Introduction

Businesses and governments increasingly face environmental challenges in their operations, ranging from stricter regulatory compliance, public scrutiny, higher compliance costs, resource availability, climate change, and waste disposal (Büyüközkan et al. 2019; Collivignarelli et al. 2020; Liu et al. 2020). Increased awareness of regulators, suppliers, and clients on environmental issues leads to external pressure to limit environmental footprint related to manufacturing and consumption patterns of offered products and services. Until recently, the standard practice was end of pipe solutions that take action on the side effects of manufacturing activities when and where the actual pollution occurs. For instance, the solution to air pollution created by a thermal power plant was believed to be installing flue gas desulphurization equipment or a WWT plant in the case of a manufacturing facility. This understanding of environmental management is globally transforming. Therefore, selecting the appropriate WWT process at the start is ever more important. To cope with this subject, this paper proposes an integrated model that aims to enhance the process of making decisions in terms of quality and effectiveness for selecting the most appropriate WWT plant investment and technology alternative.

Selecting the most appropriate technology and design for environmentally friendly processes requires a methodological examination of large data sets in terms of environment, economics, and technology. Management of waste and wastewater usually contains conflicting elements regarding economic, environmental, and social aspects, requiring compromise decisions. For this reason, decision-makers need a comprehensive approach that works under uncertainty for deciding on waste management solutions. Such decision problems can be tackled with multi-criteria decision-making (MCDM) approaches (Gherghel et al. 2020). MCDM refers to taking decisions by considering multiple, usually conflicting criteria. The concept of uncertainty, which is a natural aspect of decision-makers’ judgments, is usually not included in the research of traditional MCDM approaches. In real-world problems, on the other hand, it is not easy to translate decision-makers’ judgments into absolute terms of 1-0 or true-false. In simulating real decision processes where phenomena are imprecise and vague, computing based on degrees of truth is more reliable. The fuzzy set theory (Zadeh 1965) can be useful in handling such problems with blurred boundaries. This study follows a multi-stage fuzzy decision-making procedure to create and evaluate the most suitable WWT decision system. For this, AHP (Saaty 1980), TOPSIS (Chen 2000), PROMETHEE (Goumas and Lygerou 2000), and different economic evaluation approaches (Chan et al. 2000) will be combined in a fuzzy environment. The aim is to best reflect the judgments of decision-makers who deal with the selection problem of a WWT investment for a case study.

Although there exist several MCDM studies in this field (Kalbar et al. 2012; Molinos-Senante et al. 2015; Sawaf and Karaca 2018), there is a research gap for developing suitable selection frameworks for WWT systems that incorporate different decision parameters. This paper proposes a decision-making framework to address this gap. This decision problem needs to be handled in a multi-layer decision environment. The contributions of this study to the WWT literature can be summarized as the following:

  • It proposes a novel decision-making model by introducing different WWT problems in every phase, as well as by implementing hybrid evaluation techniques.

  • It integrates cash flow analysis and three MCDM methods, i.e., AHP, PROMETHEE, and TOPSIS, in a fuzzy decision environment.

  • It helps comprehend the theoretical processes of a WWT selection problem to better choose WWT system strategies.

To the best of the authors’ knowledge, no study incorporates these different decision processes for the WWT selection problem. This procedure offers practical guidance to the WWT industry for deciding upon appropriate WWT strategies once wastewater elimination, minimization, and recycling are accomplished.

The next section of the study offers an overview of literature about the application area and briefly presents the WWT problem of the case company. The “Materials and methods” section presents the proposed multi-stage fuzzy MCDM approach and its computational procedure. The “Results and discussion” section illustrates the application of the proposed framework on a case company, ABC based in Istanbul. Finally, the “Managerial implications” section gives managerial insights, and the “Conclusion” section concludes the paper.

Literature review on the selection of WWT systems

WWT technologies have shown significant progress since the middle of the twentieth century. As far as WWT operations are concerned, the concepts of long-term sustainability, cost-effectiveness, resilience, reliability, and resource consumption are of primary importance. Similar to other fields, different alternatives should be examined and evaluated to decide on the most appropriate solution, also for environmental management programs. Quantitative models and software simulations are frequently used for wastewater management. Studies and applications in the literature concerning WWT problems usually discuss the experimental design dimension or carry out statistical analyses to search for optimal settings (e.g., intake and outflow of the plant, the outflow water quality) to attain a higher WWT performance.

Few of these articles focus on comparing different WWT technologies or processes from a decision-making perspective with several parameters. Having said that, the evaluation of wastewater technologies and processes is attracting attention. Kalbar et al. (2016) presented an alternative selection method for selecting an appropriate WWT technology. Their study involves environmental, economic, and social aspects as an evaluation framework with a life cycle sustainability approach for assessing different technologies. It studies two real-life case applications using TOPSIS. Another method is proposed by Mahjouri et al. (2017a) for selecting WWT technologies in the steel industry. A combined AHP and TOPSIS method based on fuzzy logic is used to evaluate those treatment systems. They found high system efficiency and environmental protection compliance to be important in treatment technology. Table 1 presents a summary of recent articles that deal with WWT technology/process evaluation and suggests that MCDM and programming approaches are frequently used in these studies.

Table 1 Several WWT technology/process evaluation studies in recent years
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The state of the art given in Table 1 shows a research gap for systematic approaches for deciding on WWT systems. To the best of the authors’ knowledge, there is not any study in the literature for carrying out a holistic WWT decision process, starting with the investment phase, proceeding to choosing the WWT technology, and eventually closing with selecting the company that supports the preferred technology. While literature generally focuses on specific parts, such as WWT alternative selection, this research uses multi-stage modelling and multi-criteria analysis for this decision-making problem. Also, a real case study is proposed to offer insights into how these processes function.

Materials and methods

Multi-stage fuzzy decision-making methodology

Wastewater management is a multi-dimensional, complicated problem that is closely related to sustainable development. To deal with the WWT decision-making problem, an integrated model is proposed to compare the suitability of different alternatives. Fuzziness is unavoidable in the WWT technology selection due to its uncertain nature. This makes MCDM a suitable method for the objective of this paper. In the literature, MCDM techniques are used for several waste-themed studies. Eskandari et al. (2016) proposed a fuzzy AHP model for selecting solid waste disposal sites by considering landslide risks. More recently, Khoshand et al. (2019) used a fuzzy AHP approach to assess different alternatives for e-waste collection and processing by using a case in Iran. Another article by Zhang et al. (2020b) presented a fuzzy AHP and fuzzy comprehensive evaluation for the risk grade evaluation of sudden water pollution and demonstrated their method on the Yongding River as a case study.

The proposed MCDM approach includes four consecutive phases, in which different decision techniques are utilized. The method is presented in Fig. 1. The summary of the main calculation steps is provided below. The technical details and formulations are available in Supplementary Materials. Readers may refer to the indicated references for additional information on the techniques used in the article.

Fig. 1
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Four-phase evaluation model

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Phase I—Decision on investment

At this initial phase, the decision of “to invest” or “not to invest” in the WWT system is made. Once the decision goal is defined, a group of experts is formed, and the available alternatives and evaluation criteria sets are identified. This group of experts can consist of the personnel, experts, consultants, or managers of different departments, such as research and development, quality, and engineering. Each decision-maker is expected to independently express his or her opinion.

The importance of the evaluation criteria is determined with the fuzzy AHP algorithm. AHP, first developed in 1980 by T.L. Saaty (1980), is a numerical approach for putting a complex multi-attribute issue into a hierarchical perspective. It is an objective technique for handling decision problems among a defined set of possible alternatives. The method of fuzzy AHP is basically an integration of the AHP technique and fuzzy set theory together to describe the decision-making process more accurately. Once the evaluation criteria weights are found, the alternatives are evaluated with the help of the fuzzy PROMETHEE (F-PROMETHEE) method according to the description provided by Goumas and Lygerou (2000).

Phase II—Decision on technology

In this second phase, the ultimate aim is to select the most appropriate WWT system among various technology options. At this phase, the technology selection algorithm described by Chan et al. (2000) is utilized to calculate the advantages in a fuzzy environment. The same algorithm also includes a fuzzy cash flow analysis with an economic assessment perspective.

Phase III—Decision on system type

This phase aims to decide on the “system type for the technology which is selected in phase II” with the help of the fuzzy AHP method. The notation and calculation steps are given in phase I with formulae (1)-(7).

Phase IV—Decision on technology supporting company

This phase aims to select the “most appropriate company which will provide the wastewater system construction service.” For this purpose, fuzzy TOPSIS is utilized to compare available technology providing companies, as explained by Chen (2000).

Problem definition and data for the case study

The application of the framework will be demonstrated on a case company, ABC, based in Istanbul, Turkey. ABC Company has been a leading player in innovation and forms the future of the domestic electronics industry. Since its establishment in 1847, ABC Company is a reliable industry partner which manufactures control equipment, other facilities of control, and telephone wires. Some of the processes, such as the shaping of metals and duroplasts that are used as inputs for further processing stages, are carried out in workshops. Some other assembly components are imported. Environmental issues are of key importance, also reflected in its certification with ISO 14001. Similar to the usual practices in the electric and electronics industry, ABC Company recycles metal waste, plastic, as well as glass, paper, and batteries. Special attention is paid to toxic waste recycling, such as oil, dye waste, and mud that are generated from the bath of galvanizations, and aerosol boxes. The galvanization workshop creates toxic waste (heavy metals and other toxic chemical components) in the forms of wastewater, which must be treated before discharging it to the sewage system. To decrease the concentration of heavy metals, ABC Company sediments and precipitates its wastewater. Following the sedimentation, two material streams are obtained, a sludge with toxic remains and purified water, which is directly discharged to the sewage system. The sludge contains metal hydroxides and other metals and stays in the sedimentation basin to be cleaned. The composition of the sludge mostly depends on the type of processes; however, various kinds of metals can be found that must be separated. ABC Company collects and stores this sludge, after which it is sent to IZAYDAS, a hazardous waste disposal company, for incineration, leading to the following problems:

  • Very high water consumption, remarkably increasing operational costs

  • Increase in electricity and chemical consumption

  • High discharge and disposal fees for the mud generated in the basins

  • Need for a continuous monitoring system, complicating the management structure

The literature mentions additional functions expected from WWT plants for a circular economy, such as effective local recovery of water, sludge, and nutrients (Cossio et al. 2020). Heavy metals can be highly toxic and even fatal to humans and aquatic organisms (Chen et al. 2021). As also suggested by the Environmental Management Department of ABC Company, improved water treatment can be an effective solution to such problems. Poor design or selection of improper technology for WWT plants can be another reason for failure, which is also a concern in the literature (Cossio et al. 2020). Therefore, selection processes should be performed systematically.

Application

The expert group formed for the case study consists of five decision-makers, who are the managers and assistant managers of the Environmental Management and Quality Departments of ABC Company, as well as the executive vice president, who is responsible for these units. These experts are employed by ABC Company and therefore know the ongoing problems sufficiently well. The experts are selected such that each member has many years of relevant experience. This makes the decision committee sufficiently knowledgeable and experienced for this decision problem. Each decision-maker is treated equally. The importance of the evaluation criteria, which are found by the group, is obtained by comparing the criteria pair by pair. These experts make use of linguistic variables in evaluating the alternatives. Consensus of the experts will be sought. The evaluations are made based on evaluation criteria. Based on a literature survey, the authors have initially proposed a list of evaluation criteria for this problem. Using the feedback of the expert group about these criteria, the evaluation criteria are adapted and finalized, as explained below.

Phase I: Decision on investment

At this phase, the expert group considers economic and environmental criteria (Kalbar et al. 2012; Molinos-Senante et al. 2015; Arroyo and Molinos-Senante 2018; Sawaf and Karaca 2018; Gherghel et al. 2020) to take the decision “A1 - Not to invest” or “A2 - To invest” in the WWT system. The detailed model of phase I is presented in Fig. 2.

Fig. 2
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Overview of phase I

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Economic criterion—C1

This criterion covers the incurred costs. Water (C11), electricity (C12), discharge (C13), and chemical (C14) costs constitute the operating costs of the investment. Considering that WWT achieves 90% water savings, the investment is expected to fare well for this criterion. The frequency of monitoring (C15) represents the number of controls carried out during an entire day. When an operation transforms from a continuous to a discontinuous one, this monitoring frequency will naturally decrease. These criteria can change depending on the issues that the companies are taking forward (such as the cost of labor).

Environmental criterion—C2

This criterion includes sub-criteria that are related to the environmental impacts caused by current practices and by the WWT system in question. Environmental impact (C21) considers the amount of generated toxic waste, and C22 assesses how the existing system and the WWT benefit natural resources.

At this point, experts give linguistic evaluation inputs between criteria using the scale given in Step 1.1 of phase I. Linguistic evaluation matrix of C11–C15 is given in Table 2 as a sample evaluation. Table 2 gives the linguistic evaluations of experts, and Table 3 shows their fuzzy number equivalents. Evaluations of criteria C21–C22 and C1–C2 are found to be identical, and linguistic data from decision-makers is provided as “L” when C1 is compared to C2. Consequently, the weights are found as C1= (0.471, 0.667, 0.816) and C2= (0.272, 0.333, 0.471) (Tables 4 and 5).

Table 2 Linguistic evaluation matrix for criteria C11–C15
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Table 3 Fuzzy evaluation matrix for criteria C11–C15
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Table 4 Data of the first phase
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As an example for fuzzy AHP steps, linguistic evaluation of C11 against other criteria are shown in Table 3, with the following fuzzy values: C11–C11 = C11 – C12 = C11 – C13 = C11 – C14 = C11 – C15 = (1,2,3). The triangular fuzzy weight of criteria C11 can be calculated (Lockström et al. 2010; Tuzkaya and Önüt 2008; Tuzkaya et al. 2009):

$$ {\mathrm{w}}_1^{\mathrm{l}}=\frac{{\left(1\times 1\times 1\times 1\times 1\right)}^{1/5}}{{\left(1\times 2\times 2\times 2\times 2\right)}^{1/5}+{\left(1/2\times 1\times 1/2\times 3\times 2\right)}^{1/5}+{\left(1/2\times 2\times 1\times 2\times 3\right)}^{1/5}+{\left(1/2\times 1/3\times 1/2\times 1\times 1/2\right)}^{1/5}+{\left(1/2\times 1/2\times 1/3\times 1/2\times 1\right)}^{1/5}} $$
$$ {\mathrm{w}}_1^{\mathrm{m}}=\frac{{\left(1\times 2\times 2\times 2\times 2\right)}^{1/5}}{{\left(1\times 2\times 2\times 2\times 2\right)}^{1/5}+{\left(1/2\times 1\times 1/2\times 3\times 2\right)}^{1/5}+{\left(1/2\times 2\times 1\times 2\times 3\right)}^{1/5}+{\left(1/2\times 1/3\times 1/2\times 1\times 1/2\right)}^{1/5}+{\left(1/2\times 1/2\times 1/3\times 1/2\times 1\right)}^{1/5}} $$
$$ {\mathrm{w}}_1^{\mathrm{u}}=\frac{{\left(1\times 3\times 3\times 3\times 3\right)}^{1/5}}{{\left(1\times 2\times 2\times 2\times 2\right)}^{1/5}+{\left(1/2\times 1\times 1/2\times 3\times 2\right)}^{1/5}+{\left(1/2\times 2\times 1\times 2\times 3\right)}^{1/5}+{\left(1/2\times 1/3\times 1/2\times 1\times 1/2\right)}^{1/5}+{\left(1/2\times 1/2\times 1/3\times 1/2\times 1\right)}^{1/5}} $$

The weight is calculated as \( {\tilde{\mathrm{w}}}_1=\left({\mathrm{w}}_1^{\mathrm{l}},{\mathrm{w}}_1^{\mathrm{m}},{\mathrm{w}}_1^{\mathrm{u}}\right)=\left(0.184,0.319,0.442\right) \).

The consistency of the obtained results is checked with the CR to verify if the pair-wise comparisons are consistent among themselves. For this purpose, the priority vector and Principal Eigenvalue (λmax) are needed. The priority vector is calculated by taking the average across each of the rows of the normalized matrix. The Principal Eigenvalue is obtained from the average of the divisions between the multiplication of each element of the priority vector and evaluation matrix and priority vector. Normalized evaluation matrix and priority vector are also shown in Table 3.

The priority vector is multiplied with the reciprocal evaluation matrix, and the values obtained are 1.69, 1.08, 1.37, 0.68, and 0.51. After the division with the priority vector, values are equal to 5.36, 5.34, 5.37, 5.17, and 5.19. Their average gives the Principal Eigenvalue, λmax = 5.285. The random consistency index (RI) for n=5 is 1.12 according to Saaty’s scale.

$$ \mathrm{CI}=\left(5.285-5\right)/\left(5-1\right)=0.071 $$
$$ \mathrm{CR}=\mathrm{CI}/\mathrm{RI}=0.071/1.12=0.064<0.10\ \left(\mathrm{i}.\mathrm{e}.,\mathrm{consistent}\right). $$

Following the identification of the weights of the evaluation criteria, the F-PROMETHEE technique is applied to evaluate the two available alternatives. Table 4 shows the evaluation data of the expert group and the results. Based on the evaluations, the leaving flows ϕ+ and entering flows ϕ− are calculated. According to the outranking rule of F-PROMETHEE given in Step 2.3 of phase II, A2 (“to invest”) is by a far margin the preferred decision (ϕ+2 > ϕ+1 and ϕ−2 < ϕ−1).

Phase II: Decision on technology

ABC has carried out a technical study that compared various water treatment methods and decided that the most suitable WWT technology for its needs is the use of an ion exchanger (alternatives in phase II are based on this technology). Ion exchangers can help purify the water from cyanides and heavy metals.

There are two alternatives for ion exchangers, with different methods. For alternative A3, the wastewater generated by the CN and alkali baths and the wastewater coming from the Cr and acidic baths is combined and then sent to the ion-cathode exchanger. Then they are sent to the ion-anode exchanger without paying attention to ions’ signs of the wastewater. For alternative A4, the wastewater that comes from the CN and alkali baths is sent to the ion-anode exchanger. At the same time, the wastewater that comes from the Cr and acidic baths is separately directed to the ion-cathode exchanger. With this method, wastewater streams having different signs are not mixed.

These two alternatives are compared based on facility management, economic, volumetric capacity, and water quality criteria (Arroyo and Molinos-Senante 2018; Chen et al. 2018; Garrone et al. 2018; Gherghel et al. 2020). Here, facility management implies those processes that make the system easier to manage and maintain (Sawaf and Karaca 2018). Economic feature is represented by the net present value (NPV) of the considered investment. Volumetric capacity is the total amount of daily wastewater that can be treated and recycled with the associated system. The last criterion, water quality, stands for the threshold limits for the chemicals, heavy metals, and other contaminants dissolved in the discharged water. A detailed model of phase II is presented in Fig. 3.

Fig. 3
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Overview of phase II

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Assessment data submitted by the experts is shown in Table 5. It also lists the results of the assessment, which concludes that the alternative A4 should be chosen as it has a higher score of importance weight.

Table 5 Data for the second phase
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Phase III: Decision on system type

In this phase, based on the market research of ABC Company, the alternatives in question are either implementing a modular (A5) or a central (A6) system. While A6 is a standard ion exchange system, A5 has mobile modular ion exchange units. The central system includes a holding tank, pre-filtration with bag filters followed by cartridges, and two ion exchange tanks. The modular system uses the same cation exchange resin as the system in the mine that treats the major metal source. These alternatives are compared based on economic (C1), technical (C2), and administrative (C3) characteristics of the alternative (Molinos-Senante et al. 2015; Arroyo and Molinos-Senante 2018; Sawaf and Karaca 2018; Zhang et al. 2020a). C1 includes capital, personnel, operational, and maintenance costs. C2 includes applicability and performance. C3 includes reliability and sustainability. A detailed model of phase III is presented in Fig. 4.

Fig. 4
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Overview of phase III

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The evaluations submitted by the experts of ABC Company Istanbul are shown in Table 6. Table 7 gives the results obtained. Accordingly, the central system (A6) should be preferred over the modular alternative as it has a higher evaluation weight for each of the criteria.

Table 6 Evaluations of the third phase
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Table 7 Results of the third phase
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Phase IV: Decision on technology supporting company

The candidate technology providers are also determined by the experts of ABC Company (as A7, A8, and A9) and evaluated based on six criteria (Kalbar et al. 2012; Molinos-Senante et al. 2015; Chen et al. 2018; Garrone et al. 2018; Zhang et al. 2020a) supported by our literature survey (Fig. 5).

Fig. 5
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Overview of phase IV

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  • Initial cost of the investment—C1: This criterion refers to the initial investment cost proposed by the companies.

  • References—C2: This criterion stands for the proven experience of companies to ensure their capability, such as having recently constructed similar plants for other clients.

  • Popularity—C3: This represents the image, public acceptance, and recognition of this firm in the market.

  • Quality—C4: This is the offered service quality of that company.

  • Experience with the company—C5: This criterion checks whether ABC Istanbul has received acceptable services from this company in the past.

  • After-sales services—C6: This criterion is about the characteristics and the quality of the after-sales services.

The evaluation data of the experts for this stage is given in Table 8. Table 9 shows the obtained results, indicating that the most suitable company is A8 with the highest coefficient of closeness.

Table 8 Evaluations of the fourth phase
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Table 9 Results of the fourth phase
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Results and discussion

Managerial implications

The findings of this study provide clues for both administrators and researchers. WWT selection will not only have implications for the environmental footprint for many companies; it also leads to cost savings and other benefits. Each phase of the proposed framework can be adapted individually or wholly, according to the needs of the firms. The final adaptation can be made according to the different criteria. Although the obtained results are specific to the case study of this article, the proposed analytical decision methods can also be used to decide on the best alternatives for other types of WWT. Besides being an individual support tool, this proposed framework can also be used for supporting the decisions of the senior management by offering a structured input for WWT selection. According to Ozturk (2018), Turkey is a candidate member of the European Union, and the harmonization process of the EU acquis has been initiated with the environmental protection laws. Therefore, Turkey is aligning its national laws, and regulations with the European Union environmental legislation. New industry installations will be subjected to stricter environmental requirements, and existing conventional WWT facilities will be upgraded for compliance in the future. ABC Company also aims to revise its treatment processes accordingly. The selection of an appropriate treatment process is an important issue before the design and implementation of treatment plants.

Table 10 presents the results of the case application in this study. According to the case company, WWT enables companies to reduce their water consumption by up to 90%. It can allow to recycle and reuse the treated effluent in the manufacturing processes, thereby reducing freshwater consumption and related operational costs (Gholipour et al. 2020). Another point is that the use of such a WWT system also makes the process become discontinuous, lessening the frequency of monitoring (C5 in the first phase). To summarize the first phase of the case study, economic criteria are more important than environmental criteria.

Table 10 Summary for the proposed WWT Framework’s Application
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Ion exchangers (the evaluated alternative in the second phase) prevent sludge formation, which is composed of metals and other chemicals so that there is no more toxic waste to discharge. The second phase shows that ion exchangers, which do not mix wastewater streams with different signs, are more desired. When the question is about selecting the most suitable system type for ion exchangers, the third phase indicates that implementing a central system is better than a modular system according to economic, technical, and administrative characteristics. Finally, the fourth phase selects the most suitable technology provider company that will construct the WWT system. The results of the case study support the literature about using adsorption mechanism via ion exchange. The literature has extensively explored various treatment methods, such as chemical oxidation and biological treatment, for removing metal complexes from industrial effluents. Ion exchange methods have so far been one of the most widely accepted technologies, thanks to their low cost, short equilibrium time, ease of implementation, and reusability (Vidal et al. 2012; Chen et al. 2021). ABC Company also agrees with these benefits. When the results of this case study are presented to the expert group, it is observed that they agree with the experts’ judgments. Several observations were made by the case company showing that the selected alternatives in the decision phases were appropriate and correct and that this analytical method gave good results. ABC Company also stated that the standard ion exchange system (central system) can remove metals from the source effectively enough to treat the entire mine discharge and meet water quality standards. Even though this WWT system has increased the firm’s capital and operational expenditures, the termination of high discharge fees and transportation and disposal costs have brought further gains to the company. The environmental impacts of wastewater and the efficient use of resources provide additional benefits.

In real-world cases, decisions should be supported by multiple criteria and logical methods. In this paper, ABC Company’s expert group reaches similar or the same results in the case study without this application framework and methods. However, when problems are supported with real analytical techniques, the results become more tangible, convincing, and reliable. Regarding the advantages and appropriateness of the proposed method for the problems to be solved, the criteria used in the framework are considered to be independent. AHP is selected especially for parts where linguistic evaluations can be performed between independent criteria. Several studies also emphasize the condition of the AHP method as the independency of the criteria from each other (Büyüközkan and Çifçi 2012; Kazuva et al. 2020; Uliasz-Misiak et al. 2021).

WWT problems are frequently handled with MCDM methodologies, as Table 1 shows. Here, AHP acts as a value measurement model by decomposing a decision problem into its hierarchical components and prioritizing a set of weighted criteria. In phases I and III, this method also supported the translation of the subjective decision-maker opinions into measurable numeric relations. Also, in phase I, PROMETHEE as an outranking method simultaneously dealt with qualitative and quantitative criteria for the decision of investment. This method compared the alternatives pairwise for each criterion, finding the strength of preferring “to invest” over “not to invest.” In phase II, as the economic criterion is represented by the net present value (NPV) of the considered investment, cash flow analysis is used to define the cash position of ABC Company. According to Kahraman et al. (2002), experts’ knowledge about discounting cash flows consists of many uncertainties rather than randomness in an ambiguous economic decision environment. Cash amounts and interest rates are usually predicted using educated guesses based on expected values or other statistical techniques to obtain them. Fuzzy numbers can handle the difficulties in estimating these parameters. Finally, in phase IV, TOPSIS as a simple and effective MCDM model, measured how well the technology supporting company alternatives meet the desired criteria goals. Also, when fuzzy logic is integrated into these methods, the decision tool becomes more flexible and works more similar to human reasoning by handling the problems with imprecise data.

The use of fuzzy sets introduces robustness in decision-making processes by facilitating the comparison in the traditional weighting methods by addressing the uncertainty associated with human judgments. The literature also supports the features of fuzzy logic when integrated into decision-making methods such as removing bias from decision criteria and increasing the reliability of evaluation results (Büyüközkan and Çifçi 2011; Ali et al. 2021; Tang et al. 2021; Wang and Yang 2021). According to Ali et al. (2021), uncertainty is better addressed by using fuzzy numbers instead of crisp values under the assumption that this is a good solution that decision-makers can provide. Also, the fuzzification of the rating approach provides a way to better deal with decision-makers’ uncertainty regarding the boundaries of their preferences. As a result, a hybrid analytic framework is built to strengthen the decision-making process.

Comparative analysis

Another crucial point is the evaluation approach’s feasibility. The proposed hybrid approach consists of different multi-attribute evaluation and decision methods. Especially in the fuzzy AHP steps of the study, criteria priorities can be changed when other fusion methods are applied. This difference can lead to diverse evaluation results. Therefore, a comparative analysis is applied.

For MCDM problems, different aggregation methods are employed in the literature. After research on these methods, it is decided to perform a comparative analysis to confirm the feasibility of the fuzzy AHP prioritization step. In this study, the logarithmic least-squares method (LSM) (Eq. 6) is used to obtain the final weights. To make a comparison, the Ordered Weighted Aggregation (OWA) operator (Yager 1988) is applied, which also handles aggregation and prioritization issues. Readers are referred to that article for more detailed information. A sample comparison is performed for the third phase of the proposed evaluation framework, and the changes in the ranking are controlled. The outcomes of the analysis are displayed in Fig. 6.

Fig. 6
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Results of the comparative analysis for phase III

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According to the results, two methods provided equivalent alternative rankings (A6 > A5) with different weights. Although these weighting operators supply different weight scales, the results indicate A6 as the best alternative. The result of LSM can be seen in Table 7 with the middle values of fuzzy results. Here, the results of the OWA operator act in a similar way. It shows that both of these methods are consistent and valid for weighting purposes in decision-making. Based on this comparative analysis, it can also be concluded that these methods give different weights and do have an impact on the results. Even if the ranking did not change, the effects of varying weighting methods can be seen more clearly as the ranking changes with different evaluations, which includes similar criteria weights.

Conclusion

This paper introduced an integrated fuzzy MCDM evaluation model as a solution alternative for the WWT investment problem. Its usability is validated on a case study with ABC Company, Istanbul. Real-life multi-criteria problems are usually solved with uncertain and imprecise inputs. The fuzzy set theory can be an adequate tool to handle such situations. Once the relevant evaluation criteria are properly identified, the proposed four-phase evaluation framework is deployed step by step by combining different MCDM algorithms. The framework allows experts to express their preferences in a more systematic and accountable selection process.

Evaluation criteria are determined at every phase of the study, based on a literature review and expert opinions. Then, critical decisions are made, such as “to invest or not to invest” and “to select the most suitable technology, system type, or candidate constructor company.” This study contributes to the state of the art by proposing a new evaluation framework that includes different stages of the decision model including quantitative and qualitative data. Moreover, it is the first publication that handles all of the possible strategic decision-making stages for a WWT investment process, integrating AHP, PROMETHEE, cash flow analysis, and TOPSIS techniques in a fuzzy environment with group decision-making. This guides researchers and business managers to better understand the process of WWT investment problem and thus helps select WWT system strategies. A case study is provided to validate the presented approach.

The proposed integrated method can also be useful to form other suitable decision-making processes for other purposes. To the knowledge of the authors, this paper is the first study that deals with four phases of a WWT system investment and selection using a combined decision-making methodology. The study also has its limitations. The case study showed that the evaluation framework is reasonable and easily applicable to the strategic decisions about WWT. With the judgment of experts in this case study, it is considered that the criteria of the framework are sufficient, and the methodology is reliable. Nevertheless, for future work, evaluation criteria and the framework can be enriched. Another perspective can be the application of different MCDM approaches and fuzzy extensions for comparison purposes.