Selecting renewable desalination using uncertain data: an MCDM framework combining mixed objective weighting and interval MARCOS Open Access

Water shortage and energy depletion are major issues facing the world. Due to increased population, industrialization, and living standards, desalination technologies have been regarded as promising solutions for water scarcity (Benghanem et al. 2022). However, as energy-intensive processes, desalination technologies that are powered by fossil fuels consume plenty of power while generating a large amount of greenhouse gases (GHGs), resulting in the necessity of integrating renewable energy into desalination technologies (Tigrine et al. 2021).

Desalination technologies can be categorized into thermal and membrane processes. The thermal processes, like multi-effect distillation (MED) and multi-stage flash distillation (MSF), belong to the phase-change technologies, which use evaporators and condensers to generate potable water from seawater or brackish water by resorting to the vaporization principle. The membrane processes, like reverse osmosis (RO) and electrodialysis (ED), belong to the non-phase-change technologies, which employ physical barriers to separate the salts from the seawater for producing freshwater (Gude 2016). However, the membrane processes of RO and ED rely heavily on electrical power for operation, while the thermal processes of MED and MSF consume much more energy, including both thermal and electrical (Abdelkareem et al. 2018). The challenge highlights the necessity of developing and practicing renewable desalination systems by integrating renewable energy resources into the thermal or membrane processes. Recently, some efforts have been made in renewable desalination systems. For instance, solar collectors are used for supporting a MED plant with a capacity of 72 m³/day, where a water production cost of US$4.95/m³ is achieved (Cunha & Pontes 2022). In the work of Kabiri et al. (2021), environmental friendliness and economic benefit have been confirmed by integrating solar thermal into the MSF technology. Solar photovoltaic (PV) instead of solar collectors is applied to power the membrane technology of RO and the result verifies both the technical and economic feasibility of the renewable desalination combination (Mostafaeipour et al. 2019). In the literature (Rosales-Asensio et al. 2019), wind power is also utilized to drive the RO process and the cost of water could be reduced by enhancing the feasibility and efficiency of this renewable desalination. Besides the above-mentioned technologies and energy resources, other desalination processes like mechanical vapor compression (MVC) (Tzen 2018), ED reversal (EDR) (He et al. 2020), humidification dehumidification (HDH) (He et al. 2022), as well as other powers such as geothermal (Behnam et al. 2022) and wave energy (Brodersen et al. 2022) could be integrated into renewable desalination systems.

Given those varieties of desalination technologies could be powered by different renewable energy resources, how to identify the most appropriate renewable desalination among multiple alternatives becomes a challenging task. Appropriate renewable desalination should consider several aspects, including technological efficiency, environmental impacts, economic feasibility, and social responsibility. Consequently, the overall performance of renewable desalination is better defined using multi-dimensional criteria, which results in the necessity of applying multi-criteria decision-making (MCDM) in the identification. As summarized in Table 1, the feasibility of the application of MCDM in renewable desalination systems has been confirmed by several studies.

As observed in Table 1, when selecting appropriate renewable energy, multiple criteria should be considered. Since the relative importance regarding each assessment criterion is associated with the contribution of the criterion to the overall performance of renewable desalination, adopting a proper weighting method plays a critical role in generating a rational decision output. Based on the collected data of the criteria and the determined weights, different ranking techniques can be utilized in prioritizing renewable desalination alternatives. However, it is hard to tell which method is better because different ranking methods with divergent computational mechanisms will generate discrepant results. As also observed in Table 1, the quality of the evaluation data used in the decision-making could be improved. On the one side, quantitative information cannot avoid excessive disturbance from subjective factors; on the other side, because of many uncertainties (Skourtos et al. 2021) qualitative data are always volatile rather than deterministic. Therefore, to better use the uncertain data from the multi-dimensional criteria in renewable desalination selection, two mathematical limitations need to be addressed, as specified below.

The first limitation is the lack of a rational method to grant objectivity and fairness to the weighting result. Specifically, pair-wise comparisons (like AHP) are the most frequently adopted weighting methods, which determine the relative importance of the criteria according to subjective preferences. However, by heavily relying on the users’ experiences, the subjective weights would be manipulated by the users consciously or unconsciously. In contrast, objective ones (like entropy) can assign weights to the criteria by analyzing their qualitative information. With the growing number of valuable data available in renewable desalination systems, weighting the criteria objectively has been well accepted by recent literature (Rezk et al. 2021; Huang 2022). However, traditional objective methods assign weights by analyzing the dispersions among the evaluation data, failing to consider the correlations between the interrelated criteria. As declared in Li et al. (2020), using multi-criteria to depict the overall performance of energy-related systems is challenging because the involved criteria could have complex interrelationships; more importantly, ignoring the interrelationships would lead to a biased weighting result (Xu et al. 2020b).

The second limitation is that the ranking method should be improved to ensure consistency with the uncertain data and stability in the decision output. Among the MCDM, the compensatory ranking approaches, especially TOPSIS (technique for order of preference by similarity to ideal solution) and its variations, have been quite favored in previous work regarding desalination systems (Vivekh et al. 2017; Wang et al. 2019; Xu et al. 2020b), since they can consider both the best and the worst scenarios in the decision issues and thus offer a complete ranking result by analyzing the weighted evaluation data. However, when the number of criteria and alternatives grows, the evaluation data become complex because of uncertainty, which may increase the sensitivity and instability of the ranking results caused by the fluctuations in weights and performance ratings in the criteria (Trung 2022).

This study proposes a generic mathematical framework in renewable desalination selection to upgrade the weighting and ranking technique under uncertain data conditions by introducing a novel mixed objective weighting (MOW) method and extending a ranking technique. To improve the objectiveness and fairness in the weighting result, the MOW combines the variations and correlations among the performance ratings of the criteria. In this method, on the one side, the dispersion regarding the criteria is measured by using interval MEREC (method based on the removal effects of criteria), which assigns a greater dispersion level to a criterion when its removal leads to more impact on the overall performance (Keshavarz-Ghorabaee et al. 2021). On the other side, complex interrelationships among the criteria can be addressed by proposing interval GANP (grey-relational coefficient-based analytic network process), where the ANP measures the correlation degrees by resorting to the objective datasets generated by the grey relational coefficient (GRC). In addition, dispersions and correlations are integrated into the MOWs by creating a constrained optimization programming. To guarantee consistency with the uncertain data and stability in the prioritization, MARCOS (measurement of alternatives and ranking according to compromise solution), a relatively new ranking method, is extended into interval number conditions to identify the most appropriate renewable desalination. The most attractive feature of MARCOS is the ability to maintain stability in the decision output by integrating three well-recognized concepts in MCDM. Specifically, the ideal and anti-ideal reference points, relationships between the reference points and a set of alternatives, as well as the utility degree approach, are properly reconciled to guarantee the reliability of the MARCOS (Deveci et al. 2021; Gong et al. 2021). Therefore, after extending the MARCOS into uncertain conditions, massive criteria and alternatives in renewable desalination can be well evaluated. In general, the contributions of the proposed hybrid MCDM framework include:

• The MOWs are generated from the performance ratings of the criteria, which eliminate human manipulation; more importantly, by capturing and integrating both the dispersions and correlations among the numerical data, the MOW method can grant fairness and rationality in the weighting result.

• Interval MARCOS enables prioritization under uncertain conditions by fully using the evaluation data while well preserving their original uncertainties; meanwhile, this method reconciles three comparison concepts to rank the alternatives, which improves the stability and robustness of the decision output.

The rest of this work is organized as follows: Section 2 introduces the related mathematical methods, Section 3 uses a case study to test the feasibility of the framework, Section 4 provides the results comparison, and Section 5 offers the conclusions and future directions.

Eight steps are involved in the MOW method. Interval MEREC (Steps 1–3) calculates the dispersion of the criteria, interval GANP (Steps 4–7) obtains the correlations between the criteria and constrained optimization programming (Step 8) integrates the dispersions and the correlations into the objective weighting.

MEREC fully utilizes the performance ratings of the criteria and thus offers a rational way to measure their variations and dispersions. Considering the uncertain feature of the evaluation data, the traditional MEREC (Keshavarz-Ghorabaee et al. 2021) is extended into the interval number conditions for measuring the dispersion levels among the criteria, via the following actions.

Step 1: Transforming data. The original collected data of the criteria's performance ratings should be transformed using Equation (1). Notably, different transforming formulas are needed according to the benefit or cost feature of a certain criterion.

Step 2: Calculating the overall performance and the criterion-removed performance. First, a logarithmic measurement (Equation (2)) is used to calculate the alternative's overall performance. Subsequently, a similar measurement (Equation (3)) determines the criterion-removed performance. Compared with Equation (2), the performance calculated by Equation (3) is based on removing each criterion separately (Keshavarz-Ghorabaee et al. 2021).

ANP has been widely practiced for analyzing interrelated criteria. However, the initial relationships in ANP are created based on subjective assumptions, failing to offer an objective way to calculate the inherent correlations. This work introduces a novel technique by combining the grey relational coefficient (GRC) with the ANP, where the GRC is used to provide the statistic-based relationships and enables the ANP to determine the correlations objectively. The introduced GANP includes four steps, which are also implemented under uncertain conditions.

Subsequently, the value of is taken as original data for implementing the ANP method.

As a relatively new ranking method proposed by Stević et al. (2020), MARCOS belongs to the compensatory MCDM methods, which can offer a complete sequence of alternatives by resorting to the utility degree approach and the reference point sorting approach. Considering the involved uncertainty in the evaluation data, the traditional MARCOS is extended into interval number conditions for implementing the prioritization: see Steps 9–11.

A hybrid MCDM framework is developed in this study for evaluating renewable desalination. In this section, an illustrative case is investigated to test the feasibility of the framework. To be specific, this case study includes four alternatives and they are solar thermal-multi-stage flash (A1), solar thermal-MED (A2), photovoltaic-RO (A3), and wind power-RO (A4). Notably, the involved alternatives are applied for the framework demonstration. Users can add new alternatives or delete the original ones when applying the MCDM framework according to their research purpose. For more information regarding the alternatives, reference can be made to the literature (Abdelkareem et al. 2018; Xu et al. 2020b).

The overall performance of the alternatives is defined by an eight-criteria system that considers four dimensions. As shown in Table 2, the categorized feature regarding each dimension is depicted by two criteria, which could be either benefit criteria or cost criteria. Similarly, the evaluation criteria system could be freely created by users based on the actual conditions of the investigated alternatives and the stakeholders' interests. For being in line with the real-world decision issues, the evaluation data regarding the criteria are denoted as interval values, as shown in Table 3.

The interval MARCOS method ranks the four renewable desalination alternatives. Specifically, the IM, NM, and the weighted matrix should be created sequentially (see Step 9). As summarized in Table 4, the weighted matrix consists of the four alternatives, as well as the worst and best ones. Subsequently, according to Step 10, the utility degree of each alternative regarding the worst (⁠⁠) or the best (⁠⁠) reference alternative is also determined, while the results are also given in Table 4. Based on this, the utility function of the ith alternative is calculated, as shown in the last column in Table 4.

Table 4

Weighted matrix and the results of interval MARCOS in the case study

.	C1 .	C2 .	C3 .	C4 .	C5 .	C6 .	C7 .	C8 .	.	.	.
W	0.002	0.034	0.009	0.017	0.241	0.041	0.043	0.052	1.000	0.439	0.631
A1	[0.002, 0.002]	[0.034, 0.042]	[0.023, 0.113]	[0.017, 0.020]	[0.156, 0.179]	[0.055, 0.066]	[0.043, 0.068]	[0.069, 0.104]	[0.908, 1.355]	[0.398, 0.594]	[0.500, 1.372]
A2	[0.003, 0.003]	[0.042, 0.112]	[0.039, 0.049]	[0.036, 0.044]	[0.153, 0.241]	[0.041, 0.047]	[0.063, 0.098]	[0.069, 0.104]	[1.019, 1.591]	[0.447, 0.698]	[0.661, 2.156]
A3	[0.027, 0.071]	[0.042, 0.112]	[0.009, 0.010]	[0.006, 0.007]	[0.152, 0.280]	[0.110, 0.110]	[0.044, 0.066]	[0.069, 0.104]	[1.048, 1.730]	[0.460, 0.759]	[0.708, 2.780]
A4	[0.146, 0.211]	[0.070, 0.140]	[0.012, 0.017]	[0.089, 0.109]	[0.115, 0.181]	[0.094, 0.110]	[0.044, 0.066]	[0.052, 0.069]	[1.418, 2.060]	[0.622, 0.904]	[1.555, 5.013]
B	0.211	0.140	0.113	0.109	0.115	0.110	0.098	0.104	2.279	1.000	7.472

.	C1 .	C2 .	C3 .	C4 .	C5 .	C6 .	C7 .	C8 .	.	.	.
W	0.002	0.034	0.009	0.017	0.241	0.041	0.043	0.052	1.000	0.439	0.631
A1	[0.002, 0.002]	[0.034, 0.042]	[0.023, 0.113]	[0.017, 0.020]	[0.156, 0.179]	[0.055, 0.066]	[0.043, 0.068]	[0.069, 0.104]	[0.908, 1.355]	[0.398, 0.594]	[0.500, 1.372]
A2	[0.003, 0.003]	[0.042, 0.112]	[0.039, 0.049]	[0.036, 0.044]	[0.153, 0.241]	[0.041, 0.047]	[0.063, 0.098]	[0.069, 0.104]	[1.019, 1.591]	[0.447, 0.698]	[0.661, 2.156]
A3	[0.027, 0.071]	[0.042, 0.112]	[0.009, 0.010]	[0.006, 0.007]	[0.152, 0.280]	[0.110, 0.110]	[0.044, 0.066]	[0.069, 0.104]	[1.048, 1.730]	[0.460, 0.759]	[0.708, 2.780]
A4	[0.146, 0.211]	[0.070, 0.140]	[0.012, 0.017]	[0.089, 0.109]	[0.115, 0.181]	[0.094, 0.110]	[0.044, 0.066]	[0.052, 0.069]	[1.418, 2.060]	[0.622, 0.904]	[1.555, 5.013]
B	0.211	0.140	0.113	0.109	0.115	0.110	0.098	0.104	2.279	1.000	7.472

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In this section, two comparative items are implemented to confirm the effectiveness of the introduced weighting and ranking methods.

In Equation (25), could be either the dispersion or the correlation regarding the jth criterion (see Figure 2) and is the corresponding dispersion-based weight or the correlation-based weight. As noted in Figure 4, the dispersion-based weights calculated by interval MARCOS are different from the correlation-based weights derived from interval DANP; while the MOW method can reconcile discrepancies in the two weights. Taking C1 as an example, it is regarded as the most important criterion (0.241) from the viewpoint of dispersion but is assigned a moderate weight (0.121) according to correlation. Meanwhile, after combining the dispersion and correlation, the MOW concerning C1 equals 0.211. Accordingly, it could be demonstrated that only taking the values generated from interval MARCOS or interval GRC would overestimate or underestimate the relative importance of the criteria, which implies the necessity for combining the dispersions and correlations into the MOWs.

Since the utilized MARCOS is a modified ranking technique under uncertain conditions, its feasibility should be confirmed. Consequently, two well-practiced MCDM methods in their interval version are employed to prioritize the four alternatives using the same decision-making dataset. Specifically, interval TOPSIS (Jahanshahloo et al. 2009) and interval VIKOR (Sayadi et al. 2009), respectively, generate the final score of each alternative, while the sequence derived from each method can be determined by using the possibility measurement (Step 11). The ranking results are summarized in Table 5, where the top two appropriate options are the wind power-RO and the photovoltaic-RO, while the rest of the two alternatives including the solar thermal-MSF and solar thermal-MED, respectively, ranked fourth and third, signifying that combining the RO technology with renewables would be superior to the thermal-based desalination alternatives.

Renewable desalination could benefit water supply and energy utilization, which is increasingly used to address water shortage and energy depletion. With the development of desalination technologies and renewable energy systems, using renewables to power desalination has expanded rapidly in the past decade and could be expected to increase more quickly over the coming years. Therefore, developing a systematic framework is of great significance for identifying the most appropriate renewable desalination among multiple alternatives. This study proposes an MCDM framework to assess alternatives by considering multi-dimensional criteria and uncertain data, where a novel weighting method (MOW) is introduced and a ranking method (MARCOS) is modified. In the framework, the MOW method can integrate the dispersions and correlations among the criteria to generate objective weights; interval MARCOS can be used in uncertain conditions to rank the sequence. To test the feasibility of the framework, an illustrative case concerning four renewable desalination alternatives is studied by using an eight-criteria evaluation system. In addition, the advantages and effectiveness of the involved methods are verified by comparing the results.

Compared with existing works, this study could have two mathematical contributions: on the one side, the weights of the multi-criteria are obtained by resorting to the statistical features of the evaluation data, which can avoid subjective manipulation and thus improve the weights' reliability. Notably, the MOW method combines the techniques of interval MEREC and interval GANP for simultaneously considering the dispersions and correlations among the criteria, which can offer a more rational weighting result by avoiding bias. On the other side, interval MARCOS can well preserve the original uncertainty in the evaluation data by resorting to the interval numbers. More importantly, this method adopts the utility degree approach and the reference point sorting approach to prioritize the alternatives, which can improve the stability and robustness of the decision output.

Despite the effectiveness of the proposed framework, it does have some limitations. For instance, it is suggested to use some systematic approaches to select proper criteria for building the assessment system; it needs to consider other types of uncertain data in the decision-making; and it requires providing a broader investigation by considering more desalination technologies and renewable energy resources, even including hybrid technologies and combinations between the renewables.

This work is funded by the Science and Technology Research Program of Chongqing Municipal Education Commission, China, Grant No. KJQN202003208.

All relevant data are included in the paper or its Supplementary Information.

The author declares there is no conflict.