Assessment of the Effectiveness of Collective Decisions for Maintenance-Rehabilitation Works of Water Pipelines Using a Qualitative Risk-based Group Decision-Making Model

Among the most important decisions in water companies are planning the Maintenance-Rehabilitation Works (MRWs) of water pipelines. Since the MRWs are costly, it is essential to use the collective decisions of an expert team for planning these works. However, the effectiveness of these group decisions is not very clear and has been less considered in previous studies. Hence, the main objective of this research is to assess the effectiveness of these collective decisions. For this purpose, the MRWs of water pipes are determined based on two methods. In the �rst, the collective decision of experts is omitted, and in the second one, these decisions are considered. Finally, the results obtained from these methods are compared. The method used in this work for collective decisions is based on the nominal group technique. Furthermore, since there is deep uncertainty in water network data as well as hesitation in the group decisions, a qualitative (fuzzy) risk-based group decision-making model is developed in this research. The water pipelines studied in this work, as the case study, are addressed to pipes, which have been proposed by water companies in the six provinces of Iran. The MRWs of these pipes are determined, �rst, using the collective decision of 76 experts in these water companies; and then, without this group decision making. The results of comparing these methods indicated that group decisions do not have a signi�cant effect on prioritizing water pipelines for the MRWs. While, in determining the renovation strategies of pipes, the viewpoints of experts could have a decisive effect on the results. Furthermore, it was found that increasing the number of decision criteria could lead to more realistic results; whereas, the number of assessed pipelines as well as the number of decision makers does not have an obvious effect on the results.


Introduction
Water Distribution Networks (WDNs) are among the main infrastructure in human societies; thus, the Maintenance-Rehabilitation Works (MRWs) of these networks have always been one of the most important concerns of water companies.Hence in the last decade, many studies have been conducted in regards to MRWs of water networks (Ramos et  Hence, it is essential to consider an appropriate method for planning MRWs of water pipelines, so that, leading to improve the hydraulic-mechanical operation of these pipes.For this purpose, various methods have been developed since 2000.Some of these studies are focused to use multi-criteria Decision-Making  2021) proposed a novel approach for a hybrid method of design-rehabilitation of WDNs.A new version of NSGA-II in combination with EPANET 2 software was developed in their studies to assess the ageing phenomena in WDNs.However, it seems that the uncertainty in WDN data was not considered in this study.Wu and Abdul-Nour (2020) presented the results of a study in which different multi-criteria group DMMs were investigated to select a sewer network design.In this research, four applied DMMs including AHP, TOPSIS, ELECTRE III and PROMETHEE II were assessed.Finally, the best results were obtained from PROMETHEE II and TOPSIS methods.However, this research focused on the design of municipal sewer networks and urban WDNs were not considered by researchers.Xiao Zhou et al. (2019) presented a new framework by Fully-linear DenseNet to identify the accurate burst locations in WDNs; so that, can be used for MRWs planning.However, proposing a prioritization plan for repairing the pipes was not considered in this research.
Tscheikner-Gratl et al. (2017) assessed ve multi-criteria DMMs namely ELECTRE, AHP, WSM, TOPSIS and PROMETHEE to prioritize the rehabilitation of WDNs.The results of this study indicated that the output of these DMMs is not the same for renovation planning and each model can offer different programs.However, in this study, group and risk-based DMMs have not been studied.Fontana and Morais (2016) presented a model that can be used to plan preventive maintenance works of WDNs to reduce the volume of water loss.In this research, a combined DMM consisting of a multivariate value analysis model with the SMARTER method as well as linear programming has been used.However, in this research, prioritizing the maintenance works of pipes has not been considered by researchers.
Since the operation of WDNs is so complex, it is usually needed to use the collective viewpoints of a specialized team for decision-making of pipes' MRWs In this study, it was found that methods such as the Delphi can be useful for multi-attribute group DMMS.However, in this study, the assessment of the effectiveness of group DMMs for planning the renovation of WDNs has not been considered.this research to implement group decisions.The case study of this work was related to a network in a city in Egypt.However, in this study, only the results of several group DMMs in the assessment of the condition of the pipes have been investigated; thus, the effectiveness of these methods in planning the maintenance of WDNs has not been considered.Salehi et al. (2018) have been developed a model called the WDSR model, which was a multi-attribute group DMM based on the Fuzzy TOPSIS method.This model was developed only to prioritize pipes and areas of WDNs for planning network renovation.However, in this model, the assessment of the effectiveness of group DMMs in prioritizing pipes has not been considered.da Silva Monte et al. (2016) presented the results of a study in which the techniques for determining the weight of different decision makers in group DMM was investigated.The eld of this study was related to the maintenance of wells in WDNs, in which decision-makers consisted of 3 experts with different views.However, in this study, the maintenance of the water pipeline has not been considered and the viewpoints of a limited number of decision makers have been assessed.Choi et al. (2015) has assessed the condition of pipes in WDNs.Based on this research, they provided a method to maintain and repair the pipes in each zone of the network.Moreover, a group decision of 25 experts was used to weight different zones of the network based on their performance index; and the AHP method was applied to determine these weights.Finally, the ELECTRE method was used to prioritize network zones.However, in this study, the pipes prioritization for renovation was not considered and the effectiveness of group DMM was not assessed.
Given the most studies in the eld of WDNs renovation, it is obvious that mainly the effectiveness of group DMMs used in this eld has been less considered; while, these decisions could be useful for Maintenance-Rehabilitation Works (MRWs) of distribution networks.The e ciency of group DMMs has been recently considered in other elds (Hsieh et al. 2020); nevertheless, not has been used in the WDNs design and operation eld.
The main objective of the present study is to assess the effectiveness of collective decisions in planning the MRWs of water pipelines.In this regard, the speci c pipes proposed by the 6 water companies of Iran have been investigated; and then, using the viewpoints of 76 experts in these companies, the MRWs of the pipes were planned.Accordingly, the nominal group technique was used in this research for collective decision.In addition, to assess the effectiveness of group decisions a DMM has been developed in the present work; and then, the results of two methods including no-group DMM and group DMM were ).However, as mentioned previously, in the model of the present work, the numerical analysis of risk (quantitative) has been omitted; and as a new approach, only qualitative risk-based decision-making was considered for planning MRWs of the water pipelines.This is because that the deep uncertainty in WNDs data and hesitation in group decisions could lead to more complex analysis in the quantitative risk-based methods.The results of this work indicate that the opinions of experts do not have a signi cant effect on pipe prioritization for MRWs.However, decision-makers' viewpoints can be effective and decisive in determining pipe renovation strategies.

Material And Methods
The main objective of this research is to assess the effectiveness of collective decisions for planning MRWs of the water pipelines in WDNs.For this purpose, a qualitative risk-based model was developed using a multi-criteria group DMM. Figure 1 illustrates the analytic steps of this model.

Figure 1 near here
As illustrated in Figure 1, the analytic steps of the developed model in this research are described separately below:

Step 1. Determining the decision criteria
To plan MRWs of the water pipelines in WDNs, identifying the effective variables in pipes prioritization is of great importance.Therefore, during the studies conducted in the previous years (Salehi et al. 2018a, Salehi et al. 2020), 42 and 48 criteria have been recognized as effective in determining the priority of pipe for rehabilitation.In the present study, the criteria affecting the priority of pipes for MRWs were developed to 50; and were divided into two categories of criteria and sub-criteria.Figure 2 shows the criteria and sub-criteria effective in the prioritization of pipe for MRWs.

Figure 2 near here
The model developed in this research is well-established, which can analyse any network with any number of criteria as well as any number of pipes.Furthermore, it is possible to assess network data with uncertainty using this model.Therefore, even networks with 1 or 2 criteria (accurate or imprecise) and with any number of pipes can be assessed by this model.

Step 2. Selecting the case studies
In this step, the case studies of research were selected.For this purpose, to consider a wide range of different regions of Iran, WDNs from the six provinces were chosen.Furthermore, for selecting these provinces, the various combinations of the numbers of decision makers/pipes/criteria were considered.Finally, a total of 76 decision-makers participated in these provinces.The dispersion of these six provinces and the numbers of decision makers/pipes/criteria in their water companies are shown in Figure 3.The number of pipes studied in this work was proposed by each water company.In addition, the numbers of criteria were determined based on data available in water companies.In this work, the selection of decision makers was based on their knowledge and work experience and was completely voluntary.The educational degrees and work experiences of these decision makers are presented in Table 1 in percentage.(2020).For this purpose, in each case study, the conditions of the water pipelines were investigated in regards to 50 criteria.However, it should be noted that all criteria do not have the same role in pipe failure.Indeed, as shown in Table 2, some of these criteria are effective in PFP and others affect PFC.While, some of these criteria have a simultaneously in uence on the probability and consequence of pipe failures (Table 2).The major information in

Step 4. Planning the maintenance-rehabilitation works of pipes
In this study, lling the form of the pipes' qualitative risk (Table 3) by the network operator, the priority and renovation strategy of pipes were determined.To analyse this form, a multi-criteria decision model was developed based on the TOPSIS method, which has been introduced rstly by Yoon and Hwang (1981).
The reason for using this method is its signi cant ability in planning the design and rehabilitation of water and sewer networks (Salehi et  x max + ( c ) , x max ( mc ) x max + ( c ) { ( ) Afterwards, two target and theoretical pipes which have the highest and least failure risk were calculated using the following formula: Pipe with highest risk (the most critical pipe for maintenance-rehabilitation works) =V Pipe with least risk (the least important pipe for maintenance-rehabilitation works These best and worse pipes are calculated only to measure the distances of real water pipelines from them for determining the pipes' priorities/strategies for MRWs.Indeed, these pipes are theoretical and do not exist in real WDNs.
In the next stage, the distance of each water pipeline was measured from the pipes with the highest and least risks.This distance was determined using the below formula: Distance of water pipeline from the pipes with the highest/least risk Finally, the priority of each water pipeline for MRWs was determined by the following formula: This index is a number between zero and one, which the closer it is to the number 1, the higher the priority of the water pipeline for MRWs.
In addition, to determine the strategy of MRWs for each water pipeline two other indices were determined using the same formula of number 6 as follows:

Figure 4near here
As previously mentioned in Figure 1, this research has been conducted in two methods.In the rst method, the decision criteria were weighted using group decision making.For this purpose, the nominal group technique as one of the main methods of group DMMs (Figueira et al. 2005) was used.Hence, to assess the viewpoints of the decision makers, a decision form was provided and presented to experts using the instant message (Kilgour and Eden 2010).The general format of this form was obtained from the previous studies (Salehi et al. 2018a, Salehi et al. 2020).Table 2 shows the form used in this study for weighting the criteria.It should be mentioned that since the main objective in this research is assessing the effect of collective decision for planning the MRWs of the water pipelines, the weighting of experts is omitted for a correct judgment of the effect of expert viewpoints.GD ic : The i th linguistic value assigned to c th criterion by expert to determine the importance of c th criterion i = 1(very low),2 (low),…,7 (very high), c = 01,02,…,50 As shown in Table 4, each of the linguistic values is related to a trapezoidal fuzzy number.Accordingly, the weight obtained for each criterion would be a fuzzy value.This value was achieved using the following formula: In the second method of this research, analytic steps of Fuzzy TOPSIS were performed without using group decision making.Finally, the results of two methods including group DMM and no-group DMM were compared.

Results & Discussion
The results obtained from this research are presented in Figure 5 and Tables 5 and 6.The discussion of these results is as follows: 3.As represented in Figure 5, the results of the two methods in determining the MRWs strategies of pipes is more than 60% in 3 water companies (Sarbaz, Ferdos and Shahr-e-Kord).While, compared to other cities (Ardabil, Marivan and Mashhad), this similarity for pipe priorities is less in these water companies.
On the other hand, as shown in Figure 3, the criteria studied in water companies of Sarbaz and Shahr-e-Kord is less than other companies.Therefore, considering Figures 3 and 5, it seems that reducing the number of criteria studied can almost lead to the reversal of the results.Accordingly, regarding to the viewpoints of network operators and the results presented in previous paragraphs, it can be generally said that reducing the number of decision criteria can have an adverse effect on the accuracy of the results of group decisions.
4. The least similarity of the results is related to the MRWs strategy of the pipes in Mashhad and Marivan.It means that the most effective group decision on determining the strategy of pipe renovation is related to the water companies of these two cities.However, the number of pipes in these two cities was signi cantly different.Hence, the number of pipes studied in Mashhad was equal to 13, whereas, in Marivan was equal to 5.This result indicates that the number of pipes does not affect the obtained results.Thus, the model developed in this study can be robust, and provides accurate results with any number of pipes. 5.As represented in Figure 3, it is clear that the most number of decision makers are related to water companies of Khorasan Razavi (Mashhad), Chaharmahal and Bakhtiari (Shahr-e-Kord), and Sistan and Baluchestan (Sarbaz).However, considering the results presented in Figure 5, it is obvious that the viewpoints of decision makers are signi cantly different in these companies.In addition, the results of Ardabil are very close to Shahr-e-Kord and, the results of Mashhad are close to Marivan.While, the number of decision makers in Ardabil province was 9, and for Chaharmahal and Bakhtiari province (Shahr-e-Kord), the 14 experts were volunteers.There is also a signi cant difference between the number of decision makers in Khorasan Razavi (Mashhad) and Kurdistan (Marivan) provinces.Hence, 23 decision makers participated in the Water Company of Khorasan Razavi, whereas, 9 experts were proposed in Kurdistan Province for this research.Accordingly, it can be concluded that increasing the number of decision makers does not necessarily make the results to be better or worse; and the viewpoints of decision makers are more important than their number.
6. Considering Table 1 and Figure 5, It seems that for planning the MRWs of pipes, increasing the level of education degree in decision makers (Ardabil and Khorasan Razavi provinces) as well as work experience in them (Ardabil and Kurdistan provinces) can be effective in improving the results of collective decisions.However, only increasing work experience (Khorasan Razavi Province), could not necessarily lead to better results for group decisions in renovation planning of water pipelines.7. Based on results obtained from this research, it can be stated that using a qualitative risk-based method could be useful in elds with deep uncertainty as well as hesitation in group decisions such as collective decisions for planning the water pipelines' MRWs.

Conclusion
Maintenance-Rehabilitation Works (MRWs) is one of the most important activities in water companies.In particular, in the case of water pipelines of Water Distribution Networks (WDNs), the planning of these works should be coherent, e cient, and cost-effective.Therefore, considering the complexities of operation and maintenance in WDNs, using collective decisions is inevitable in this eld.However, group decision-making for planning MRWs of the water pipelines does not necessarily lead to effective programs.Indeed, it is essential rstly to assess the effectiveness of group decisions in pipes renovation planning.This important subject was considered in this research.Hence, to assess the effectiveness of collective decisions in water companies of Iran, six provinces were selected; and the viewpoints of 76 experts in these companies were investigated for planning MRWs of the water pipelines.To assess the hesitant viewpoints of experts as well as imprecise data of WDNs, a qualitative risk-based group decision model was developed in this research.The results revealed that using this model could be useful for planning MRWs of the water pipelines.However, it was found that group decisions do not have a decisive effect on pipes prioritization, but could be decisive for determining the MRWs strategies of the water pipelines.Furthermore, it was shown that increasing the decision criteria could make the results more realistic; nevertheless, the numbers of pipes analysed and the numbers of experts who participated, do not have a direct effect on results; While, their viewpoints could be very effective in renovation planning of the pipes.It must be mentioned that this research has been conducted in selected water companies of Iran, and the results might be changed in another country, even in other water companies of Iran.However, it seems that the results obtained from this research could be inspired for future studies in the eld of group decisions for maintenance-rehabilitation planning of the water pipeline.The criteria and sub-criteria considered in this research Page 17/17 The number of decision makers/pipes/criteria in water companies studied in research The similarity of the results of No-Group DMMs al. 2021, Dell'Aira et al. 2021, Vieira et al. 2020, Elshaboury et al. 2020a, Cabral et al. 2019, Salehi et al. 2019, Tscheikner-Gratl et al. 2016, Choi et al. 2015, Scholten et al. 2014, Salman et al. 2013, Tabesh and Saber 2012, Saldarriaga et al. 2010).

(
Salehi et al. 2018a, Tabesh et al. 2020, Fontana and Morais 2017, Morais and Almeida 2010, Morais and de Almeida 2007).Accordingly, the DMM developed in this eld would be better a group decision model.Over the last ten years, various studies have been conducted on group DMM related to water supply systems and water resources management.In some of these studies, group decision-making was used in the eld of reducing water losses in the WDNs (Tabesh et al. 2020, Morais and de Almeida 2007, Morais et al. 2014, Mutikanga et al. 2011); However, in other studies, group DMMs have been considered in the eld of WDN management (Noori et al. 2020, Amorocho-Daza et al. 2019, Minatour et al. 2015, Haider et al. 2015, Roozbahani et al. 2012).Meanwhile, some studies of group DMMs in water networks are directly related to the network MRWs (Choi et al. 2015, Salehi et al. 2018a, Salehi et al. 2020, Bicik 2010, Fontana and Morais 2017, Morais and Almeida 2010, Elshaboury et al. 2020b, da Silva Monte et al. 2016, Trojan and Morais 2012).Zolghadr-Asli et al. (2021) recently presented review research on studies conducted in the last 20 years, in which multi-attribute DMMs in the eld of water resources management had been used.One of the factors considered in this research was the group decisions and the number of decision makers in various studies.The results of this study indicated that the use of multi-attribute DMMs for water resources management, especially in the Middle East, is increasing.
compared.Meanwhile, given the deep uncertainty involved in WDNs data (Scheidegger et al. 2013, Lee et al. 2000, Urich and Rauch 2014) as well as the hesitation in group decisions (Carneiro et al. 2021, Wu et al. 2020, Carneiro et al. 2019), a qualitative (fuzzy) risk-based approach was added to the developed model in this research.The risk-based DMM developed in this research is a new version of the RC-WDSR model, which was introduced in 2020 (Salehi et al. 2020

Figure 3
Figure 3 near here al. 2018a, Tscheikner-Gratl et al. 2017, Wu and Abdul-Nour 2020); Whereas, the other methods (e.g.AHP) do not have the desired capability to analyse decision-making problems where the number of criteria and alternatives increase (Tscheikner-Gratl et al. 2017, Wu and Abdul-Nour 2020, RazaviToosi and Samani 2019, Islam et al. 2013, Yazdani et al. 2012).In addition, considering the fuzzy-linguistic values used in this research, the model developed in this research was based on Fuzzy TOPSIS.Since the criteria considered in this research had different scales, in the rst stage of the Fuzzy TOPSIS model, the fuzzy values related to the pipes' qualitative risk were changed to descaled fuzzy values based on the formula presented below: rmc: Descaled fuzzy value of the m th water pipeline in related to c th criteria m = 1,2,…,m, c = 01,02,…,50 pipe priority index, these indices are numbers between zero and one.Considering the measured PFP and PFC indices of each water pipeline, the MRWs strategy of pipes were determined using the graph illustrated in Figure4.This gure was obtained from the research ofSalehi et al. (2020).

FiguresFigure 1
Abbreviations DMM: Decision-Making Method MRW: Maintenance-Rehabilitation Work PFP: Pipe Failure Probability PFC: Pipe Failure Consequence RC-WDSR: Risk Component-based Water Distribution System Renewal TOPSIS: Technique for Order Preferences by Similarity to an Ideal Solution WDN: Water Distribution Network

Figure 4 Determination
Figure 4 Determination of the MRWs strategy of pipes using PFP and PFC indices (Salehi et al. (2020))

Table 1
The pro le of decision-maker experts in this research In this study, to determine the pipe risk, the Pipe Failure Probability (PFP) and Pipe Failure Consequence (PFC) were assessed based on criteria determined in step 1.The method used for risk assessment in this research was based on analytic steps of the RC-WDSR model, which has been introduced in Salehi et al.

Table 2
(Salehi et al. 2020)ve on probability or consequence of pipe failure(Salehi et al. 2020) Pipe Importance in Respect To Other Urban Facilities Pipe Importance in Urban Management Plans Since there is deep uncertainty in the WDNs data and some numerical information of these networks are imprecise (Wang et al. 2019, Khameneh et al. 2019, Marques and Cunha 2020, Fletcher et al. 2017, Torres et al. 2009, Sadiq et al. 2008, Kapelan et al. 2004), quantitative risk analysis of pipe failure has been not considered in this study.Thus, the linguistic-fuzzy (qualitative) risk-based method was used to determine the condition of the pipes in relation to each criterion.Additionally, this method could be useful for collective decisions due to the hesitation in group decision-making (Wu et al. 2020, Tang et al. 2019,

Table 3
The form used in this research to determine the pipe qualitative risk

Table 3
near here In this table, each criterion was divided into seven categories.This categorization was not based on numerical classi cation, but on linguistic-fuzzy division.The condition of each pipe in relation to each criterion was determined based on the available eld data as well as the knowledge and experience of the network operator who lled the form (Table3).The fuzzy numbers assigned to linguistic values were trapezoidal fuzzy numbers.A trapezoidal fuzzy value ( x = (x min , x ave1 , x ave2 , x max )) is introduced as a four-component number, in which x min and x max indicate the minimum and maximum possible values, whereas, x ave1 and x ave2 show the most probable values for a given number.The characteristic function of this number follows in below (Anisseh and Mohd Yusuff 2011, Salehi et al. 2018b):

Table 4
The group decision-making form used in this research

Table 5 :
The similarity of the results of two methods to determine the pipe priorities