Formulation of a novel drinking water quality index equation with the application of multi-criteria decision making techniques

Water Quality Index elucidates the complexity in assessing water quality by converting the results of various parameters into a single number for a precise interpretation of the condition of concerning water. The present study focuses on implementing Multi-Criteria decision-making techniques, namely, Analytical Hierarchy Process and Analytical Networking Process, in estimating the relative weighted significance values of the water quality parameters based on three novel criteria like Cost, Potability, and Taste. The suggested Water Quality Index technique utilizes these weighted values of the water quality parameters in depicting and expressing the water quality level in the form of an index value. Dissolved Oxygen has emerged as the most persuasive factor in evaluating water quality for drinking purposes in this study. This paper has also suggested modifying the standard weighted arithmetic water quality index for higher accuracy in results. Furthermore, Sensitivity analysis is performed to corroborate the Multi-Criteria Decision Making approach in index assessment. The accuracy of the Water Quality Index analysis shall improve if a fixed set of criteria and their preference are asserted and justified based on which the water quality parameters are ranked. Their weighted significance values will be estimated accordingly.


INTRODUCTION
A country's well-being depends mainly on its quality of water, surrounding air, and ecological balance. It has become substantial to evaluate the water quality that we consume because of increasing pollution and contaminants in the surface water. Water quality is analyzed based on an extensive set of physio-chemical and biological parameters. It is advisable to consume the water only if it falls under the predefined water quality standards set by World Health Organization (WHO) for various parameters. The authors in their study, evaluate groundwater condition of villages affected by industrial growth in Ranebennur taluk, Karnataka, India, in which the majority of the groundwater samples (collected from bore wells) has been found appropriate for drinking and irrigation purposes but with a risk of decline in the level of groundwater [21]. In this study, the authors had adopted the application of Geographic Information System (GIS) in outlining the present water quality of Tapi basin, Gujarat, and uses an interpolation technique, known as Inverse Distance Weighting (IDW) to determine spatial propagation of water quality parameters by Biological Oxygen Demand (BOD), Chemical Oxygen Demand (COD), chloride and Total Dissolved Solids (TDS) [11]. Water quality is considered a criterion to check the suitability of water for a distinct purpose appertaining to chosen physicochemical and biological characteristics [2]. Water that contains a substantial number of suspended solids and other matter particles and is exceedingly turbid might work well for an agricultural activity but is not convenient for drinking purposes.
Seven water quality parameters, namely, TDS, TSS, Hardness, pH, BOD, DO, have been considered in the present study for determining the quality of the water samples. TDS represents dissolved composite matter of inorganic and organic nature that exhibits liquid in tiny, ionized, or micro-granulated suspended form. From a water consumption point of view, TSS should be as low as possible. Hard waters generate scaling in water pipelines, heaters, furnaces, and other elements [12]. Higher DO value improves the taste of the drinking water (Dabkowski 2012). TPC method depends on the augmentation of bacteria organized as colonies on a nutrient medium to get discernible to the naked eye. Accordingly, counting of colonies on a plate is carried out [17]. pH shows the intensity of acid or essential condition by pointing out the hydrogen ion activity.
Water Quality Index (WQI) provides a distinct idea of the concerned water quality by incorporating the composite influence of several parameters on the implied water quality [3]. Most of the WQI mentioned above processes have used the absolute approach in assigning priority value to the water quality parameters. This study has emphasized the relative approach in giving weightage to various parameters with the help of Multi-Criteria Decision Making (MCDM) techniques. This approach will also tell us about the most significant parameter in determining water quality based on the different criteria set by users across the world. MCDM techniques also serve the purpose of feature selection. Based on the weighted significance values, only the most consequential parameters are considered for determining the WQI. This approach will also minimize the time and cost incurred in analyzing the physio-chemical and biological parameters of the water samples.

Objectives of the Study
The objective of the present study is to establish a new process for the computation of water quality index with the help of the MCDM techniques based on three criteria, namely, Cost, Potability, and Taste. The study also shows AHP and ANP in calculating the priority weights for the water quality parameters. It suggests few adaptations in the standard WAWQI method for better preciseness in the index value. The paper also investigates the purity of drinking water collected from the water purifiers installed in the thirteen sampling sites of Jirania, Agartala, India. Finally, the study validates the competence of the MCDM based WQI approach in allocating weightage of priority to the water quality parameters with Sensitivity Analysis.

METHODS ADOPTED
The study involves testing the water samples based on seven parameters using various techniques discussed in section 2.1. Then the water quality index is computed, keeping the WAWQI as the reference but adopting few modifications for better accuracy in the results.
The detailed process of conventional WAWQI has been discussed in section 2.2. MCDM techniques, namely AHP and ANP have been used in our study to obtain the parameters' relative weights. Pivotal steps of these techniques have been elaborated in sections 2.3 and 2.4.

Water Quality Analysis through Physio-Chemical and Biological parameters
Based on the seven selected parameters, water quality in thirteen collected sampling stations is assessed. TDS concentration of various collected samples is measured with the help of a ) × 100 Va: actual value obtained of the (i th ) parameter at a given sampling station.
Vi: the ideal value of the specific parameter (0 for all parameters excepts pH and DO, which are 7.0 and 14.6 mg/lit, respectively).

Vs.: standard value
As per the prescribed method, unit weight for various water quality parameters is inversely proportional to the recommended standards for the corresponding parameters.
Wi: unit weight for the i th parameters Si: standards value for the i th parameters K: relative constant The range of WQI for various probable uses of water has been shown in table 2.
Furthermore, the condition of water based on the WQI spectrum is also given for a precise understanding of the clarity of the water [19].

Analytic Hierarchy Process
Analytical Proper treatment is required for any usage that all the concerned projects' overall risks are at the "Shallow" level [23]. AHP is carried out by following the below-mentioned steps stated in table 3 in chronological order.

Analytic Network Process
The Analytic Network Process (ANP) is a decision-finding technique that is also a generalization of AHP. In this MCDM technique, a network is developed consisting of criteria, sub-criteria, and alternatives represented equally as nodes. Each of these nodes might be compared with each other. This depicts that the ranking of alternatives and criteria in the specific problem depend on each other. The authors, in their study, used a suitable technique that consolidates GIS, ANP, and remote sensing for assessing and delineating susceptibility Multiplying the weightage of the Criteria with the relative weighted significance of the alternative for that criteria and calculate the row wise average. Normalize the average to find the weight of significance of the alternatives.
Comparing each alternative with every other alternative with respect to each of the selected criteria in the form of pair comparison matrix.
Comparing each criterion with the other corresponding to the objective in the form of pair comparison matrix.
Selecting order of preference for criteria and computing equivalent rank for the same.
Determining Equivalent number of Ranks (R): - Where, m= no. of alternatives/criteria Ranking the Alternatives in context of specific criteria as per the goal of the study and decision maker's judgment.
of flood in which ANP mathematical model was used to estimate the relative weighted significance of the several floods influencing factors [4].
In ANP, the six steps used in the AHP for the computation of weighted significance to the criteria will be carried forward. Up next, the criteria are compared with each other concerning each of the alternatives. As a result, each criterion will have another weightage of significance. In the final step, multiply the weighted relevance of criteria with the weighted relevance of alternatives (computed in the sixth step of AHP) and calculate the row-wise average. Normalize the average to find the updated relative weights of alternatives [20].

Shannon's entropy
Shannon's entropy was used in this study to aggregate the different ranking results derived from AHP and ANP MCDM techniques. This method calculates the entropy measure of each of the ranking methods and finds the weights of the selected alternatives accordingly.

Sensitivity Analysis
The study of the response of an output variable in context to alteration of input variables is known as the sensitivity analysis [13]. In this research, the one-factor-at-a-time (OFAT) sensitivity analysis method has been performed to define predominant parameters affecting the water quality Index for drinking purposes calculated through the proposed process.

General Information
The present study is conducted in the small town of Agartala, Tripura, India. The fundamental research is carried out in thirteen blocks of an educational institute in Jirania, Agartala. The study area Jirania (23.8132° N, 91.4362°E), is located on the banks of the Saidra River (Fig.1).

Selecting Sampling location
The comprehensive study is conducted in thirteen different blocks scattered across the educational institute in Jirania, Tripura. The sampling stations have been named as S1, S2, S3…. S13.

Sample Collection
One of the study's objectives is to check the efficiency of the water purifiers installed in the thirteen sampling stations; thus, two water samples have been collected from each one of the blocks for comparative analysis. The first sample comprises the tap water (Untreated water), and the second sample has been taken from the water purifier (Treated water). The tap water sample is named 'INLET,' and the treated water collected from the installed water purifier is called 'OUTLET.' Figure 2 shows the Study area of Jirania derived from Google Earth Pro software.

METHODOLOGY
All the water samples (both Inlet and Outlet) were collected from different sources, and then they were analyzed for various physicochemical and biochemical parameters. The following parameters, namely TDS, TSS, pH, BOD, DO, TPC, and Hardness, are selected to assess drinking water quality in the study and are analyzed accordingly. All the values were compared with WHO standards. The efficiency of the water purifiers in cleaning the untreated water was checked by comparative analysis of Inlet and Outlet water samples.
Up next is finding out the relative weighted significance values or the priority value of the seven water quality parameters using MCDM techniques. Three novel criteria, namely, "Cost," "Potability," and "Taste," have been considered for performing AHP and ANP.
Testing the parameter that involves maximum cost is ranked one under the criterion "Cost," and the alternative that requires the least cost in its testing is rated 7.
Wi is the relative unit weights obtained from MCDA methods for i th parameter The standard formula for Qi does not hold well for a few parameters such as pH and DO. The significance of the absolute sign in the procedure of Quality rating (Qi) has been discussed in Appendix 1. A summary of the entire work of the study has been given in figure 4. Figure 4 Detailed methodology of the study

RESULTS AND DISCUSSION
The first and the most crucial stage in computing AHP and ANP are to rank the water quality parameters (Alternatives) for the selected criteria. After an extensive literature survey and experts' opinions in the Environmental and water resources engineering domain (table 3).
Further the order of preference of each criterion has been given in table 4 based on the suitability for drinking purposes. • Performing sensitivity analysis of WQI to validate the most influential water quality parameter in determining index calculation  Based on the outcomes from AHP and ANP technique, it can be seen that Dissolved Oxygen (DO) is the most influential water quality parameter in deciding water quality for drinking purposes. Table 6 Entropy weights of ranking methods

Ranking Methods Entropy Weights
Analytical Hierarchy Process 0.55 Analytic Network Process 0.45    Efficiency of water purifiers installed in sampling stations S9, S10, S11 & S12 Figure 10 represents the comparison of the inlet and the outlet water samples of each sampling station through a line graph. It can be observed that apart from the purified water sample of S5 (WQI value-66.462), all other outlet samples are found to be of good quality.
Treated water of S8 and S12 is of Excellent quality as per the WQI method. Except for S5, the WQI value of all the Outlet samples are lower than their Inlet water samples. Figure 10 Line graph representing WQI values of the water samples S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13   Dissolved Oxygen is the most sensitive parameter in determining WQI, followed by Total Suspended Solids, which corroborates the MCDM techniques such as AHP and ANP. S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13  The proficiency to attenuate the complex and varied information into a single value to convey the data in a simplified and consistent form makes the users' water quality index precious. Potability, and taste on the drinking water quality index. Therefore, the present investigation will approximate the WQI with AHP MCDM and validate the same comparing with ANP MCDM. The weighted aggregated measure of the seven water quality parameters will be figured out using Shannon's Entropy weighted step. This proposed approach will help improve the accuracy of estimating WQI and present the most influential parameters in maintaining water quality. Thus, the users will focus on keeping the magnitude of that parameter within the standard value.

CONCLUSION
The study aimed to suggest a new method to determine the drinking water quality index with the help of MCDM techniques. Certain modifications to the standard Weighted Arithmetic Water Quality Index (WAWQI) method were proposed to improve the accuracy and reliability of the process. Allocation of weighted values to the water quality parameters was carried out using AHP and ANP MCDM techniques. The process of assigning weights was more logical than the conventional method, which was based on permissible limits of the parameters involved in the water quality analysis. The second modification uses the absolute term in the Quality rating formula to get a more precise and justified WQI value for the concerned water. The MCDM-WAWQI method results show that most of the treated water samples accumulated from the thirteen sampling stations were of good quality. Treated water taken from S12 has the best water quality (Both Inlet and Outlet) than other blocks, whereas sampling station 5 (Outlet purified water) shows unsatisfactory results. Furthermore, the selection of criteria may also vary depending upon the requirement of the consumers. These factors might result in minor alterations in the value of relative weights.

DECLARATION Ethics Approval:
The manuscript has not been submitted to more than one journal for simultaneous consideration. The submitted work is original and the work not has been published elsewhere.
Results have been presented clearly, honestly, and without fabrication, falsification or inappropriate data manipulation (including image based manipulation). Institute facility has been utilized with proper permission. The details about the author group, the Corresponding Author, and the order of authors provided in the manuscript are all correct. Research articles and non-research articles have been cited appropriately and relevant literature in support of the claims has been made.

Consent to participate:
All the authors have given their consent for participating in this research work.  suggests that water is in poor condition.