# Selection of Desalination System for Commercial Vessels by Implementing Improved Intuitionistic Fuzzy TOPSIS Method

Authors: Yunus Emre Nazligul; Devran Yazir; Bekir Sahin
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

The process of desalination of seawater on commercial vessels is a vital event in the daily life of the crew. As a result of the rapid developments in ballast water treatment operations, the question of whether ballast water treatment systems can be used as the main desalination system in the daily life of the crew on commercial vessels has been raised. This study introduces the current desalination systems on commercial vessels and their evaluation criteria. According to the literature and our professional industrial research, there are three most suitable alternatives such as “freshwater generator,” “reverse osmosis method,” and “attaching additional membrane filter to mechanical and ultraviolet (UV) ballast water treatment system.” Similarly, the evaluation criteria are determined as “installation cost of the system,” “operational cost of the system,” “risk of the system polluting the environment,” “risk of the system harming the human health,” “ease of repair and maintenance of the system,” “ease of use of the system,” and “ease of installing the system on the ship.” Due to the need for field expertise, we conducted several rounds of expert consultations. The novelty of this study is twofold. First, we improved the intuitionistic fuzzy TOPSIS (IF-TOPSIS) method by extending an expert prioritization technique. We also used an intuitionistic fuzzy scale for the expert weights. Second, as far as we know, this is the first study that employs an improved IF-TOPSIS method for desalination systems on commercial vessels. Moreover, we compared the proposed method and other methods to analyze the results. Results show that “freshwater generator” is more promising than “attaching additional membrane filter to mechanical and UV ballast water treatment system” that is prior to “reverse osmosis method.” This study helps the users and authorities understand the evaluation and select the desalination systems.


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## Body

## 1. Introduction

Water is vital for life and also has the first priority for seafarers on vessels. The water used in showers, sinks, urinals, toilet bowls, laundry, cooking, and washing dishes on ships can only be produced by desalinating seawater or by taking some freshwater from the port into a vessel’s tank. The water subject to desalination processes is called freshwater. The method used is called desalination [1]. Although the most used desalination method is distillation, the methods such as reverse osmosis, flash, and electrodialysis can also be used rarely [2].In terms of freshwater consumption, while the average daily water consumption per person is 200 liters on passenger ships, this figure is approximately 60 liters per crew per day on cargo vessels [3]. Freshwater obtained by desalination must comply with certain controls. According to the International Standards Organization (ISO) standards, the water obtained from the sea should be heated to at least 80°C and disinfected by the boiling method [4]. According to the International Convention for the Prevention of Pollution from Ships (MARPOL 73/78) Annex-IV, the high-density brine portion of the distilled brine cannot be discharged within 12 nautical miles from the shore without the presence of a wastewater treatment equipment or disinfection system on board [5].Another desalination method, which can be an alternative to the freshwater generator (distillation) and like the reverse osmosis method (membrane filtration), is the ballast water treatment system, which has recently begun to be used. The Ballast Water Treatment System Convention, which regulates this system, entered into force in 2017 with the votes of the member states in the convention organized by the International Maritime Organization (IMO) of the countries affiliated with the United Nations (UN) [6].Due to the ship’s own stability, the discharged cargo causes the ship to tend to raise the G (center of gravity) point or vice versa in a loading situation. As a result of these events, the ship’s officers must take ballast water to the ship’s lower segments, which are called ballast tanks, in order to keep the ship floating and reduce the swing period by reducing the G point of the vessel. Lowering the G point of the vessel would cause to increase in metacentric height (GM) and result in positive stability of the vessel. So, preparing the vessel that way would help to vessel's tendency to resist capsizing. It is widely known and acknowledged by UN countries and companies that these ballast water intake or discharge operations could also carry microorganisms. As a result of the understanding of the damage to the environment caused by the microbiological organisms transported by the transport of the ballast water to other regions, commercial vessels have been forced into a new process by international conventions [7]. According to the convention text, later than this convention is signed, ballast water taken onboard will be passed through various filters before being taken to the ship and discharged, and if necessary, the harmful microbiological organisms will be eliminated by methods such as UV and ozonation [8].The ballast water treatment system is an actual branch of the reverse osmosis method, which filters salt, dirt, and microorganisms through the relevant filters inside and then aims to fill the ballast tanks with purified water using the UV light or ozonation methods that kills harmful organisms [9]. The discharged ballast water passes through the ballast water treatment system for the second time, ultimately ensuring that pure, microorganism-free, and clean water is pumped out to sea [10]. In this way, the harmful organisms are not to be transported between different seas. So the harmful organisms that will multiply rapidly in the area will not be carried through ballast tanks and will not aid to kill existing microorganisms in different local ecosystems. The reason for the use of this method is the existing freshwater distillation method consumes a lot of energy per cubic meter, there is no suitable boiler on the ship that can meet the ballast tanks that occupy a large amount of volume, and the polluted water must be filtered somehow in any case [11].Another goal of this study is to determine whether the reverse osmosis method is viable to use in commercial vessels or not, which is not mentioned in the literature but is currently heavily used by North Africa, the Middle East, and South Asian countries to treat seawater. With this, finding an answer to a question “whether the ballast water treatment system can be used as an alternative to the freshwater generator during desalination of the seawater or not” will be questioned.The paper continues as follows. Literature review is conducted in Section2. Section 3 gives the proposed methodology. Then, the criteria and alternatives in line with the relevant expert opinions and literature review are defined in Section 4. The application is completed in Section 5. Finally, results, recommendations, and future studies are given in Section 6.


## 2. Literature Review

The aim of the study is to investigate whether the reverse osmosis method and ballast water treatment system can be an alternative to the seawater distillation method (known as the evaporator method), which is currently actively used on ships. There are many studies on the related desalination methods in the literature. For example, Gluekstern and Priel [12] have designed seawater reverse osmosis filtration (SWRO) plantations that could be established for Israel and found that the cost for each 150,000 m³ of desalinated freshwater production is 0.5 US dollars. They also have revealed the fact that the SWRO method can be cheaper than other systems. Choi [13] has kept the salinity rate at 10 ppm in his experiment on a freshwater generator producing 30 metric tons of freshwater per day and 1.5 metric tons per hour. He has proved that the capacity of the produced freshwater per cubic meter is not related to the low-temperature difference between weather conditions or the high-temperature difference between weather conditions. In addition, he has determined that the received seawater temperature is related to its initial temperature. Song et al. [14] have explained the relationship between the pressure applied to the transmembrane filter of the water to be treated and the percentage of recovered water. As a result of the research, water recovery starts from 500,000 Pa and becomes inefficient after 2,500,000 Pa pressure. Fritzman et al. [15] have stated that the ratio of Kw/m³ is 2 in the reverse osmosis method. Also, they have stated that Spain achieves 4.6% of all freshwater use (2,326 m³ per day) by the reverse osmosis method. This situation exemplifies the models of Israel, Cyprus, Malta, and Belgium, which are more water-scarce than Spain. Cardona et al. [16] have examined the natural gas energy consumption in SWRO systems and revealed that natural gas consumption is more efficient than other systems in freshwater production. Gurtler et al. [17] have combined the reverse osmosis method with the electrodialysis method. They have stated that by giving electricity to the saltwater with the electrodialysis method, they have reduced the salt solution ratio in the water by 1.5:1. Khawaji [18] has reviewed current R&D studies on desalination systems in Fujairah/Dubai. He has stated that reducing the cost of desalination systems can be achieved by hybrid systems. In addition, he has shown the world’s largest hybrid multistage flash and reverse osmosis system as an example. The World Health Organization (WHO) [19] has said that the following should be taken into account for purification purposes: exposed UV intensity level, pH, light absorption, the durability of the membrane in the filter, flow rate, watercolor, conductivity, local meteorological weather events, water turbidity, algal growth status, bacteria, microbiological organisms, chlorine, oxidation, and pressure. According to Caron et al. [20], the use of the reverse osmosis method has increased due to its lower cost compared to other methods. However, the membrane filters used in this method should not let the algae pass from the filter. Unfortunately, they could not find evidence that the toxins left by the algae when filtered. This result has shown that monitoring sensors for detecting algae ASP and PSP toxins must be developed, and the reverse osmosis method may not be filtrated adequately in certain circumstances. Pangarkar et al. [21] have stated that although India constitutes 16% of the world population, it has only 4% as a freshwater resource. They also have stated that the water needed by India would probably be 1,450 km³ in 2050 and the current water requirement in India is 1,086 km³. They have mentioned the potential growth of the RO system might help future India’s sustainability. Chung et al. [22] have pointed out the necessity of the desalination process. They have stated that while only 1% of the Earth is covered with freshwater, the remaining left 97% is covered with saltwater. They have designed a freshwater generator system that can operate under low temperature and pressure, responding to this need. Stated that the water can be evaporated below the boiling point at low temperatures (40–80°C) and the low pressure brings lower costs. Giernalczyk and Herdzik [23] have studied freshwater treatment for sailing ships. Their research examined the 667 DWT, 94.7 meters long, 14 meters wide sailing ship named S/V Dar Młodzieży. They have calculated that the freshwater tank of the ship is 338.1 m³, the daily freshwater consumption is 18.8 m³, and the daily water treatment is 10.62 m³. With the freshwater treatment device attached to the sailboat, the time for the ship to stop by the port for water and receive supply has been increased from approximately 18 days to 41 days. While the system’s installation cost is PLN 15,500 the water treatment cost per m³ is calculated as PLN 5. Diaconu and Dragomir [24] have shown a high percentage of salt, metal oxides, silica, and a lot of debris would remain at the bottom of the boiler of freshwater generators working with boilers. They have stated that these molecules accumulated with possible neglect or leakage can quickly pass into the freshwater tank. They have reached the outcome that the corroded metal in the boiler might be a possible defect in the filtration. They have underlined that the first condition of a successful distillation is to pass through the right filter. Youssef et al. [25] have examined the existing desalination systems and reached the outcome that the multistage flash (MSF) system is the most inefficient freshwater treatment system according to the amount of energy consumed. They have also revealed that the humidification and dehumidification distillation (HDH) method has the lowest water consumption. Guler et al. [26] have investigated the desalination costs per cubic meter according to sea temperatures and salinity rates. They have found that the lesser salinity ratio is more effective than the higher temperature ratio in terms of the desalination process environment. Kumar and Kumar [27] have referred to wastes and flue gases at high temperatures as the negative effects of global warming. They have underlined the benefits of thermoelectric generators on boilers. The benefits of this generator help reduce the greenhouse gas (GHG) factor by generating electricity, increasing efficiency, and reducing the demand, and it is the fuel cost of other natural gas power plants. They have produced a thermoelectric generator by mixing a 1:10 ratio of petroleum jelly and petroleum wax. They have also pointed out that with the help of this system, the heat of the funnel of a vessel could be used as potential electrical energy with the necessary equipment connected to the ship. Güney [28] has reminded that all new vessels launched after 2017 must plant ballast water treatment systems, and existing vessels over 400 GT with permanent ballast tanks must have ballast water treatment systems by 2024 at the latest. Also, he has compared the brands of the existing ballast water treatment systems. Pecarevic et al. [29] have examined the role of the hydrocyclone, which is used in ballast water treatment systems. As a result of the research, they have concluded that the hydrocyclone has increased the treatment capacity in cubic meters per hour at a high rate in the ballast water treatment system. Vorkapic et al. [30] have divided ballast water treatment systems into three groups. They have examined D1, D2 + UV, and D2 + EC standards. For a true comparison of each system, a 54,335 DWT LPG ship with a 17,741 m³ ballast tank has been selected as an example. They have calculated the annual costs of each system. Results have been found as the D1 system cost 4,368.96 USD, the D2 system cost 2,885.59 USD, and the D2 + EC system cost 623,61 USD. Yuksel et al. [31] have researched the seawater inlet temperature entering the freshwater generator. After the experiments, they observed that the efficiency of the produced freshwater increased with each degree increase from –273°C (absolute zero) to 30.83°C of temperature. However, they have observed that when the temperature rises above 30.83°C, the freshwater yield decreases very rapidly. Karabelas et al. [32] have analyzed the energy consumption in the reverse osmosis system. As a result of the data obtained, they have stated that the energy consumed per cubic meter to be produced is 2.37 kW/h in total and that each 10% increase in pressure at the seawater inlet will create an increase of 0.2 kW/h per m³. Enescu [33] has researched methods to generate energy from stack heat to reduce energy consumption and increase efficiency in ship fittings. He stated that thermoelectric generators work with 5–6% efficiency in flue waste-heat energies. He also stated that these generators, which can operate at temperatures up to 250°C and convert electrical energy, are one of the efficiency-increasing elements in recycling. He has stated that thermoelectric generators can reach up to 10% efficiency due to recent developments in materials science. Tokuş [34] has investigated the costs of standard D1 and D2 methods in the ballast water treatment methods determined by IMO and showed that the installation cost of the ballast water treatment system is €400,000. He also has underlined that the highest cost is not the cost of use but the investment costs. Hartanto et al. [35] have surveyed 67 maritime students returning after a 12-month long-term sea internship about the freshwater generator. The survey data obtained was evaluated in the SPSS program. After the following conclusion was reached, the differences in the pump of the freshwater generator affected the freshwater production efficiency positively by 39%, and changing the ejector positively affected the efficiency by 43.5%. Amaya-Vias et al. [36] have investigated the design of a simpler and less emissive desalination system. They have stated that the direct contact spray assisted evaporation method increased the potable water rate up to 34%, improving the microbubble method in distillation. Alrowais et al. [37] have compared DCMD, AGMD, and WGMD water treatment configurations with different membrane filters in the 0.45 and 0.20 μm range on cruise ships. They have stated that the membrane with 0.45 μm holes has 99.99% salt filtration and can be a sustainable desalination method in passenger ships with the WGMD system.When the literature research has been reviewed thoroughly, it has been seen that the existing studies mostly focused on passenger ships and shore-based desalination systems. This study, unlike other studies, has been aimed to select the most suitable desalination system for cargo vessels among the alternatives of “freshwater generator,” “reverse osmosis method,” and “adding a membrane filter if mechanical + UV ballast water treatment system available onboard.”


## 3. Methodology

Alternatives and criteria are determined based on the expert opinions by conducting several expert consultations. The alternatives are determined without leaving any room for other alternatives, since there are three different desalination methods that can be used at present, and other methods cannot be used on ships. The alternatives are selected as follows: alternative 1: freshwater generator, alternative 2: reverse osmosis method, and alternative 3: a mechanical + UV ballast water treatment system with an improved additional membrane filter.The TOPSIS method is frequently preferred in the literature because it reveals the distances between the positive and negative ideal solutions. It is easy to use, understand, and interpret the results and is also simple in ordering the alternatives. The intuitionistic fuzzy extended version of the TOPSIS method is used in this study because it is possible to assign different importance to decision-makers, to see different results by giving different importance, and to be accepted by the literature in giving intuitionistic values. The alternatives and criteria are evaluated in line with the questionnaires answered by the experts and the alternatives are listed. The results and interpretations are provided in Section6.


### 3.1. Intuitionistic Fuzzy TOPSIS Methodology

#### 3.1.1. Intuitionistic Fuzzy Sets and Scale

In this study, intuitionistic fuzzy TOPSIS methodology is utilized based on the work of Shen et al. [38] in an intuitionistic fuzzy environment, which is a complex form of fuzzy sets [39] and TOPSIS [40]. The set of alternatives is A=A1,A2,…,Am, and the set of criteria is C=C1,C2,…,Cn. The decision-making group is not equal and consists of ℓ different decision-makers. In nonidentical decision-making groups, the relative importance of the decision-makers, therefore, differs from each other.Intuitionistic fuzzy linguistic terms are used in the evaluation of decision-makers, which is given in Table1 [41], Also, Table 1 is reproduced from [42].Table 1
Linguistic variables [41, 42].
Linguistic termsμνπVery good0.750.100.15Good0.600.250.15Moderate0.500.500.00Bad0.250.600.15Very bad0.100.750.15


#### 3.1.2. Expert Prioritization by Using Intuitionistic Fuzzy Scale

Decision-makers may have less or more expertise levels than other decision-makers due to their different experiences and knowledge. The weight vector of the decision-makers isλ=λ1,λ2,…,λℓ and λ≥0,k=1,2,…,ℓ. If λk≥0,k=1,2,…l, and ∑k=1lλ=1, the weight vectors of decision-makers are applied as follows:(1)λ=μk+πkμk/μk+νk∑k=1lμk+πkμk/μk+νk.


#### 3.1.3. Intuitionistic Fuzzy TOPSIS Method

(1) First Step: After calculating the weight vectors of the decision-makers, the intuitionistic fuzzy decision matrix D=α˜ijmxn,i=1,2,…,m;j=1,2,…,n is generated in the form of α˜ij=μij,νij, where m represents alternatives and n represents criteria.(2)C1C2⋯CnD=α˜ijmxn=A1A2⋮Amα˜11∗α˜12∗⋯α˜1n∗α˜21∗α˜22∗⋯α˜2n∗⋮⋮⋱⋮α˜m1∗α˜m2∗⋯α˜mn∗.(2) Second Step: Positive ideal solution is calculated based on α˜j−+, and let C+, C−, and 1 ≤j≤n be according to(3)α˜j+=max1≤i≤mμij,min1≤i≤mνij=μj+,νj+,ifCj∈C+,min1≤i≤mμij,max1≤i≤mνij=μj+,νj+,ifCj∈C−..(3) Third Step: Negative ideal solution is calculated based on α˜j−+, and let C+, C−, and 1 ≤j≤n be according to(4)α˜j−=min1≤i≤mμij,max1≤i≤mνij=μj−,νj−,ifCj∈C+,max1≤i≤mμij,min1≤i≤mνij=μj−,νj−,ifCj∈C−.(4) Fourth Step: Positive intuitionistic fuzzy matrix D+ is calculated as follows:(5)C1C2⋯CnD+=dα˜ij,α˜j+mxn=A1A2⋮Amα˜11∗,α˜1+α˜12∗,α˜2+⋯α˜1n∗,α˜n+α˜21∗,α˜1+α˜22∗,α˜2+⋯α˜2n∗,α˜n+⋮⋮⋱⋮α˜m1∗,α˜1+α˜m2∗,α˜2+⋯α˜mn∗,α˜n+.The differences between two intuitionistic fuzzy numbersα=μα,να and β=μβ,νβ are calculated as follows:(6)dα,β=μα1+2/3πα1+πα−μβ1+2/3πβ1+πβ2+να1+2/3πα1+πα−νβ1+2/3πβ1+πβ22.According to Boran and AKay [43], μα and να will be equal to μα,μα+πα and να,να+πα at any value.(5) Fifth Step: Negative intuitive fuzzy distance matrix D− is calculated as follows:(7)C1C2⋯CnD−=dα˜ij,α˜j−mxn=A1A2⋮Amα˜11∗,α˜1−α˜12∗,α˜2−⋯α˜1n∗,α˜n−α˜21∗,α˜1−α˜22∗,α˜2−⋯α˜2n∗,α˜n−⋮⋮⋱⋮α˜m1∗,α˜1−α˜m2∗,α˜2−⋯α˜mn∗,α˜n−.(6) Sixth Step: Then, complex intuitionistic fuzzy distance matrices D∗=D−−D+ are calculated as follows:(8)C1C2⋯Cn,D∗=Zij∗mxn=A1A2⋮AmZ11∗Z12∗⋯Z1n∗Z21∗Z22∗⋯Z2n∗⋮⋮⋱⋮Zm1∗Zm2∗⋯Zmn∗,(9)C1C2⋯CnD∗=A1A2⋮Amdα˜11∗,α˜1−−dα˜11∗,α˜1+dα˜11∗,α˜2−−dα˜11∗,α˜2+⋯dα˜11∗,α˜n−−dα˜11∗,α˜n+dα˜21∗,α˜1−−dα˜21∗,α˜1+dα˜22∗,α˜2−−dα˜22∗,α˜2+⋯dα˜2n∗,α˜n−−dα˜2n∗,α˜n+⋮⋮⋱⋮dα˜m1∗,α˜1−−dα˜m1∗,α˜1+dα˜m2∗,α˜2−−dα˜m2∗,α˜2+⋯dα˜mn∗,α˜n−−dα˜mn∗,α˜n+.(7) Seventh Step: Optimal weight ωj∗ for each criterion Cj is calculated as follows:(10)ωj∗=∑i=1m∑k=1mZij−Zkj∑j=1n∑k=1mZij−Zkj.(8) Eighth Step: Weighted intuitionistic fuzzy distance for each alternative is calculated as follows:(11)D˜i=∑j=1nωj∗zij∗,i=1,2,…,m.(9) Ninth Step: Alternatives are ordered from highest to lowest according to D˜i. The most suitable alternative is obtained.


#### 3.1.4. Proposed Approach

This study utilizes intuitionistic fuzzy sets for selecting the best desalination method. As a novelty, we firstly employ expert prioritization for the IF-TOPSIS method in equation (1) by using intuitionistic fuzzy sets in Table 1, importance and the methods for expert prioritization are given [44]. The expert weights are distributed to their judgments in order to get more accurate results. Then the IF-TOPSIS method is applied. The steps of the IF-TOPSIS method for the most suitable desalination system on commercial vessels are given in Figure 1.Figure 1
Steps of the proposed approach and IF-TOPSIS methodology.


## 3.1. Intuitionistic Fuzzy TOPSIS Methodology

### 3.1.1. Intuitionistic Fuzzy Sets and Scale

In this study, intuitionistic fuzzy TOPSIS methodology is utilized based on the work of Shen et al. [38] in an intuitionistic fuzzy environment, which is a complex form of fuzzy sets [39] and TOPSIS [40]. The set of alternatives is A=A1,A2,…,Am, and the set of criteria is C=C1,C2,…,Cn. The decision-making group is not equal and consists of ℓ different decision-makers. In nonidentical decision-making groups, the relative importance of the decision-makers, therefore, differs from each other.Intuitionistic fuzzy linguistic terms are used in the evaluation of decision-makers, which is given in Table1 [41], Also, Table 1 is reproduced from [42].Table 1
Linguistic variables [41, 42].
Linguistic termsμνπVery good0.750.100.15Good0.600.250.15Moderate0.500.500.00Bad0.250.600.15Very bad0.100.750.15


### 3.1.2. Expert Prioritization by Using Intuitionistic Fuzzy Scale

Decision-makers may have less or more expertise levels than other decision-makers due to their different experiences and knowledge. The weight vector of the decision-makers isλ=λ1,λ2,…,λℓ and λ≥0,k=1,2,…,ℓ. If λk≥0,k=1,2,…l, and ∑k=1lλ=1, the weight vectors of decision-makers are applied as follows:(1)λ=μk+πkμk/μk+νk∑k=1lμk+πkμk/μk+νk.


### 3.1.3. Intuitionistic Fuzzy TOPSIS Method

(1) First Step: After calculating the weight vectors of the decision-makers, the intuitionistic fuzzy decision matrix D=α˜ijmxn,i=1,2,…,m;j=1,2,…,n is generated in the form of α˜ij=μij,νij, where m represents alternatives and n represents criteria.(2)C1C2⋯CnD=α˜ijmxn=A1A2⋮Amα˜11∗α˜12∗⋯α˜1n∗α˜21∗α˜22∗⋯α˜2n∗⋮⋮⋱⋮α˜m1∗α˜m2∗⋯α˜mn∗.(2) Second Step: Positive ideal solution is calculated based on α˜j−+, and let C+, C−, and 1 ≤j≤n be according to(3)α˜j+=max1≤i≤mμij,min1≤i≤mνij=μj+,νj+,ifCj∈C+,min1≤i≤mμij,max1≤i≤mνij=μj+,νj+,ifCj∈C−..(3) Third Step: Negative ideal solution is calculated based on α˜j−+, and let C+, C−, and 1 ≤j≤n be according to(4)α˜j−=min1≤i≤mμij,max1≤i≤mνij=μj−,νj−,ifCj∈C+,max1≤i≤mμij,min1≤i≤mνij=μj−,νj−,ifCj∈C−.(4) Fourth Step: Positive intuitionistic fuzzy matrix D+ is calculated as follows:(5)C1C2⋯CnD+=dα˜ij,α˜j+mxn=A1A2⋮Amα˜11∗,α˜1+α˜12∗,α˜2+⋯α˜1n∗,α˜n+α˜21∗,α˜1+α˜22∗,α˜2+⋯α˜2n∗,α˜n+⋮⋮⋱⋮α˜m1∗,α˜1+α˜m2∗,α˜2+⋯α˜mn∗,α˜n+.The differences between two intuitionistic fuzzy numbersα=μα,να and β=μβ,νβ are calculated as follows:(6)dα,β=μα1+2/3πα1+πα−μβ1+2/3πβ1+πβ2+να1+2/3πα1+πα−νβ1+2/3πβ1+πβ22.According to Boran and AKay [43], μα and να will be equal to μα,μα+πα and να,να+πα at any value.(5) Fifth Step: Negative intuitive fuzzy distance matrix D− is calculated as follows:(7)C1C2⋯CnD−=dα˜ij,α˜j−mxn=A1A2⋮Amα˜11∗,α˜1−α˜12∗,α˜2−⋯α˜1n∗,α˜n−α˜21∗,α˜1−α˜22∗,α˜2−⋯α˜2n∗,α˜n−⋮⋮⋱⋮α˜m1∗,α˜1−α˜m2∗,α˜2−⋯α˜mn∗,α˜n−.(6) Sixth Step: Then, complex intuitionistic fuzzy distance matrices D∗=D−−D+ are calculated as follows:(8)C1C2⋯Cn,D∗=Zij∗mxn=A1A2⋮AmZ11∗Z12∗⋯Z1n∗Z21∗Z22∗⋯Z2n∗⋮⋮⋱⋮Zm1∗Zm2∗⋯Zmn∗,(9)C1C2⋯CnD∗=A1A2⋮Amdα˜11∗,α˜1−−dα˜11∗,α˜1+dα˜11∗,α˜2−−dα˜11∗,α˜2+⋯dα˜11∗,α˜n−−dα˜11∗,α˜n+dα˜21∗,α˜1−−dα˜21∗,α˜1+dα˜22∗,α˜2−−dα˜22∗,α˜2+⋯dα˜2n∗,α˜n−−dα˜2n∗,α˜n+⋮⋮⋱⋮dα˜m1∗,α˜1−−dα˜m1∗,α˜1+dα˜m2∗,α˜2−−dα˜m2∗,α˜2+⋯dα˜mn∗,α˜n−−dα˜mn∗,α˜n+.(7) Seventh Step: Optimal weight ωj∗ for each criterion Cj is calculated as follows:(10)ωj∗=∑i=1m∑k=1mZij−Zkj∑j=1n∑k=1mZij−Zkj.(8) Eighth Step: Weighted intuitionistic fuzzy distance for each alternative is calculated as follows:(11)D˜i=∑j=1nωj∗zij∗,i=1,2,…,m.(9) Ninth Step: Alternatives are ordered from highest to lowest according to D˜i. The most suitable alternative is obtained.


### 3.1.4. Proposed Approach

This study utilizes intuitionistic fuzzy sets for selecting the best desalination method. As a novelty, we firstly employ expert prioritization for the IF-TOPSIS method in equation (1) by using intuitionistic fuzzy sets in Table 1, importance and the methods for expert prioritization are given [44]. The expert weights are distributed to their judgments in order to get more accurate results. Then the IF-TOPSIS method is applied. The steps of the IF-TOPSIS method for the most suitable desalination system on commercial vessels are given in Figure 1.Figure 1
Steps of the proposed approach and IF-TOPSIS methodology.


## 3.1.1. Intuitionistic Fuzzy Sets and Scale

In this study, intuitionistic fuzzy TOPSIS methodology is utilized based on the work of Shen et al. [38] in an intuitionistic fuzzy environment, which is a complex form of fuzzy sets [39] and TOPSIS [40]. The set of alternatives is A=A1,A2,…,Am, and the set of criteria is C=C1,C2,…,Cn. The decision-making group is not equal and consists of ℓ different decision-makers. In nonidentical decision-making groups, the relative importance of the decision-makers, therefore, differs from each other.Intuitionistic fuzzy linguistic terms are used in the evaluation of decision-makers, which is given in Table1 [41], Also, Table 1 is reproduced from [42].Table 1
Linguistic variables [41, 42].
Linguistic termsμνπVery good0.750.100.15Good0.600.250.15Moderate0.500.500.00Bad0.250.600.15Very bad0.100.750.15


## 3.1.2. Expert Prioritization by Using Intuitionistic Fuzzy Scale

Decision-makers may have less or more expertise levels than other decision-makers due to their different experiences and knowledge. The weight vector of the decision-makers isλ=λ1,λ2,…,λℓ and λ≥0,k=1,2,…,ℓ. If λk≥0,k=1,2,…l, and ∑k=1lλ=1, the weight vectors of decision-makers are applied as follows:(1)λ=μk+πkμk/μk+νk∑k=1lμk+πkμk/μk+νk.


## 3.1.3. Intuitionistic Fuzzy TOPSIS Method

(1) First Step: After calculating the weight vectors of the decision-makers, the intuitionistic fuzzy decision matrix D=α˜ijmxn,i=1,2,…,m;j=1,2,…,n is generated in the form of α˜ij=μij,νij, where m represents alternatives and n represents criteria.(2)C1C2⋯CnD=α˜ijmxn=A1A2⋮Amα˜11∗α˜12∗⋯α˜1n∗α˜21∗α˜22∗⋯α˜2n∗⋮⋮⋱⋮α˜m1∗α˜m2∗⋯α˜mn∗.(2) Second Step: Positive ideal solution is calculated based on α˜j−+, and let C+, C−, and 1 ≤j≤n be according to(3)α˜j+=max1≤i≤mμij,min1≤i≤mνij=μj+,νj+,ifCj∈C+,min1≤i≤mμij,max1≤i≤mνij=μj+,νj+,ifCj∈C−..(3) Third Step: Negative ideal solution is calculated based on α˜j−+, and let C+, C−, and 1 ≤j≤n be according to(4)α˜j−=min1≤i≤mμij,max1≤i≤mνij=μj−,νj−,ifCj∈C+,max1≤i≤mμij,min1≤i≤mνij=μj−,νj−,ifCj∈C−.(4) Fourth Step: Positive intuitionistic fuzzy matrix D+ is calculated as follows:(5)C1C2⋯CnD+=dα˜ij,α˜j+mxn=A1A2⋮Amα˜11∗,α˜1+α˜12∗,α˜2+⋯α˜1n∗,α˜n+α˜21∗,α˜1+α˜22∗,α˜2+⋯α˜2n∗,α˜n+⋮⋮⋱⋮α˜m1∗,α˜1+α˜m2∗,α˜2+⋯α˜mn∗,α˜n+.The differences between two intuitionistic fuzzy numbersα=μα,να and β=μβ,νβ are calculated as follows:(6)dα,β=μα1+2/3πα1+πα−μβ1+2/3πβ1+πβ2+να1+2/3πα1+πα−νβ1+2/3πβ1+πβ22.According to Boran and AKay [43], μα and να will be equal to μα,μα+πα and να,να+πα at any value.(5) Fifth Step: Negative intuitive fuzzy distance matrix D− is calculated as follows:(7)C1C2⋯CnD−=dα˜ij,α˜j−mxn=A1A2⋮Amα˜11∗,α˜1−α˜12∗,α˜2−⋯α˜1n∗,α˜n−α˜21∗,α˜1−α˜22∗,α˜2−⋯α˜2n∗,α˜n−⋮⋮⋱⋮α˜m1∗,α˜1−α˜m2∗,α˜2−⋯α˜mn∗,α˜n−.(6) Sixth Step: Then, complex intuitionistic fuzzy distance matrices D∗=D−−D+ are calculated as follows:(8)C1C2⋯Cn,D∗=Zij∗mxn=A1A2⋮AmZ11∗Z12∗⋯Z1n∗Z21∗Z22∗⋯Z2n∗⋮⋮⋱⋮Zm1∗Zm2∗⋯Zmn∗,(9)C1C2⋯CnD∗=A1A2⋮Amdα˜11∗,α˜1−−dα˜11∗,α˜1+dα˜11∗,α˜2−−dα˜11∗,α˜2+⋯dα˜11∗,α˜n−−dα˜11∗,α˜n+dα˜21∗,α˜1−−dα˜21∗,α˜1+dα˜22∗,α˜2−−dα˜22∗,α˜2+⋯dα˜2n∗,α˜n−−dα˜2n∗,α˜n+⋮⋮⋱⋮dα˜m1∗,α˜1−−dα˜m1∗,α˜1+dα˜m2∗,α˜2−−dα˜m2∗,α˜2+⋯dα˜mn∗,α˜n−−dα˜mn∗,α˜n+.(7) Seventh Step: Optimal weight ωj∗ for each criterion Cj is calculated as follows:(10)ωj∗=∑i=1m∑k=1mZij−Zkj∑j=1n∑k=1mZij−Zkj.(8) Eighth Step: Weighted intuitionistic fuzzy distance for each alternative is calculated as follows:(11)D˜i=∑j=1nωj∗zij∗,i=1,2,…,m.(9) Ninth Step: Alternatives are ordered from highest to lowest according to D˜i. The most suitable alternative is obtained.


## 3.1.4. Proposed Approach

This study utilizes intuitionistic fuzzy sets for selecting the best desalination method. As a novelty, we firstly employ expert prioritization for the IF-TOPSIS method in equation (1) by using intuitionistic fuzzy sets in Table 1, importance and the methods for expert prioritization are given [44]. The expert weights are distributed to their judgments in order to get more accurate results. Then the IF-TOPSIS method is applied. The steps of the IF-TOPSIS method for the most suitable desalination system on commercial vessels are given in Figure 1.Figure 1
Steps of the proposed approach and IF-TOPSIS methodology.


## 4. Particulars of Criteria and Alternatives

Three alternatives and seven criteria are determined by the literature review and expert consultations. As a result of the questionnaires that are answered by 13 different field experts, the relevant weights are calculated. The hierarchy of the proposed problem is given in Figure2.Figure 2
Hierarchical structure for the best desalination method.The criteria and their definitions are given in Table2.Table 2
Definition of criteria and subcriteria.
Main criteriaSubcriteriaDescriptionCost criterion (CC)System installation cost (C1)It is the infrastructure cost required for the installation of the system. It varies according to the complexity of the system and the amount of freshwater to be obtained.System operation cost (C2)Distillation and filtration costs will be compared mutually. The operating costs of distillation with the heat coming from the chimney and the electricity-consuming filter pump coming from the alternator will be compared.Safety criterion (SC)Environment pollution risk of the system (C3)The risks of a possible failure, leakage into the sea, or polluting the sea of the systems will be compared.Risk to human health (C4)In a possible unusual, emergency and/or a leak into the freshwater tank, the risks of affecting the human health of the systems will be mutually evaluated.Technical criterion (TC)Easiness of maintenance (C5)Every freshwater tank needs to be cleaned, and every freshwater treatment system needs to be maintained at regular intervals. The criterion of easiness of maintenance will be compared for each alternative.User-friendliness (C6)The ease of use of the system is very important and some long-term ballast operations can be tiring. In this criterion, operation time, difficulty, and easiness will be compared.Easiness for ship deployment (C7)Deployment of the system on the ship plays a very effective role in system selection. In some cases, the system that does not comply with the relevant ship design or does not have enough free space for the installation of the system on the ship prevents the installation of the freshwater treatment system to be selected in the future.The criteria of easiness for ship deployment, having sufficient space, being suitable for installation in design, and ease of installation are highly important criteria for future system deployment.The alternatives and their definitions for the proposed problem are given in Table3.Table 3
The alternatives and their definitions.
AlternativeDescriptionFreshwater generator (A1)The freshwater generator is a desalination system that is permanently used on ships that do not make short voyages and do not supply freshwater from the port. This system is also known as the evaporator. This system, which boils seawater and distills it with high energy consumption, is used conventionally on ships.Reverse osmosis method (A2)This method, which can provide compression with high pressure by means of a pump, filters the freshwater and removes all other beneficial and harmful components, especially sodium chloride, from seawater. Over time, the development of nanotechnology in membrane filters and the production of freshwater at high flow have made the reverse osmosis method attractive.Installation of a membrane filter in addition to existing mechanical + UV ballast water treatment systems (A3)It is a very complex system, which was started to be used on ships in 2017. It contains UV radiation and hydrocyclones that kill harmful microorganisms that can be transported through ballast waters, especially filtration.The question of removing the use of the conventional freshwater generator by installing an additional membrane filter on this mechanical system has been raised.


## 5. Application

### 5.1. Step-by-Step Application of IF-TOPSIS

Since the expertise levels of the decision-makers for the alternatives and criteria are different, the intuitionistic fuzzy TOPSIS method is implemented based on the opinions of the decision-makers, and the alternatives are evaluated by assigning different importance levels.


#### 5.1.1. First Step

The weights of decision-makers are calculated according to equation1. Table 4 is reproduced from Yıldırım’s work [45].Table 4
Grading the decision-makers with intuitionistic fuzzy linguistic variables and impact percentages of all decision-makers [45].
Decision-makerYears of expertise in desalination systemsPositionDegreeμνπEffective percentage on result (%)Expert 13Third officerB.Sc.0.100.750.151.42Expert 25Second officerB.Sc.0.500.500.006.05Expert 311AcademicianPh.D.0.750.100.1510.68Expert 44AcademicianM.Sc.0.250.600.153.56Expert 512First officerB.Sc.0.750.100.1510.68Expert 67AcademicianPh.D.0.600.250.158.54Expert 710AcademicianPh.D.0.750.100.1510.68Expert 88First officerB.Sc.0.600.250.158.54Expert 98First officerB.Sc.0.600.250.158.54Expert 108First officerB.Sc.0.600.250.158.54Expert 1114MasterB.Sc.0.750.100.1510.68Expert 125Second officerB.Sc.0.500.500.006.05Expert 135Second officerB.Sc.0.500.500.006.05The data obtained from the questionnaires were multiplied by the percentage of influence of each decision-maker on the result. The combined group decision-making values obtained are shown in Table5, with all three rows representing alternative 1, alternative 2, and alternative 3.Table 5
Forming of intuitionistic fuzzy decision matrix.
C1C2C3μvπμvπμvπ0.7380.1160.1500.1050.7340.1500.7120.1480.1500.1000.7500.1500.5170.4610.0360.1160.7380.1500.2150.6440.1500.4800.5110.0160.1250.7310.150C4C5C6C7μvπμvπμvπμvπ0.6910.1910.1280.7380.1600.1050.1000.7500.1500.7380.1600.1050.1160.7380.1500.1250.7310.1500.5440.4220.0540.1000.7500.1500.2370.6180.1500.1000.7500.1500.3320.5740.1090.2050.6560.150


#### 5.1.2. Second Step

The positive ideal solution setα˜j+ is α˜+ = (α˜1+,α˜2+,α˜3+,α˜4+,α˜5+,α˜6+,α˜7+). A positive intuitionistic fuzzy solution is obtained for each criterion by using equation (3) and is shown in Table 6.Table 6
Positive ideal solution of each criterion.
αj+μνπα1+0.7350.1160.146α2+0.5170.4610.022α1+3+0.7120.1480.140α4+0.6910.1910.117α5+0.7380.1600.101α6+0.5440.4220.034α7+0.7380.1600.101


#### 5.1.3. Third Step

The negative ideal solution setα˜j‒ is α˜‒ = α˜1‒,α˜2‒,α˜3‒,α˜4‒,α˜5‒,α˜6‒,α˜7‒. A negative intuitionistic fuzzy solution is obtained for each criterion by using equation 4 and is shown in Table 7.Table 7
Negative ideal solution of each criterion.
α˜j−μνπα˜1−0.1000.7500.150α˜2−0.1050.7340.160α˜3−0.1160.7380.146α˜4−0.1160.7380.146α˜5−0.1000.7500.150α˜6−0.1000.7500.150α˜7−0.1000.7500.150


#### 5.1.4. Fourth Step

Using equation (5), the positive intuitionistic fuzzy distance matrix D+ is obtained as follows:(12)C1C2C3C4C5C6C7D+=dαij.αj+3x7=A1A2A30.0020.3800.0040.0050.0020.4250.0020.7080.0050.6590.6190.6490.0070.6730.5850.0440.6500.4840.6730.1930.562.


#### 5.1.5. Fifth Step

Using equation (7), the negative intuitionistic fuzzy distance matrix D− is obtained as follows:(13)C1C2C3C4C5C6C7D−=dαij.αj−3x7=A1A2A30.7090.0050.6600.6200.6740.0000.6740.0000.3830.00200020.0240.4260.0000.1230.3390.0080.1330.0000.2320.111.


#### 5.1.6. Sixth Step

Complex intuitionistic fuzzy distance matrices are calculated by the help ofD∗=D−−D+, which is expressed in equations (8) and (9).(14)C1C2C3C4C5C6C7D∗=Zij∗3x7=A1A2A30.707−0.3750.6560.6150.672−0.4250.672−0.7080.378−0.657−0.617−0.6240.419−0.673−0.4620.295−0.642−0.351−0.673−0.040−0.450.


#### 5.1.7. Seventh Step

According to (10), the optimal weights of the criteria are determined.(15)∑i=13∑k=13Zi1−Zk1=5.663,∑i=13∑k=13Zi2−Zk2=3.012,∑i=13∑k=13Zi3−Zk3=5.253,∑i=13∑k=13Zi4−Zk4=4.929,∑i=13∑k=13Zi5−Zk5=5.381,∑i=13∑k=13Zi6−Zk6=4.060,∑i=13∑k=13Zi7−Zk7=5.381.Then it is calculated as∑j=17∑i=13∑k=13Zij−Zkj5.663+3.012+5.253+4.929+5.381+4.060+5.381=33.667, and weights of criteria are obtained as follows:(16)ω1∗=5.66333.667=0.168,ω2∗=3.01233.667=0.089,ω3∗=5.25333.667=0.156,ω4∗=4.92933.667=0.146,ω5∗=5.38133.667=0.160,ω6∗=4.06033.667=0.121,ω7∗=5.38133.667=0.160.


#### 5.1.8. Eighth Step

Based on (11), the weighted intuitionistic fuzzy distance is calculated for each alternative Di∗ value.(17)D˜1=∑j=17ω1∗z1j∗=0.441,D˜=∑j=17ω1∗z2j∗=−0.435,D˜3=∑j=17ω1∗z3j∗=−0.378.


#### 5.1.9. Ninth Step

Intuitionistic fuzzy distance values for each alternative found in the eighth step are ordered from the highest to the lowest. The highestD˜i score was determined as the most suitable alternative among the alternatives. In Table 8, the result of the most suitable desalination system alternatives is compared based on the seven criteria and shown as follows.Table 8
Ranking of the most suitable desalination systems.
RankDesalination systemD˜iA1Freshwater generator0.441A3Installation of a membrane filter in addition to existing mechanical + UV ballast water treatment systems–0.378A2Reverse osmosis method–0.435


### 5.2. Analysis of Results and Discussion

In this study, we embedded the expert prioritization concept based on the study of Yıldırım [45] as given in equation (1). We also tested other similar formulas such as the weighted product model (WPM) is a popular multicriteria decision analysis [46, 47] such as for k = 1, 2, 3, …, n.(18)PMg=∏j=1nMkjwj.However, this formula is not suitable for our problem because of the value of the linguistic expression of “Moderate”. value is 0 and as it can be easily seen that 0 value makes all calculations equal to 0.We implemented several different techniques to compare the rankings as given in Table9. We see that the rankings are exactly the same with fuzzy AHP methods. It also shows the conventional TOPSIS and the proposed IF-TOPSIS are different that is normal since the IF-TOPSIS method is completely different in terms of its methodology. Its superiorities are given in the study of Shen [38].Table 9
Ranking of the most suitable desalination systems.
Fuzzy AHP (Chang) [48].Fuzzy AHP (Buckley) [49]Conventional TOPSIS [50].IF-TOPSIS [39].ValueRankValueRankValueRankValueRankA140.39%159.94%10.91110.4411A236.04%223.65%20.7933–0.3782A323.57%316.41%30.8262–0.4353There are other models in the literature related to TOPSIS. According to Akram et al. [51] research, complex spherical fuzzy TOPSIS (CSF-TOPSIS) shows the characteristics of complex spherical fuzzy sets with the TOPSIS method. CSF sets include the trend to cover both aspects of information related to fulfilment, shortage, and displeasure nature of human decisions. Another model, which has been shown in Akram et al. [52] research, shows that the Pythagorean fuzzy hybrid order of preference by similarity to an ideal solution (PFH-TOPSIS) approach calculates the distances of failure modes from the Pythagorean fuzzy PIS and Pythagorean fuzzy NIS. To judge failure modes, the Pythagorean fuzzy hybrid elimination and choice translating reality I (PFH-ELECTRE I) method constructs Pythagorean fuzzy concordance and Pythagorean fuzzy discordance matrices. The relevant model with the IF-TOPSIS model has been shown in Akram et al. [53] research. In the complex spherical fuzzy TOPSIS (CPF-TOPSIS) method, the allocated alternatives has been compared according to on being superior and inferior to other alternatives based on score or accuracy by linguistic terms. In complex Pythagorean fuzzy concordance and discordance, sets compare the alternatives being dominant to the rest of the alternatives on score degree, accuracy degree, and indeterminacy. In the CPF-ELECTRE I method, outranking decision graphs are shown to obtain the best alternative. The structure of both methods illustrates with the help of flow charts. According to Akram et al. [54], a comparison of bipolar fuzzy TOPSIS (BF-TOPSIS) and bipolar fuzzy ELECTRE I (BF-ELECTRE-I) have been explained. The graphically presented methods visualize the viability, suitability, and achievability of the diagnostic process. While the BF-TOPSIS gives us one disease as diagnosis, BF-ELECTRE-I gives the set of diseases as a diagnosis. Moreover, the comparison analysis shows that diagnostic process is more reliable and precise.


## 5.1. Step-by-Step Application of IF-TOPSIS

Since the expertise levels of the decision-makers for the alternatives and criteria are different, the intuitionistic fuzzy TOPSIS method is implemented based on the opinions of the decision-makers, and the alternatives are evaluated by assigning different importance levels.


### 5.1.1. First Step

The weights of decision-makers are calculated according to equation1. Table 4 is reproduced from Yıldırım’s work [45].Table 4
Grading the decision-makers with intuitionistic fuzzy linguistic variables and impact percentages of all decision-makers [45].
Decision-makerYears of expertise in desalination systemsPositionDegreeμνπEffective percentage on result (%)Expert 13Third officerB.Sc.0.100.750.151.42Expert 25Second officerB.Sc.0.500.500.006.05Expert 311AcademicianPh.D.0.750.100.1510.68Expert 44AcademicianM.Sc.0.250.600.153.56Expert 512First officerB.Sc.0.750.100.1510.68Expert 67AcademicianPh.D.0.600.250.158.54Expert 710AcademicianPh.D.0.750.100.1510.68Expert 88First officerB.Sc.0.600.250.158.54Expert 98First officerB.Sc.0.600.250.158.54Expert 108First officerB.Sc.0.600.250.158.54Expert 1114MasterB.Sc.0.750.100.1510.68Expert 125Second officerB.Sc.0.500.500.006.05Expert 135Second officerB.Sc.0.500.500.006.05The data obtained from the questionnaires were multiplied by the percentage of influence of each decision-maker on the result. The combined group decision-making values obtained are shown in Table5, with all three rows representing alternative 1, alternative 2, and alternative 3.Table 5
Forming of intuitionistic fuzzy decision matrix.
C1C2C3μvπμvπμvπ0.7380.1160.1500.1050.7340.1500.7120.1480.1500.1000.7500.1500.5170.4610.0360.1160.7380.1500.2150.6440.1500.4800.5110.0160.1250.7310.150C4C5C6C7μvπμvπμvπμvπ0.6910.1910.1280.7380.1600.1050.1000.7500.1500.7380.1600.1050.1160.7380.1500.1250.7310.1500.5440.4220.0540.1000.7500.1500.2370.6180.1500.1000.7500.1500.3320.5740.1090.2050.6560.150


### 5.1.2. Second Step

The positive ideal solution setα˜j+ is α˜+ = (α˜1+,α˜2+,α˜3+,α˜4+,α˜5+,α˜6+,α˜7+). A positive intuitionistic fuzzy solution is obtained for each criterion by using equation (3) and is shown in Table 6.Table 6
Positive ideal solution of each criterion.
αj+μνπα1+0.7350.1160.146α2+0.5170.4610.022α1+3+0.7120.1480.140α4+0.6910.1910.117α5+0.7380.1600.101α6+0.5440.4220.034α7+0.7380.1600.101


### 5.1.3. Third Step

The negative ideal solution setα˜j‒ is α˜‒ = α˜1‒,α˜2‒,α˜3‒,α˜4‒,α˜5‒,α˜6‒,α˜7‒. A negative intuitionistic fuzzy solution is obtained for each criterion by using equation 4 and is shown in Table 7.Table 7
Negative ideal solution of each criterion.
α˜j−μνπα˜1−0.1000.7500.150α˜2−0.1050.7340.160α˜3−0.1160.7380.146α˜4−0.1160.7380.146α˜5−0.1000.7500.150α˜6−0.1000.7500.150α˜7−0.1000.7500.150


### 5.1.4. Fourth Step

Using equation (5), the positive intuitionistic fuzzy distance matrix D+ is obtained as follows:(12)C1C2C3C4C5C6C7D+=dαij.αj+3x7=A1A2A30.0020.3800.0040.0050.0020.4250.0020.7080.0050.6590.6190.6490.0070.6730.5850.0440.6500.4840.6730.1930.562.


### 5.1.5. Fifth Step

Using equation (7), the negative intuitionistic fuzzy distance matrix D− is obtained as follows:(13)C1C2C3C4C5C6C7D−=dαij.αj−3x7=A1A2A30.7090.0050.6600.6200.6740.0000.6740.0000.3830.00200020.0240.4260.0000.1230.3390.0080.1330.0000.2320.111.


### 5.1.6. Sixth Step

Complex intuitionistic fuzzy distance matrices are calculated by the help ofD∗=D−−D+, which is expressed in equations (8) and (9).(14)C1C2C3C4C5C6C7D∗=Zij∗3x7=A1A2A30.707−0.3750.6560.6150.672−0.4250.672−0.7080.378−0.657−0.617−0.6240.419−0.673−0.4620.295−0.642−0.351−0.673−0.040−0.450.


### 5.1.7. Seventh Step

According to (10), the optimal weights of the criteria are determined.(15)∑i=13∑k=13Zi1−Zk1=5.663,∑i=13∑k=13Zi2−Zk2=3.012,∑i=13∑k=13Zi3−Zk3=5.253,∑i=13∑k=13Zi4−Zk4=4.929,∑i=13∑k=13Zi5−Zk5=5.381,∑i=13∑k=13Zi6−Zk6=4.060,∑i=13∑k=13Zi7−Zk7=5.381.Then it is calculated as∑j=17∑i=13∑k=13Zij−Zkj5.663+3.012+5.253+4.929+5.381+4.060+5.381=33.667, and weights of criteria are obtained as follows:(16)ω1∗=5.66333.667=0.168,ω2∗=3.01233.667=0.089,ω3∗=5.25333.667=0.156,ω4∗=4.92933.667=0.146,ω5∗=5.38133.667=0.160,ω6∗=4.06033.667=0.121,ω7∗=5.38133.667=0.160.


### 5.1.8. Eighth Step

Based on (11), the weighted intuitionistic fuzzy distance is calculated for each alternative Di∗ value.(17)D˜1=∑j=17ω1∗z1j∗=0.441,D˜=∑j=17ω1∗z2j∗=−0.435,D˜3=∑j=17ω1∗z3j∗=−0.378.


### 5.1.9. Ninth Step

Intuitionistic fuzzy distance values for each alternative found in the eighth step are ordered from the highest to the lowest. The highestD˜i score was determined as the most suitable alternative among the alternatives. In Table 8, the result of the most suitable desalination system alternatives is compared based on the seven criteria and shown as follows.Table 8
Ranking of the most suitable desalination systems.
RankDesalination systemD˜iA1Freshwater generator0.441A3Installation of a membrane filter in addition to existing mechanical + UV ballast water treatment systems–0.378A2Reverse osmosis method–0.435


## 5.1.1. First Step

The weights of decision-makers are calculated according to equation1. Table 4 is reproduced from Yıldırım’s work [45].Table 4
Grading the decision-makers with intuitionistic fuzzy linguistic variables and impact percentages of all decision-makers [45].
Decision-makerYears of expertise in desalination systemsPositionDegreeμνπEffective percentage on result (%)Expert 13Third officerB.Sc.0.100.750.151.42Expert 25Second officerB.Sc.0.500.500.006.05Expert 311AcademicianPh.D.0.750.100.1510.68Expert 44AcademicianM.Sc.0.250.600.153.56Expert 512First officerB.Sc.0.750.100.1510.68Expert 67AcademicianPh.D.0.600.250.158.54Expert 710AcademicianPh.D.0.750.100.1510.68Expert 88First officerB.Sc.0.600.250.158.54Expert 98First officerB.Sc.0.600.250.158.54Expert 108First officerB.Sc.0.600.250.158.54Expert 1114MasterB.Sc.0.750.100.1510.68Expert 125Second officerB.Sc.0.500.500.006.05Expert 135Second officerB.Sc.0.500.500.006.05The data obtained from the questionnaires were multiplied by the percentage of influence of each decision-maker on the result. The combined group decision-making values obtained are shown in Table5, with all three rows representing alternative 1, alternative 2, and alternative 3.Table 5
Forming of intuitionistic fuzzy decision matrix.
C1C2C3μvπμvπμvπ0.7380.1160.1500.1050.7340.1500.7120.1480.1500.1000.7500.1500.5170.4610.0360.1160.7380.1500.2150.6440.1500.4800.5110.0160.1250.7310.150C4C5C6C7μvπμvπμvπμvπ0.6910.1910.1280.7380.1600.1050.1000.7500.1500.7380.1600.1050.1160.7380.1500.1250.7310.1500.5440.4220.0540.1000.7500.1500.2370.6180.1500.1000.7500.1500.3320.5740.1090.2050.6560.150


## 5.1.2. Second Step

The positive ideal solution setα˜j+ is α˜+ = (α˜1+,α˜2+,α˜3+,α˜4+,α˜5+,α˜6+,α˜7+). A positive intuitionistic fuzzy solution is obtained for each criterion by using equation (3) and is shown in Table 6.Table 6
Positive ideal solution of each criterion.
αj+μνπα1+0.7350.1160.146α2+0.5170.4610.022α1+3+0.7120.1480.140α4+0.6910.1910.117α5+0.7380.1600.101α6+0.5440.4220.034α7+0.7380.1600.101


## 5.1.3. Third Step

The negative ideal solution setα˜j‒ is α˜‒ = α˜1‒,α˜2‒,α˜3‒,α˜4‒,α˜5‒,α˜6‒,α˜7‒. A negative intuitionistic fuzzy solution is obtained for each criterion by using equation 4 and is shown in Table 7.Table 7
Negative ideal solution of each criterion.
α˜j−μνπα˜1−0.1000.7500.150α˜2−0.1050.7340.160α˜3−0.1160.7380.146α˜4−0.1160.7380.146α˜5−0.1000.7500.150α˜6−0.1000.7500.150α˜7−0.1000.7500.150


## 5.1.4. Fourth Step

Using equation (5), the positive intuitionistic fuzzy distance matrix D+ is obtained as follows:(12)C1C2C3C4C5C6C7D+=dαij.αj+3x7=A1A2A30.0020.3800.0040.0050.0020.4250.0020.7080.0050.6590.6190.6490.0070.6730.5850.0440.6500.4840.6730.1930.562.


## 5.1.5. Fifth Step

Using equation (7), the negative intuitionistic fuzzy distance matrix D− is obtained as follows:(13)C1C2C3C4C5C6C7D−=dαij.αj−3x7=A1A2A30.7090.0050.6600.6200.6740.0000.6740.0000.3830.00200020.0240.4260.0000.1230.3390.0080.1330.0000.2320.111.


## 5.1.6. Sixth Step

Complex intuitionistic fuzzy distance matrices are calculated by the help ofD∗=D−−D+, which is expressed in equations (8) and (9).(14)C1C2C3C4C5C6C7D∗=Zij∗3x7=A1A2A30.707−0.3750.6560.6150.672−0.4250.672−0.7080.378−0.657−0.617−0.6240.419−0.673−0.4620.295−0.642−0.351−0.673−0.040−0.450.


## 5.1.7. Seventh Step

According to (10), the optimal weights of the criteria are determined.(15)∑i=13∑k=13Zi1−Zk1=5.663,∑i=13∑k=13Zi2−Zk2=3.012,∑i=13∑k=13Zi3−Zk3=5.253,∑i=13∑k=13Zi4−Zk4=4.929,∑i=13∑k=13Zi5−Zk5=5.381,∑i=13∑k=13Zi6−Zk6=4.060,∑i=13∑k=13Zi7−Zk7=5.381.Then it is calculated as∑j=17∑i=13∑k=13Zij−Zkj5.663+3.012+5.253+4.929+5.381+4.060+5.381=33.667, and weights of criteria are obtained as follows:(16)ω1∗=5.66333.667=0.168,ω2∗=3.01233.667=0.089,ω3∗=5.25333.667=0.156,ω4∗=4.92933.667=0.146,ω5∗=5.38133.667=0.160,ω6∗=4.06033.667=0.121,ω7∗=5.38133.667=0.160.


## 5.1.8. Eighth Step

Based on (11), the weighted intuitionistic fuzzy distance is calculated for each alternative Di∗ value.(17)D˜1=∑j=17ω1∗z1j∗=0.441,D˜=∑j=17ω1∗z2j∗=−0.435,D˜3=∑j=17ω1∗z3j∗=−0.378.


## 5.1.9. Ninth Step

Intuitionistic fuzzy distance values for each alternative found in the eighth step are ordered from the highest to the lowest. The highestD˜i score was determined as the most suitable alternative among the alternatives. In Table 8, the result of the most suitable desalination system alternatives is compared based on the seven criteria and shown as follows.Table 8
Ranking of the most suitable desalination systems.
RankDesalination systemD˜iA1Freshwater generator0.441A3Installation of a membrane filter in addition to existing mechanical + UV ballast water treatment systems–0.378A2Reverse osmosis method–0.435


## 5.2. Analysis of Results and Discussion

In this study, we embedded the expert prioritization concept based on the study of Yıldırım [45] as given in equation (1). We also tested other similar formulas such as the weighted product model (WPM) is a popular multicriteria decision analysis [46, 47] such as for k = 1, 2, 3, …, n.(18)PMg=∏j=1nMkjwj.However, this formula is not suitable for our problem because of the value of the linguistic expression of “Moderate”. value is 0 and as it can be easily seen that 0 value makes all calculations equal to 0.We implemented several different techniques to compare the rankings as given in Table9. We see that the rankings are exactly the same with fuzzy AHP methods. It also shows the conventional TOPSIS and the proposed IF-TOPSIS are different that is normal since the IF-TOPSIS method is completely different in terms of its methodology. Its superiorities are given in the study of Shen [38].Table 9
Ranking of the most suitable desalination systems.
Fuzzy AHP (Chang) [48].Fuzzy AHP (Buckley) [49]Conventional TOPSIS [50].IF-TOPSIS [39].ValueRankValueRankValueRankValueRankA140.39%159.94%10.91110.4411A236.04%223.65%20.7933–0.3782A323.57%316.41%30.8262–0.4353There are other models in the literature related to TOPSIS. According to Akram et al. [51] research, complex spherical fuzzy TOPSIS (CSF-TOPSIS) shows the characteristics of complex spherical fuzzy sets with the TOPSIS method. CSF sets include the trend to cover both aspects of information related to fulfilment, shortage, and displeasure nature of human decisions. Another model, which has been shown in Akram et al. [52] research, shows that the Pythagorean fuzzy hybrid order of preference by similarity to an ideal solution (PFH-TOPSIS) approach calculates the distances of failure modes from the Pythagorean fuzzy PIS and Pythagorean fuzzy NIS. To judge failure modes, the Pythagorean fuzzy hybrid elimination and choice translating reality I (PFH-ELECTRE I) method constructs Pythagorean fuzzy concordance and Pythagorean fuzzy discordance matrices. The relevant model with the IF-TOPSIS model has been shown in Akram et al. [53] research. In the complex spherical fuzzy TOPSIS (CPF-TOPSIS) method, the allocated alternatives has been compared according to on being superior and inferior to other alternatives based on score or accuracy by linguistic terms. In complex Pythagorean fuzzy concordance and discordance, sets compare the alternatives being dominant to the rest of the alternatives on score degree, accuracy degree, and indeterminacy. In the CPF-ELECTRE I method, outranking decision graphs are shown to obtain the best alternative. The structure of both methods illustrates with the help of flow charts. According to Akram et al. [54], a comparison of bipolar fuzzy TOPSIS (BF-TOPSIS) and bipolar fuzzy ELECTRE I (BF-ELECTRE-I) have been explained. The graphically presented methods visualize the viability, suitability, and achievability of the diagnostic process. While the BF-TOPSIS gives us one disease as diagnosis, BF-ELECTRE-I gives the set of diseases as a diagnosis. Moreover, the comparison analysis shows that diagnostic process is more reliable and precise.


## 6. Conclusions and Recommendations

Freshwater is the main source of life for the crew in commercial vessels. The importance of production methods in freshwater and its energy efficiency has been increasing day by day. The ever-tightening MARPOL Annex VI and flag state protocols and the inspections on NOx and SOx gases put pressure on the shipowners about the environmental damage caused by the vessel emissions. Ecological and efficiency concerns in the maritime environment and the recent developments in ballast water treatment systems have raised a new question: “whether the new water treatment systems already planted on vessels can be used as desalination systems instead of old conventional freshwater generators?”According to literature, there are similar studies in the literature related to future desalination systems on vessels. Tomaszewka et al. [55] investigated the “treatment of bilge water with reverse osmosis and UV methods” and stated that the water obtained completely removed from the oil with the reverse osmosis and UV system. Jadmiko et al. [56] investigated a possible photovoltaic freshwater treatment system with the reverse osmosis system on the roll-on/roll-off passenger (RO-PAX) vessels and stated that it can be discussed whether the reverse osmosis system is economical but only with the help of installed solar separators and batteries on vessels. There are other similar issues in the literature but the question of whether the ballast water treatment system can be used instead of the conventional freshwater generator system or not has not been questioned. Lu et al. [57] have investigated whether the reverse osmosis method can be used in nonballast vessels. They stated that using the reverse osmosis method on “vessels without ballast tanks” would save more on spending and provide a robust water supply.As a result of the literature research, it has been revealed that the current desalination on vessels research mostly focused on passenger ships due to high passenger capacity and excessive water consumption. Apart from the other studies in the literature, in this study, the most suitable desalination system has been investigated in nonpassenger vessels and limited to commercial vessels other than passenger ships.To solve the question, the questionnaire has been carried out by taking the opinions of thirteen experts in both desalination and maritime research or job area. In these questionnaires, it has been asked from field experts to compare three different alternative desalination methods that could be placed on commercial vessels. The questionnaires have been carried out by pairwise comparison of these three alternatives according to seven different criteria to reach the most suitable desalination system. As the expertise levels of the decision-makers for the alternatives and criteria are different, an improved intuitionistic fuzzy TOPSIS method is implemented based on the opinions of the decision-makers, and the alternatives are evaluated by assigning different importance levels. As a result of the data obtained, the most suitable desalination method has been ranked as follows: freshwater generator (0.441) > installation of additional membrane filters to the existing mechanical + UV ballast water treatment system on the ship (–0.378) > reverse osmosis method (–0.435). The order of the criteria is the system’s risk to human health (34.62%) > the environment pollution risk of system (20.46%) > system operation cost (18.34%) > system installation cost (9.42%) > easiness for ship deployment (7.35%) > easiness of maintenance (6.01%) > user-friendliness (3.81%). According to the results, it has been concluded that the rankings of the results obtained from each methodology have been compatible with each other.According to the obtained results, the conventional freshwater generator still maintains its current value. Another remarkable situation has emerged among the alternatives. The findings revealed that the alternative of “installing additional membrane filters to the mechanical + UV ballast water treatment system existing on the vessel” is more suitable than the “reverse osmosis method” alternative. In the study, the results have been interpreted as follows: due to the requirement of a ballast water treatment system on vessels with an International Oil Pollution Prevention Certificate (IOPP) after 2017, in commercial vessels that do not have passengers, the RO systems can be replaced with a “ballast water treatment system” in the future.Results have also been answered yes to the question of whether the existing reverse osmosis systems can be integrated with the ballast water treatment system in passenger ships. The reason why the freshwater generator ranks first in the alternative ranking is due to the simple fact of the reverse osmosis system, which has a higher energy consumption initially. The RO system can help reduce the cost by producing high flow rate water dramatically. Although the RO system is quite reliable and cheap and requires low maintenance for the seawater desalination process, the RO system only depends on the high flow of water rate. This high flow of volume production makes this system only suitable for crowded commercial vessels or onshore facilities. Other than military/service or cruise vessels, this system has a lot of other downsides, with respect to its benefits in m3/per capita. Also, when it is compared to the freshwater generator, there is a great threat to the marine environment and ecology due to the marine outfall of waste high-level brine water into the sea.In the following studies, it has been kindly recommended to increase the number of alternatives by adding other desalination methods, such as “multistage flash distillation” and “electrodialysis water treatment methods,” and extensive research of RO systems with downsides and dangers to nature with countermeasures. Also, it has been recommended to increase the number of criteria by creating new criteria such as “green energy consumption in the system” and contribute to the literature by adding other multicriteria decision-making methodologies such as BF-ELECTRE I, CPF-ELECTRE I, PFH-ELECTRE I, CSF-TOPSIS, or other newly constructed models.



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*Source: 5739682-2022-05-09.xml*