs of the new developed indices, which were finally developed and applied involving entropy and fuzzy logic-based approaches in this paper. After the introduction of possible effluent applications and the selected parameters, the FEQI and the EEQI were calculated for all applications.

In the fuzzy effluent quality index, at the beginning for each parameter, the membership functions in each specified application were determined. These functions specify the usable range for each parameter in each application. Due to the large number of parameters, the fuzzy system becomes complex and in order to reduce the complexity of the fuzzy system, we classified the parameters using factor analysis which will be explained below. In this study, the fuzzy system has nine fuzzy inference systems (FISs) according to Figure 3, the value of FIS9 determines the value of the FEQI. In EEQI, first the weight of the parameters was calculated using entropy and this index value was determined using the relation provided.

Eventually, according to the values of indices, the possible applications were sorted and the best one was selected. The flowchart of this procedure is illustrated in Figure 1.

Figure 1

Flowchart of the proposed method to determine the best option of effluent application.

Figure 1

Flowchart of the proposed method to determine the best option of effluent application.

Used data

For the purposes of this research, data were acquired from the monthly sampled effluents of Arak treatment plant, Markazi Province, Iran, from 2013 to 2017 (Figure 2 illustrates the location of the study area). Table 1 shows the summary of statistics and quality parameters of the effluents. Presently, the effluent of this wastewater treatment plant is used mainly for agricultural purposes, i.e. irrigation uses.

Table 1

Statistics summary of Arak treatment plant effluent parameters, 2013–2017

Parameter Unit Max. Min. Mean Median Standard division 
pH mg/L 8.6 7.36 7.87 7.79 0.31 
BOD5 mg/L 72 14 25.13 24 10.06 
NO3 mg/L 29 0.98 8.71 48 8.43 
PO4 mg/L 57 15.85 14 10.22 
TDS mg/L 926 452 677.36 680 77.27 
TSS mg/L 212 32 78.69 64 41.26 
Ca mg/L 104.2 64 81.69 81.7 9.04 
Mg mg/L 41.79 18.27 28.35 28.1 4.88 
As mg/L 0.0007 0.0006 0.00062 0.0006 0.0000447 
Cd mg/L 0.03 0.02 0.022 0.02 0.00447 
Hg mg/L 0.0004 0.0002 0.0003 0.0003 0.000707 
Pb mg/L 0.2 0.1 0.14 0.1 0.0547 
Cr mg/L 0.08 0.06 0.066 0.06 0.08944 
Al mg/L 3.6 0.3 2.94 3.6 1.4758 
Intestinal nematodes Arithmetic mean no. of eggs per liter 0.45 0.384 0.1663 
Fecal coliforms Arithmetic mean no. of eggs per liter 1,600 79 1,318.44 1,600 485.42 
Parameter Unit Max. Min. Mean Median Standard division 
pH mg/L 8.6 7.36 7.87 7.79 0.31 
BOD5 mg/L 72 14 25.13 24 10.06 
NO3 mg/L 29 0.98 8.71 48 8.43 
PO4 mg/L 57 15.85 14 10.22 
TDS mg/L 926 452 677.36 680 77.27 
TSS mg/L 212 32 78.69 64 41.26 
Ca mg/L 104.2 64 81.69 81.7 9.04 
Mg mg/L 41.79 18.27 28.35 28.1 4.88 
As mg/L 0.0007 0.0006 0.00062 0.0006 0.0000447 
Cd mg/L 0.03 0.02 0.022 0.02 0.00447 
Hg mg/L 0.0004 0.0002 0.0003 0.0003 0.000707 
Pb mg/L 0.2 0.1 0.14 0.1 0.0547 
Cr mg/L 0.08 0.06 0.066 0.06 0.08944 
Al mg/L 3.6 0.3 2.94 3.6 1.4758 
Intestinal nematodes Arithmetic mean no. of eggs per liter 0.45 0.384 0.1663 
Fecal coliforms Arithmetic mean no. of eggs per liter 1,600 79 1,318.44 1,600 485.42 
Figure 2

Study site.

Figure 2

Study site.

The use of entropy in calculating EEQI

The Shannon entropy was first presented by Shannon in 1948 (Shannon 1948). Generally, entropy is used to express uncertainty about an accidental process or the amount of the load of a parameter (Shyu et al. 2011). On the other hand, entropy means disorder in physical science and it is an expression of pioneering information in communications and information science. In other words, mathematically, an inverse relationship exists between the amount of information and the probability of occurrences. If the occurrence of an event could be exactly predicted, the probability values will be major, and reciprocally, the Shannon entropy will be minor. Therefore, their weights are calculated by the amounts of uncertainties (anti-entropies) of those criteria (Ozkul et al. 2000; Kawachi et al. 2001). The calculation of the entropy has been determined in this paper in order to determine the weight and the EEQI index as follows (also see Abbasi & Abbasi 2012).

For calculating EEQI, weight parameters were used to determine Equations (1)–(6) below. For ‘m’ effluent samples were taken to evaluate the effluent quality (i = 1, 2, … , m), and for each sample having ‘n’ evaluated parameters (j = 1, 2, … , n), Eigen value matrix X was constructed using Equation (1) (Shannon 1948): 
formula
(1)
The data were normalized using Equation (2) in order to remove the damaging effects of different units of the parameters: 
formula
(2)
After the normalization, the standard-grade matrix, Y, was obtained involving Equation (3): 
formula
(3)
and the ratio of the index value of the jth index in the ith sample was equal to: 
formula
(4)
The amount of entropy of each category was also calculated using Equation (5) below. It is worth noting that the smaller the values of Ej, the larger the effects of jth index: 
formula
(5)
Then the entropy weight can be calculated using Equation (6): 
formula
(6)
Then the quality-rating scale of each criterion can be calculated using Equation (7): 
formula
(7)
where Cj is the concentration of each chemical parameter from all water samples (mg/L), and Sj is the water quality standard of any parameter (mg/L).
The WQI method has been widely used in water quality assessments of groundwater and surface water, and it has played an increasingly important role in water resource management (Mirzabeygi et al. 2017). In this research, the water quality index is calculated as explained by Abbasi & Abbasi (2012), as follows: 
formula
(8)

It should be mentioned that in the entropy method, judgments and personal opinion are removed regarding the weight of parameters. Eventually, the effluent quality index was prepared based on these weights and effluent quality standards.

In this paper, we proposed and used a summarized standard table (Table 2) which is based on FAO (1973), standards of wastewater used in irrigation (EPA 2004, 2006; WHO 2004) and finally, Iranian relevant standards (ISIRI No. 1053, No. 2439). By using the calculated values of the ‘effluent quality index’, the effluents were then classified into five levels from ‘excellent’ to ‘extremely poor’, as suggested by Pei-Yue et al. (2010) (see Table 3).

Table 2

Proposed standards for applications (FAO, WHO and Iran standards)

Parameter/Application Industrial Artificial groundwater recharge Environmental Irrigation of green spaces Oilseed production Fodder production 
Intestinal nematodes 
Al 
Cr 0.5 
Pb 
Hg 0.001 0.001 0.001 0.001 0.001 0.001 
Cd 0.05 0.1 0.1 0.05 0.05 0.05 
As 0.1 0.1 0.1 0.1 0.1 0.1 
pHmax 
pH 6.5 
BOD5 250 30 30 50 150 250 
NO3 50 10 50 25 50 50 
PO4 20 15 20 
TSS 120 250 40 50 250 250 
Ca 75 200 75 400 400 400 
Mg 100 100 100 60 60 60 
Fecal coliforms 1,000 1,000 1,000 1,000 1,000 1,000 
TDS 100 400 500 2,000 400 2,000 
Parameter/Application Industrial Artificial groundwater recharge Environmental Irrigation of green spaces Oilseed production Fodder production 
Intestinal nematodes 
Al 
Cr 0.5 
Pb 
Hg 0.001 0.001 0.001 0.001 0.001 0.001 
Cd 0.05 0.1 0.1 0.05 0.05 0.05 
As 0.1 0.1 0.1 0.1 0.1 0.1 
pHmax 
pH 6.5 
BOD5 250 30 30 50 150 250 
NO3 50 10 50 25 50 50 
PO4 20 15 20 
TSS 120 250 40 50 250 250 
Ca 75 200 75 400 400 400 
Mg 100 100 100 60 60 60 
Fecal coliforms 1,000 1,000 1,000 1,000 1,000 1,000 
TDS 100 400 500 2,000 400 2,000 
Table 3

Classification of EEQI (Pei-Yue et al. 2010)

EEQI value Effluent quality Rank 
<50 Excellent 
50–100 Good 
100–150 Poor 
150–200 Very poor 
>200 Uselessness 
EEQI value Effluent quality Rank 
<50 Excellent 
50–100 Good 
100–150 Poor 
150–200 Very poor 
>200 Uselessness 

Fuzzy inference system

Zadeh (1965) presented the first concept of linguistic or fuzzy variables. One of the features of fuzzy logic is the incorporation of human knowledge and experiences and also using the ‘if-then’ rules that can be answered for any of the suitable system outputs according to the system input conditions. An FIS is based on these rules, as expressed below. In each rule, the part that implies the condition is called ‘antecedent’ and the result is the ‘consequent’. Fuzzy inference is created from the combined fuzzy logic (see Yager & Filev (1994) for more details). FIS is composed of four sections: fuzzy rule base, fuzzy inference engine, fuzzifier and defuzzifier. Fuzzy logic is used to merge the most related physicochemical parameters in an integrated score, known as the fuzzy water quality (FWQ) index (Ocampo-Duque et al. 2007).

Development of the fuzzy effluent quality index

So far, various fuzzy models have been proposed by researchers to manage different purposes. Two of the most famous models are the Mamdani and Sugeno models. Due to its simplicity, reliability and suitability for environmental issues, the Mamdani fuzzy system is used in many water tests (Icaga 2007; Gharibi et al. 2012). In the current paper, the Mamdani fuzzy model has been used to classify the effluents to be allocated in different usages. To achieve this goal, 16 water quality parameters were considered to design and develop a fuzzy effluent quality system based on the Mamdani approach. In developing a fuzzy model, the variable amount of each membership function represents a degree of the membership and the effect of the amount is then definite in the outputs (for more details see Araghinejad (2013)). In this paper, the membership functions were designed for each possible application based on the standards which were explained earlier in Table 2, using Equations (9) and (10) below. The functions with four values were recognized as the trapezoidal memberships and in the same way the functions with three values were related to triangular memberships and were designed using the following equations (see also Zadeh 1965): 
formula
(9)
 
formula
(10)

In the next step, in order to determine the exact effect of each parameter or a set of parameters on the effluent quality index, the ‘factor analysis’ was used (Shyu et al. 2011). The results of the factor analysis for nine parameters of Arak treatment plant data (2013–2017) are given in Table 4. It is worth noting that the heavy metals and intestinal nematodes were divided into two separate categories because, basically, they have different characters. Moreover, as can be seen in Table 4, more than 70% of qualitative changes in the effluent have been included by three of the following factors (see the variance row). The first factor with 27.3% of changes had the maximum role and the second factor with 23.8% and then the third factor with 19.7% were the most effective factors on the quality of the effluents. According to Table 4, the first factor parameters including TDS, pH and fecal coliform are important in all applications and the second factor including NO3, BOD5 and PO4 have quite important roles in the fields of artificial groundwater recharge, environmentally and agriculturally because they play an important role in soil structure. The third factor, which includes TSS, calcium, and magnesium, has a significant impact on industrial applications.

Table 4

Rotation load of factors based on the rotated Varimax

 Factors
 
Parameter 
pH 0.75  0.314 
BOD5 –0.435 0.565  
NO3  0.893  
PO4  0.881  
TDS 0.705  –0.0514 
TSS   0.826 
Ca   –0.663 
Mg 0.351  0.420 
Fecal coliforms –0.734   
Eigenvalue 2.118 1.873 1.509 
% of variance 27.306 23.808 19.744 
Cumulative % variance 27.306 51.114 70.88 
 Factors
 
Parameter 
pH 0.75  0.314 
BOD5 –0.435 0.565  
NO3  0.893  
PO4  0.881  
TDS 0.705  –0.0514 
TSS   0.826 
Ca   –0.663 
Mg 0.351  0.420 
Fecal coliforms –0.734   
Eigenvalue 2.118 1.873 1.509 
% of variance 27.306 23.808 19.744 
Cumulative % variance 27.306 51.114 70.88 

As shown in Figure 3, FEQI consists of nine FIS (i.e. Inf.1 to Inf.9). The first FIS includes the first factor and has 225 rules due to pH. In the same manner, the second and third FIS are created involving the second and third factors, respectively, and have 125 rules and an output. The fourth and fifth FIS are comprised of heavy metal parameters, contained eight rules because these parameters have two membership functions and also a sixth FIS is defined only using one parameter and two rules. Finally, the fuzzy inference system provided the FEQI index. The profile of FEQI membership function is shown in Figure 4, in the range of excellent, good, poor and so on. In the first to third FIS, for each parameter except pH, five membership functions were considered. pH has a special condition, because both small and large amounts of this parameter can create undesirable problems in water quality issues. Therefore, nine memberships were considered for those parameters. The heavy metal and intestinal nematode parameters were designed using two separate membership functions, because if their values exceeded a little more than the standard limit, the effluent would be considered as an unusable source. Each parameter has different standards according to the type of effluent application, therefore the membership functions for each parameter and the type of effluent application, due to special situations and the parameter standards, were different. In this paper, fuzzy inference systems were intended for all applications, e.g. membership functions for application of effluent in green space, and also some rules of this system are illustrated in Tables 5 and 6, respectively.

Figure 3

Diagram of the proposed process for designing FEQI.

Figure 3

Diagram of the proposed process for designing FEQI.

Table 5

Characteristics of the applied membership functions for each parameter of the green space application

Characteristics   
Parameter pH pH 
Linguistic variable 
Excellent 6.75 7.5 8.25 – – – – – 
Good 6.75 7.5 – 7.5 8.25 – 
Poor 6.75 – 8.25 10 – 
Very poor – 10 11 – 
Uselessness 10 11 14 14 
Parameter Fecal coliforms TDS 
Linguistic variable 
Excellent 500 1,000 1,000 2,000 
Good 500 1,000 2,000 – 1,000 2,000 3,000 – 
Poor 1,000 2,000 3,000 – 2,000 3,000 4,000 – 
Very poor 2,000 3,000 4,000 – 3,000 4,000 5,000 6,000 
Uselessness 3,000 4,000 5,000 5,000 5,000 6,000 7,000 7,000 
Parameter NO3 PO4 
Linguistic variable 
Excellent 10 25 15 
Good 10 25 35 – 15 30 – 
Poor 25 35 55 – 15 30 50 – 
Very poor 35 55 65 – 30 50 80 – 
Uselessness 55 65 100 100 50 80 100 100 
Parameter BOD5 TSS 
Linguistic variable 
Excellent 30 70 20 50 
Good 30 70 120 – 20 50 80 – 
Poor 70 120 230 – 50 80 120 – 
Very poor 120 230 320 – 80 120 180 – 
Uselessness 230 320 500 500 120 180 250 250 
Parameter Ca Mg 
Linguistic variable 
Excellent 200 400 20 60 
Good 200 400 500 – 20 60 80 – 
Poor 400 500 600 – 60 80 100 – 
Very poor 500 600 650 – 80 100 200 – 
Uselessness 600 650 700 700 100 200 300 300 
Parameter Cd As 
Linguistic variable 
usable 0.025 0.075 0.05 0.15 
Uselessness 0.025 0.075 0.05 0.15 
Parameter Pb Hg 
Linguistic variable 
usable 0.5 1.5 0.005 0.015 
Uselessness 0.5 1.5 0.005 0.015 
Parameter Cr Al 
Linguistic variable 
usable 0.5 1.5 
Uselessness 0.5 1.5 10 10 
Parameter Intestinal nematodes 
Linguistic variable     
usable 0.5 1.5     
Uselessness 0.5 1.5     
Characteristics   
Parameter pH pH 
Linguistic variable 
Excellent 6.75 7.5 8.25 – – – – – 
Good 6.75 7.5 – 7.5 8.25 – 
Poor 6.75 – 8.25 10 – 
Very poor – 10 11 – 
Uselessness 10 11 14 14 
Parameter Fecal coliforms TDS 
Linguistic variable 
Excellent 500 1,000 1,000 2,000 
Good 500 1,000 2,000 – 1,000 2,000 3,000 – 
Poor 1,000 2,000 3,000 – 2,000 3,000 4,000 – 
Very poor 2,000 3,000 4,000 – 3,000 4,000 5,000 6,000 
Uselessness 3,000 4,000 5,000 5,000 5,000 6,000 7,000 7,000 
Parameter NO3 PO4 
Linguistic variable 
Excellent 10 25 15 
Good 10 25 35 – 15 30 – 
Poor 25 35 55 – 15 30 50 – 
Very poor 35 55 65 – 30 50 80 – 
Uselessness 55 65 100 100 50 80 100 100 
Parameter BOD5 TSS 
Linguistic variable 
Excellent 30 70 20 50 
Good 30 70 120 – 20 50 80 – 
Poor 70 120 230 – 50 80 120 – 
Very poor 120 230 320 – 80 120 180 – 
Uselessness 230 320 500 500 120 180 250 250 
Parameter Ca Mg 
Linguistic variable 
Excellent 200 400 20 60 
Good 200 400 500 – 20 60 80 – 
Poor 400 500 600 – 60 80 100 – 
Very poor 500 600 650 – 80 100 200 – 
Uselessness 600 650 700 700 100 200 300 300 
Parameter Cd As 
Linguistic variable 
usable 0.025 0.075 0.05 0.15 
Uselessness 0.025 0.075 0.05 0.15 
Parameter Pb Hg 
Linguistic variable 
usable 0.5 1.5 0.005 0.015 
Uselessness 0.5 1.5 0.005 0.015 
Parameter Cr Al 
Linguistic variable 
usable 0.5 1.5 
Uselessness 0.5 1.5 10 10 
Parameter Intestinal nematodes 
Linguistic variable     
usable 0.5 1.5     
Uselessness 0.5 1.5     
Table 6

Some utilized rules for FEQI development for green space application

FIS The rules no. Consequent Antecedent 
If Is And if Is And if Is Then 
Output 1 pH Uselessness TDS Excellent E. coli Uselessness Uselessness 
24 pH Uselessness TDS Uselessness E. coli Very poor Uselessness 
75 pH Good TDS Excellent E. coli Excellent Good 
208 pH Good TDS Good E. coli Very poor Poor 
FIS The rules no. Consequent Antecedent 
If Is And if Is And if Is Then 
Output 1 pH Uselessness TDS Excellent E. coli Uselessness Uselessness 
24 pH Uselessness TDS Uselessness E. coli Very poor Uselessness 
75 pH Good TDS Excellent E. coli Excellent Good 
208 pH Good TDS Good E. coli Very poor Poor 
Figure 4

Profile of membership functions, FEQI.

Figure 4

Profile of membership functions, FEQI.

It should be noted that in this paper MATLAB software, version 2014, was used to determine the weights of entropy and also in order to develop the fuzzy inference system.

RESULTS AND DISCUSSION

As shown in Table 5, pH has nine membership functions and the average amounts of that are in the range of 6.75–9. It is worth noting that the smaller or larger amounts of the mentioned limit have negative effects on the water quality. Some of the rules which were used in developing FEQI, as an example for the green space application, are shown in Table 5. Fleming et al. (2014) explained that a major advantage of the fuzzy logic approach for constructing environmental indices, relative to conventional approaches based on weighted averages, is that the rules of a fuzzy expert system can be built of such good quality that having it in one parameter does not hide bad quality in another. For instance, according to Table 6, in the 75th rule, although the two parameters are in the range of excellent, the result is considered as good range. Also, as in the fifth rule, although the two parameters are in the range of very bad and one other parameter is evaluated as excellent, in consequence the quality is determined as very bad. It should be noted that, due to the importance and possible hazards of effluent usages on human health and the environment, these roles were strictly developed. The parameters with higher weights have greater impacts on the water quality index. Therefore, according to Table 7, TSS and then PO4 with weights of 0.1128 and 0.109 are the most effective parameters. Also, Cd, As, Cr and Hg have the minimum impacts on the index. Actually, each parameter weight has shown its stability, e.g. cadmium with an amount of 0.0225 has the most variability and changes. The comparisons of the EEQI index with FEQI are presented in Figures 59 and Table 8. Figure 4 and Table 3 illustrate the classification of the indices and according to them, if the values of indices are greater than 100, then the effluent is unusable. Based on the results of the fuzzy index, Arak effluents of 2013 year can be used only for irrigating green spaces. However, for the same year, according to the outputs of the entropy index, the effluents can be used for three applications including green space, fodder production and industrial. Based on Figures 68, the FEQI, three types of applications including green spaces, fodder production and industrial were approved in 2014, 2016 and 2017 years. Moreover, for 2015, this index approved all of the applications, except for environmental purposes.

Table 7

Entropy weights for each parameter

Parameters         
Parameter TDS pH Mg Ca TSS PO4 NO3 BOD5 
Entropy weight 0.0795 0.0803 0.0698 0.0696 0.1128 0.109 0.052 0.0506 
Parameter Fecal coliforms Intestinal nematodes Al Cr Pb Hg Cd As 
Entropy weight 0.0995 0.0669 0.0529 0.0305 0.0497 0.0315 0.0225 0.0309 
Parameters         
Parameter TDS pH Mg Ca TSS PO4 NO3 BOD5 
Entropy weight 0.0795 0.0803 0.0698 0.0696 0.1128 0.109 0.052 0.0506 
Parameter Fecal coliforms Intestinal nematodes Al Cr Pb Hg Cd As 
Entropy weight 0.0995 0.0669 0.0529 0.0305 0.0497 0.0315 0.0225 0.0309 
Table 8

Results indicators, EEQI and FEQI for wastewater treatment plant of Arak for different applications, 2013–2017

Applications 2013
 
2014
 
2015
 
2016
 
2017
 
EEQI FEQI EEQI FEQI EEQI FEQI EEQI FEQI EEQI FEQI 
Environmental 138.3 141.16 91.17 121.58 91.31 129.1 77.9 121.58 90.83 121.58 
Irrigation of green spaces 86.42 92.35 57.16 83.32 60.62 71.62 50.51 61.08 61.04 97.36 
Fodder production 56.87 105.93 37.10 63.22 42.27 52.75 31.61 52.34 42.13 52.07 
Oilseed production 105.93 140.83 66.91 106.78 66.7 95.37 52.54 110.48 65.9 102.34 
Industrial 68.34 110.59 48.15 92.14 54.22 52.75 43.04 52.34 53.97 52.34 
Artificial groundwater recharge 145.81 140.83 76.01 110.43 80.28 95.37 57 110.48 71.04 102.34 
Applications 2013
 
2014
 
2015
 
2016
 
2017
 
EEQI FEQI EEQI FEQI EEQI FEQI EEQI FEQI EEQI FEQI 
Environmental 138.3 141.16 91.17 121.58 91.31 129.1 77.9 121.58 90.83 121.58 
Irrigation of green spaces 86.42 92.35 57.16 83.32 60.62 71.62 50.51 61.08 61.04 97.36 
Fodder production 56.87 105.93 37.10 63.22 42.27 52.75 31.61 52.34 42.13 52.07 
Oilseed production 105.93 140.83 66.91 106.78 66.7 95.37 52.54 110.48 65.9 102.34 
Industrial 68.34 110.59 48.15 92.14 54.22 52.75 43.04 52.34 53.97 52.34 
Artificial groundwater recharge 145.81 140.83 76.01 110.43 80.28 95.37 57 110.48 71.04 102.34 
Figure 5

Time series (2013–2014) EEQI and FEQI for applications.

Figure 5

Time series (2013–2014) EEQI and FEQI for applications.

Figure 6

Comparison of FEQI and EEQI for all applications, 2013–2014.

Figure 6

Comparison of FEQI and EEQI for all applications, 2013–2014.

Figure 7

Comparison of FEQI and EEQI for all applications, 2015–2016.

Figure 7

Comparison of FEQI and EEQI for all applications, 2015–2016.

Figure 8

Comparison of FEQI and EEQI for all applications in 2017.

Figure 8

Comparison of FEQI and EEQI for all applications in 2017.

Figure 9

Comparison of changes in EEQI and FEQI.

Figure 9

Comparison of changes in EEQI and FEQI.

According to Table 8 and Figure 5, the environmental purpose application had the largest values of FEQI among all applications between the years 2014–2017. Also, the minimum value in those years was equal to 121.58, which recommends that the effluent is not suitable for any application. The best application in 2014, according to FEQI, with an amount of 63.22, is fodder production. Also, the best options in 2015 and 2016, respectively, are fodder production and industry, with values equal to 52.75 and 52.34. Also, in 2017 fodder production again is the best possible application, with the value of 52.07.

On the other hand, according to the entropy index, the fodder production is introduced as the best type of application, with a value of 56.87 in 2013. This index showed that all applications are suitable for the use of effluent in 2014–2017. The highest value of entropy index in those years is related to the use of effluent for artificial groundwater recharge. According to this index, the best application of all years is related to fodder production which had the highest index value in 2013 at 56.87. Based on that, some items are italicized in Table 8 and highlighted in Figure 5. It can be concluded that three types of applications, including fodder production, irrigation of green spaces and industry, are top selections in most cases. Figure 9 shows the mean values of the six applications. As can be seen from the figure, the quality of the studied effluents has improved during the past five years. As a conclusion, according to Figure 9, FEQI has been larger than EEQI, because FEQI has always produced higher values than EEQI. In the year 2013, fecal coliform and phosphate were two parameters that had higher than fodder production standards. Therefore, the fuzzy index shows 105.93 values. So the use of this application was not approved. In this case, Lermontov et al. (2009) stated that the fuzzy quality index is not dependent on particular parameters. The entropy index in this year is equal to 56.86 and the difference between these two indices shows that the fuzzy index is more sensitive than the entropy one.

In 2017, only fecal coliform exceeded the fodder production standards and the values of fuzzy and entropy indices were 50.07 and 42.13 respectively, which both proved the usage of the effluent and reflected that the effluent quality in the study period was improved and the indices were sensitive enough to the changes of different parameters as well.

CONCLUSIONS

The main aim of the current paper was to present a new method to specify the best applications of effluents according to the effluent characteristics based on fuzzy and entropy approaches. Evaluation and feasibility of the proposed approaches were investigated considering six types of common applications of effluents including industrial, environmental purposes, fodder production, oilseed production, irrigation of green spaces and artificial groundwater recharge. The characteristics of 60 monthly effluent samples from 2013 to 2017 were used, which were measured and recorded by Arak city Wastewater Treatment Plant, Iran. Factor analysis was used to analyze the above-mentioned data and determine the correlation and relationship in the parameters. Factor analysis results provided three FISs. The FISs were created according to the standards of wastewater treatment for each parameter and six possible applications. To calculate the EEQI, the weights of parameters were determined based on the entropy method and according to the standards of any application. The results showed that the fuzzy index presented higher values than the entropy index, and hence introduced fewer applications for reuse. However, it was observed that both indices in most cases offer similar change trends. According to the results the FEQI and EEQI have improved to amounts of 33.9 and 36.1 respectively over the last five years. Each of the indices has their own advantages, e.g. the FEQI proved the capability of knowledge-based models along with overcoming the uncertainties of decision-making and on the other hand, the EEQI demonstrated the ability to eliminate judgments of experts. Also, the entropy index has such simple calculations and results in a good agreement with the fuzzy index.

ACKNOWLEDGEMENTS

The authors are grateful to the University of Tehran along with the Water and Wastewater Corporation of Arak Province, Iran, for providing data and facilities for conducting the present research.

REFERENCES

REFERENCES
Abbasi
T.
&
Abbasi
S. A.
2012
Water Quality Indices
.
Elsevier
,
Amsterdam
,
The Netherlands
.
Amiri
V.
,
Rezaei
M.
&
Sohrabi
N.
2014
Groundwater quality assessment using entropy weighted water quality index (EWQI) in Lenjanat
.
Iran. Environ. Earth Sci.
72
(
9
),
3479
3490
.
Araghinejad
S.
2013
Data-driven Modeling: Using MATLAB® in Water Resources and Environmental Engineering
, Vol.
67
.
Springer Science & Business Media
,
Berlin
,
Germany
.
Behmel
S.
,
Damour
M.
,
Ludwig
R.
&
Rodriguez
M.
2016
Water quality monitoring strategies – a review and future perspectives
.
Sci. Total Environ.
571
,
1312
1329
.
Cabanillas
J.
,
Ginebreda
A.
,
Guillén
D.
,
Martinez
E.
,
Barcelo
D.
,
Moragas
L.
,
Robusté
J.
&
Darbra
R. M.
2012
Fuzzy logic based risk assessment of effluents from waste-water treatment plants
.
Sci. Total Environ.
439
,
202
210
.
EPA
2004
Guidelines for Water Reuse
.
United States Environmental Protection Agency, Office of Science and Technology
,
Washington, DC
,
USA
.
EPA
2006
National Recommended Water Quality Criteria
.
United States Environmental Protection Agency, Office of Science and Technology
,
Washington, DC
,
USA
.
FAO
1973
Salinity – An International Source Book, Irrigation, Drainage
.
FAO/UNESCO/Hutchinson
,
London
.
Gharibi
H.
,
Mahvi
A. H.
,
Nabizadeh
R.
,
Arabalibeik
H.
,
Yunesian
M.
&
Sowlat
M. H.
2012
A novel approach in water quality assessment based on fuzzy logic
.
J. Environ. Manage.
112
,
87
95
.
Gorgij
A. D.
,
Kisi
O.
,
Moghaddam
A. A.
&
Taghipour
A.
2017
Groundwater quality ranking for drinking purposes, using the entropy method and the spatial autocorrelation index
.
Environ. Earth Sci.
76
(
7
),
269
278
.
ISIRI (No. 1053)
1984
Specifications for Drinking Water
,
4th edn
.
Institute of Standards and Industrial Research of Iran
,
Iran
.
ISIRI (No. 2439)
1985
Specifications of Industrial Effluents
.
Institute of Standards and Industrial Research of Iran
,
Iran
.
Jianhua
W.
,
Peiyue
L.
&
Hui
Q.
2011
Groundwater quality in Jingyuan County, a semi-humid area in Northwest China
.
J. Chem.
8
(
2
),
787
793
.
Jing
X.
,
Yao
G.
,
Liu
D.
,
Liang
Y.
,
Luo
M.
,
Zhou
Z.
&
Wang
P.
2017
Effects of wastewater irrigation and sewage sludge application on soil residues of chiral fungicide benalaxyl
.
Environ. Pollut.
224
,
1
6
.
Kawachi
T.
,
Maruyama
T.
&
Singh
V. P.
2001
Rainfall entropy for delineation of water resources zones in Japan
.
J. Hydrol.
246
(
1–4
),
36
44
.
Lermontov
A.
,
Yokoyama
L.
,
Lermontov
M.
&
Machado
M. A. S.
2009
River quality analysis using fuzzy water quality index: Ribeira do Iguape river watershed, Brazil
.
Ecol. Indic.
9
(
6
),
1188
1197
.
Mirzabeygi
M.
,
Yousefi
N.
,
Abbasnia
A.
,
Youzi
H.
,
Alikhani
M.
&
Mahvi
A. H.
2017
Evaluation of groundwater quality and assessment of scaling potential and corrosiveness of water supply networks, Iran
.
J. Water Supply Res. Technol. Aqua.
66
(
6
),
416
425
.
Mourhir
A.
,
Rachidi
T.
&
Karim
M.
2014
River water quality index for Morocco using a fuzzy inference system
.
Environ. Syst. Res.
3
(
1
),
21
33
.
Ocampo-Duque
W.
,
Schuhmacher
M.
&
Domingo
J. L.
2007
A neural-fuzzy approach to classify the ecological status in surface waters
.
Environ. Pollut.
148
(
2
),
634
641
.
Ozkul
S.
,
Harmancioglu
N. B.
&
Singh
V. P.
2000
Entropy-based assessment of water quality monitoring networks
.
J. Hydrol. Eng.
5
(
1
),
90
100
.
Pei-Yue
L.
,
Hui
Q.
&
Jian-Hua
W.
2010
Groundwater quality assessment based on improved water quality index in Pengyang County, Ningxia, Northwest China
.
J. Chem.
7
(
S1
),
S209
S216
.
Rahimi
M.
,
Ebrahimi
K.
&
Liaght
A. M.
2017
Development of an effluent quality index based on entropy approach
. In:
The 4th International Conference on Environmental Planning and Management
,
May 2017
,
Tehran, Iran
.
Sahoo
M. M.
,
Patra
K.
,
Swain
J.
&
Khatua
K.
2017
Evaluation of water quality with application of Bayes’ rule and entropy weight method
.
Eur. J. Environ. Civil Eng.
21
(
6
),
730
752
.
Shannon
C. E.
1948
A mathematical theory of communications
.
Bell Syst. Tech. J.
27
,
379
423
.
World Health Organization
2004
Guidelines for Drinking Water Quality: Training Pack
.
WHO
,
Geneva
,
Switzerland
.
Yager
R. R.
&
Filev
D. P.
1994
Essentials of fuzzy modeling and control
.
SIGART Bull.
6
(
4
),
388
.
Zadeh
L. A.
1965
Information and control
.
Fuzzy Sets
8
(
3
),
338
353
.