1 Introduction

In recent years, there are many concerns about the increased air pollution caused by shipping activities. After many years of political deliberations, the maritime industry concluded that regulation is unavoidable. According to many studies, about 3% of the total CO₂ emissions are produced by the maritime industry [5, 10]. In addition to this, future scenarios predict that maritime CO₂ emissions will be doubled by 2050 [5, 10, 11].

However, the complexity of climate change has demonstrated the need for more research in this field, and new approaches to understand, model, and forecast the exact attribute of climate change. The shipping industry has acknowledged that addressing the challenge of global climate change is beyond the capacity of a single country. Therefore, the International Maritime Organization (IMO) was held responsible to lead and reinforce a comprehensive global climate change strategy.

In July 2011, the IMO decided the adoption of energy efficiency measures, namely the Energy Efficiency Design Index (EEDI) and the Ship Energy Efficiency Management Plan (SEEMP). However, there is some skepticism about whether these measures will manage to reduce CO₂ emissions from international shipping [2, 5]. In this light, several market-based measures (MBMs) have also been considered, especially after the pressure that the European Union put toward the maritime industry. According to the Marine Environmental Protection Committee (MEPC), these measures may provide a fiscal incentive for ship owners to empower their ships with more energy-efficient technology, which will eventually contribute to the offsetting of growing ship emissions. These mechanisms are based on economic tools such as levies and emission trade in an effort to internalize the external cost caused to the environment. The IMO is still reviewing these proposals in view of specific criteria. Interestingly enough, these include several variations of the emission trade mechanism, making this tool appear as a “favorite” through the decision-making process.

However, the picture is rather complex and multifaceted once all possible scenarios are considered. Apart from traditional factors that influence the development of an environmental model [19], there are also specific factors related to the maritime industry, like the future growth and the future need for shipping transportation. In addition to these, maritime transportation is highly affected by the oil price as fuel cost is the industry’s major operational cost. Other factors that could influence future shipping CO₂ emissions under a specific regime includes the cap that the industry will pose and the international carbon price, as it has been formed through other emission trade mechanisms. These factors were more or less modeled under various methodologies in order to predict future emissions as well as the cost of their mitigation. Eide et al. [9] used an activity-based modeling for all the ships up to 2030, including a gradual development of CO₂ reduction measures. Corbett et al. [6] explored policy impacts of a fuel tax and a speed reduction using a profit-maximizing function, and Psaraftis et al. [29] investigated the role of speed, by modeling the total fuel consumption under different scenarios.

Taking these into account, the IMO study attempted to project future emission reduction and their cost according to the mechanism of each of these measures, based on specific scenarios. As one would expect, these results consist of a long and rather complex list of annexes, which make comparisons for the decision particularly difficult. The aim of this paper is the development of a modeling tool for decision making and strategic planning for shipping emissions. The fuzzy logic methodology was used to solve the complex decision-making problem of environmental management concerning shipping emissions. More specifically, this methodology was used for assessing and evaluating a number of MBMs devoted to address maritime emissions and making future prediction about shipping emission reduction.

The remainder of this paper is organized as follows. Section 2 discusses the process of developing MBMs and presents the predominant versions of these measures. Sections 3 and 4 analyze our methodology and the model development process, respectively. Section 5 presents the results as well as the evaluation of our model. Section 6 summarizes and concludes the paper.

2 Developing Mitigation Tools for Shipping Emissions: The MBMs

Looking at the history of the process of regulating shipping greenhouse gas (GHG) emissions, it should be mentioned that >10 proposals were originally submitted to the MEPC. The IMO study has evaluated 10 of these according to the criteria and the scenarios mentioned before. However, some of them were afterward withdrawn or merged. Most importantly, though, some of them could not be evaluated due to insufficient mechanism design or lack of data. Consequently, this study will only refer to five of them. A brief presentation of these five measures is provided below.

1. The Global Emission Trading System (ETS) (MEPC 61/4/22) [26] includes a global cap-and-trade system to control maritime emissions, with allowances sold in a global auction. There will also be a target year and a cap on the total emissions of the sector. Ships will be registered in an international ETS body and deliver emission allowances according to their CO₂ emissions. According to the proposal, the returns from auctioning allowances would be used for mitigating projects as well as programs, policies, and other activities in developing countries.

2. The GHG Fund (MEPC 60/4/8) [25] aims to set a global CO₂ reduction target for the maritime industry. Ships will have to pay a levy on every ton of bunker fuel purchased in order to meet this target. This measure also demands the registration of bunker fuel suppliers in order to be able to provide a Bunker Delivery Note for future inspections. The target is essential for this mechanism, as it will define the size of the GHG contribution. The revenues will be used to purchase offset credits to match the projected gap between industry emissions and the target.

3. The Port State Leverage (PSL) proposal (MEPC 60/4/40) [24] includes a standardized emissions charge on all ships when arriving at a port, based on the amount of fuel consumed on that voyage (not bunker suppliers). This is a simple mechanism directly aimed at reducing maritime emissions of CO₂ without taking into account any design, operations, or energy source. The levy will be set based on a global emission reduction target, and it could reward ships exceeding efficiency targets.

4. The Rebate Mechanism (RM), as proposed in MEPC 60/4/55 by the International Union for Conservation of Nature (IUCN), calculates the rebate through the country’s share of global imports by value. It can be implemented in parallel with any maritime MBM, which generates revenue, such as levies or emission trade systems. The Rebate Mechanism proposal does not set an efficiency target or target line for net emissions from international shipping. However, it can deliver both in-sector and out-of-sector reductions through carbon levy and mitigation projects accordingly.

The proposals have diverse characteristics ranging from imposing a contribution to setting an emission trading mechanism. A detailed description of the proposals and the stakeholders’ views is given by Lema and Papaioannou [21]. In the IMO study, all of them have been evaluated under the same criteria and modeled according to the same scenarios. Specifically, the modeling scenarios included

• Two scenarios for the growth rates (1.65% and 2.8%);

• Three scenarios for the target/caps (0%, 10%, and 20% below the 2007 level);

• Twenty-eight percent of the revenues used for mitigation in the proposal of the rebate mechanism;

• Two scenarios for the carbon price (average and high) and two scenarios for the fuel price (reference and high).

Although this study has been done in great depth to analyze the proposed MBMs, it did not lack reservations. The complexity and the variegation of the proposal’s mechanisms and the modeling scenarios are of course a natural limitation for the model. However, one would expect that the exact model of each measure would be clearly analyzed in the proposal with regard to assisting the decision process or for future research purposes. Unfortunately, this is not the case. The models are not made available to public, assuming that there was no need for further details. Generally, the assumptions made through the scenario process have a key role in the results, including the emission reductions, the costs, and the revenues [31]. Given the fact that the majority of them cannot be substantiated and the lack of the exact model, it seems natural that the industry had strong reservations toward this study. Furthermore, some critics dispute several aspects of the study, with the most important being how an increase in fuel prices will result in emission reduction [28].

All these characteristics obviously imply that predicting the mitigation of maritime CO₂ emissions is a complex and highly challenging task. According to Eide et al. [9], “shipping markets are highly cyclical and volatile and external forces (e.g. world economy) are reinforced by internal mechanisms (e.g. group mentality and speculation).” For this reason, we propose a fuzzy logic modeling approach that interprets uncertainty and vagueness in an efficient way.

3 Methodology

When it comes to decision making, it is generally understood that human perceptions are usually judged subjectively. However, uncertainty abounds in climate change, and this is a major obstacle when designing a CO₂ mitigation framework [7, 13, 37]. Regarding shipping CO₂ emissions, the maritime industry has long ago recognized the need for a system that will be able to manage the complexity of the field. However, the wide range of available MBMs demonstrate the necessity of a coherent system to contribute to the decision process.

Analysis of environmental policy issues and decision making is traditionally carried out using multicriteria analysis methods [12]. Zadeh [40] was the first who proposed fuzzy logic as a methodology for decision making. Since then, several studies have used this methodology on environmental policy issues like sustainability [1], environmental impact assessments [22, 33, 39], or environmental vulnerability [38]. In addition to these, Silvert [34] proposed fuzzy indices of environmental conditions and Dimitrov [8] used fuzzy logic to manage social complexity and consensus seeking in environmental policy issues. In the environmental economics field, Kunch and Springael [20] have studied a fuzzy logic system for a tax policy that will reduce CO₂ emissions as well as a fuzzy methodology for evaluating tradable CO₂ permits. Other studies proposed variegation approaches toward political problems combining fuzzy logic with multiple-criteria decision making [27, 30].

The aim of this paper was the development of a modeling approach that will contribute to the decision making of the proposed MBMs. Fuzzy logic systems are ideal for this purpose, as they can integrate all the scenarios, and the criteria involved in this problem under a rational and transparent system. For the purposes of the study, a fuzzy inference system (FIS) was developed based on a set of 26 if-then rules. Next, each measure will run in the investigated FIS. The rules arise from authors’ field knowledge and are the same for all the proposed measures. The input and output variables (box 2) are the same as those that have been set from the IMO Expert Group study. This study evaluated the proposed MBM, developing a fuzzy logic model that involved the specific economic scenarios (inputs) and their results on the evaluating criteria (outputs). Despite the criticism toward this study, these are the only available data at the moment, as the IMO has not released any updated data yet.

However, it should be mentioned that the arithmetic comparison of the results is not the main objective of the paper. What is important in this method is the integration of uncertainty and complexity of this decision-making process through the FIS. This new integrated modeling approach will elaborate all the input and output data with simulated implementation of the proposed MBMs toward 2030.

4 Constructing the Fuzzy Logic Model of an MBM

The aim of the constructed model is to contribute to the decision-making process that is held from the IMO concerning the proposed MBMs; for compatibility and comparison reasons, the components of our model has to “mimic” the one that was chosen from the IMO. Due to the fact that the exact models of the measures are not publicly available, this model will only use the variables and the result values on the criteria as derived from the IMO Expert Group study [18]. However, the decision upon an MBM is a rather complex task due to the vast number of variables that should be taken into account. As a result, the study that describes the implementation of the proposed MBM measures is composed of a large number of input (scenarios) and output (environmental-economic effects) variables. A problem that should be avoided is “the curse of dimensionality,” which occurs when we have numerous variables and the number of rules increases exponentially [32], and this may cause problems of stability and continuality to the fuzzy logic model. The most obvious way that it can be managed is by keeping a low number of variables and reducing complexity; Setnes [32] also suggested that decomposing the fuzzy logic model and simplifying the rule base can reduce dimensionality. For this reason, we kept only the variables of the scenarios that affect all the examined MBM. Regarding the output variables (results), we examined only two variables, namely the emission reduction and the cost for the same reason. All other criteria (even quality criteria) could also be examined with a fuzzy logic model; however, this is beyond the scope of this study and is proposed for future research.

As presented in Figure 1, the fuzzification process involves the construction of the membership functions of input and output variables. To define these values, the first step of this study involves statistical analysis of the values derived from the IMO study. The results are presented in Appendix I, for each MBM.

Figure 1:

An Overview of the Fuzzy Logic Modeling.

4.1 Input Variables

When developing the membership function, data expressed in any form or other descriptive statistics can be used as a base to construct a membership function. In social studies, using data from previous works for meta-analysis is rather common, as obtaining new data is usually difficult and time consuming. There are a variety of possible conversion methods, each with its own mathematical and methodological strengths and weaknesses [14].

In our study, for all the input variables, their domain interval is evenly divided into three fuzzy sets using the mean of their range values. Any kind of membership function can be used; however, we preferred the Gaussian-shaped one for its smoothness. The three fuzzy sets intersect at the point that they form four equal areas of α, in a way that

Range values = 4α.

The formula of the Gaussian membership function is

f(x; σ; μ) = e−(x − μ)22σ2,

where μ is the position of the center of the peak and σ determines the width of the Gaussian function.

The point at which the curves overlap on the x-axis is 0.3678, as the literature suggests an overlapping level between 0.25 and 0.50 [16]. At this point, the Gaussian function has the width of a=2σ, which is e⁻¹=0.3678.

Regarding the selection of the variables, the IMO study used many variables in developing different “scenarios” for future figures. These scenarios are common in estimating the results for all the MBMs. For the purposes of our analysis and modeling, the starting point is the year 2015 and the time point to be analyzed is the year 2030. In our case, we use the most important of these as input variables as follows:

• Emission growth: This variable refers to the future growth of shipping emissions. It is known that shipping emission growth is strongly related to the world economic growth, which increases transportation needs. The IMO study has taken into account the IUCN scenarios, which include two growth scenarios (1.65% and 2.8%). In this study, we consider three possible levels of growth – low: 1.7–2.25, average: 1.7–2.8, and high: 2.25–2.8.

• Fuel price: Fuel cost is an important component of running cost in shipping companies, and it greatly affects many aspects of maritime transportation, like the ship’s speed and, consequently, the equilibrium between supply and demand of maritime transportation services. The IMO study has predicted prices for both distillated and residual fuel in 2030. These prices range between $68 and $330 per barrel. In this study, we have three levels of oil price – low: $70–200, average: $70–330, and high: $200–330.

• Carbon price: A common concept of most of the proposed measures is that shipping companies will be able to buy carbon permits to offset the amount of CO₂ they have emitted. The price of these carbon permits will be subject to the world’s supply with developing countries being in the forefront of expected suppliers. Some MBMs even propose that “green ships” that meet their target may be able to sell their excessive permits. According to the IMO study, the expected price of carbon in 2030 is $40 (average) and $100 (high) per ton. In this study, we have three levels of carbon price – low: $40–70, average: $40–100, and high: $70–100.

• Extra efficiency: Apparently, technological improvements will gradually take place, giving a boost of efficiency in new or existing ships. New legislation, like the EEDI and SEEMP, is expected to contribute toward this direction. This will have a significant effect on the mitigation efforts as it will directly reduce the emissions, without any interference of oil or carbon price. Of course, such investment usually demands a stable economic environment, which some MBMs are aiming to provide. The study of the IMO Expert Group considered two levels of extra efficiency, namely 0 and 0.6. For the needs of our study, we have set three levels of extra efficiency – low: 0–0.0.3, average: 0–0.6, and high: 0.3–0.6.

• Emission cap: It is generally understood that the emission cap determines the amount of CO₂ emissions that has to be offset. This is usually expressed as a percentage of the total emissions of business as usual (BAU). For those proposed measures that suggest the emission cap as part of their mechanisms (GHG Fund and ETS), the IMO Expert Group study has set the cap as 0%, 10%, or 20% of BAU. In this study, we have three levels for the emission cap – low 0–0.1, average 0–0.2, and high 0.1–0.2.

In Table 1, we present an example of the membership functions for the variable of growth.

Table 1:

Fuzzification of the Input Variables.

Input variable: growth	Fuzzy set
	Low: 1.7–2.25, average: 1.7–2.8, high: 2.25–2.8

4.2 Output Variables

In constructing the membership functions for the output variables, we followed the same pattern. Specifically, we divided their internal into five fuzzy sets using the mean of their range values. We also have the curves overlapping at the 0.3678 point. The range of the output variables, as well as their mean and standard deviation, as derived from the IMO study is presented in Appendix I for all the MBMs.

• Emission reductions: This is probably the most important variable of our results as it measures the environmental effect of the MBMs. The variable is composed of the amount of in-sector and out-of-sector reductions (sum), and is expressed in tons of CO₂. For the purposes of our model, we set five levels of emission reductions, which are labeled as very low, low, average high, and very high.

• Cost: Every MBM is based on a specific economic tool that intends to make shipping companies (the polluters) pay for the externalities they cause on the environment. This variable contains the total financial cost (in billion dollars) that the shipping industry will bear for offsetting the emissions defined by the specific cap. Appendix I contains data for the financial cost of the proposed MBM apart from SECT, which does not include a mechanism to quantify the exact cost. In our model, we use four levels of costs – very low, low, average high, and very high.

In Table 2, we can see an example of the membership functions of the output variables for one of the MBMs, namely ETS.

Table 2:

Fuzzification of the Output Variables.

MBM	Variables	Fuzzy sets
ETS		Emissions – very low: 155–266, low: 155–376, average: 266–487, high: 376–599, very high: 487–599
		Cost – very low: 40–62, low: 40–80, average: 46–98, high: 78–117, very high: 96–118

Let X be the universe of discourse and its elements be denoted as x.

In fuzzy theory, a fuzzy set A of universe X is defined by function μ_A(x) called the membership function of set A.

With μ_A:x→[0 1].

In our case, we define the antecedents:

An input variable x₁ for growth, with linguistic terms A_i1 and its membership function μ_A1.

An input variable x₂ for oil prices, with linguistic terms A_i2 and its membership function μ_A2.

An input variable x₃ for carbon, prices with linguistic terms A_i3 and its membership function μ_A3.

An input variable x₄ for extra efficiency, with linguistic terms A_i4 and its membership function μ_A4.

An input variable x₅ for the emission cap, with linguistic terms A_i5 and its membership function μ_A5.

With μ_Ai (x): x→[0 1].

The linguistic terms A_ij are fuzzy sets defined in the domains of

xi ∈ X ⊂ R,

Aij ∈ A, A = {low, average, high}.

Similarly, for the consequent we define:

An output variable y₁ for emission reductions, with linguistic terms B_i1 and its membership function μ_B1.

An output variable y₂ for cost, with linguistic terms B_i2 and its membership function μ_B2.

With μ_yi: y→[0 1].

The linguistic terms P_i and Q_i are fuzzy sets defined in the domains of

yi ∈ Y ⊂ ℝ,

Bij ∈ B, B = {very low, low, average, high, very high},

where A_i ε A and B_i ε B.

4.3 Fuzzy Rules

A vital part of constructing a fuzzy logic system is the development of the “if-then” fuzzy rules. These rules are used to specify the behavior of the system under study and, for this reason, they consist the core of the system. A typical fuzzy if-then rule is composed as follows: “If x₁ is A_i1 and x₂ is A_i2 and … then y₁ is B_i1 and y₂ is B_i2.

Once the collection of fuzzy rules is completed, the fuzzy inference engine combines the rules and then it carries out a mapping from the fuzzy set A’ in U to fuzzy set B’ according to each rule.

In our case, the fuzzy set A_ij is obtained as the Cartesian product of fuzzy sets A_ij, where A_ij: A_i1×A_i2 … A_in.

The degree of fulfillment is given by

λ = μAi1(x1) ∧ μAi2(x2) ⋯ ∧ μAim(xm),

with 1≤i≤K.

These rules can be obtained from human experts of the fields or from domain knowledge [16]. In our case, the rules were derived from the field of environmental economics, as described in classical handbooks by Hanley et al. [15] and Tietenberg and Lewis [36]. Most of the rules depict common concepts related to market equilibrium, abatement cost, and externalities [3, 20]. Some more specific parameters of the rules (like future extra efficiency) and their effects are described in the IMO Expert Group study [18] as common concepts or as part of the mechanisms. In Figure 2, the scheme presents the sources that contributed to the development of the fuzzy rules.

Figure 2:

Developing Fuzzy Rules.

In order to find the combined effect of all the fuzzy variables, a fuzzy inference method is applied. One of the most common inference methods used is Mamdani’s method because of its simple structure that is generally considered to be more suitable for models with discrete values.

When developing a fuzzy rule, we use the concept of “and,” “or,” and sometimes “not.” For this study, the connection “and” is used in all the rules in order to resemble the IMO decision process. It should be noted that the fuzzy “and” is an extension of the Boolean “and” to numbers that are not just 0 or 1, but between 0 and 1.

Furthermore, we use the MIN fuzzy implication, which interprets the fuzzy implication as the minimum operation given by the following relationship:

Rc = A × B = ∫X × Y μA(x) ∧ μB(y)/(x, y).

5 Results

Viewing the rules gives the overall picture of the developed fuzzy system as each line corresponds to a rule. In Figure 3, five rules of the GHG inference scheme are presented.

Figure 3:

Examples of Fuzzy Rules through the Fuzzy Toolbox, Matlab Software.

On the left-hand side, the input variables are depicted, with the corresponding membership function; on the right-hand side, we have the output variables. In the lower right corner is the result of fuzzy reasoning or defuzzification, which shows how the output of its rule is combined to make an aggregated defuzzified value.

Different input values can be tried by moving the distance of the red vertical line. This is particularly interesting in our case, as it permits the user to view the output results with different scenarios. Below we present the results of our study, using the default results of the input variables, which are as follows: growth 2.25, oil price 200, carbon price 70, extra efficiency 0.3, and emission cap 0.1.

As the inputs were the same for all of our systems, we present the results of the output variables in Table 3.

The first two MBMs, namely the GHG Fund and ETS, appear to have similar results in emission reduction, but have a significant difference in cost. Taking both output variables into account, we could say that the GHG Fund performs better than the other proposed MBMs, as it can achieve more emission reductions with less cost. On the other hand, PSL seems to have less potential regarding emission reduction while it also has high cost. Finally, RM is rather effective in reducing emissions but has higher cost than the GHG Fund. In general, it seems that the emissions mostly declined in prices in parallel with a lower emission growth and a higher emission cap. The results for each MBM are fully presented in Appendix III.

In general, results from using our application allow us to confirm that the emission reductions are highly dependent on the annual emission growth and the emission cap that will be set. The extra efficiency also has a significant effect as the emission reductions appear to lessen when extra efficiency is rising. On the other hand, the cost of the MBM is mostly driven by the fuel price and the carbon price, as well as the emission cap.

6 Concluding Remarks

As analyzed before, a tool for the evaluation of MBMs is not only useful for estimating the amount of emission reduction and their cost, but it can also help the stakeholders obtain a good perspective of the MBMs’ characteristics and make a more informed decision. In our study, we used fuzzy membership functions to capture the vagueness inherent in the scenario (input) and criterion (output) variables. We believe that this modeling is more reasonable in representing the actual real-world conditions, due to the fact that the membership functions comprise terms closer to the human notation and cognition. Additionally, fuzzy systems provide a more transparent representation of the system under study, as the rules are closer to the human reasoning and the users can easily understand and evaluate them.

In order to avoid the curse of dimensionality, we preferred to implement only a strong core of rules and not an extensive combination of all the variables. When compared to the IMO study results, not all MBMs responded the same. This can be the subject of a future research in the field, especially under the light of new, updated data. It is important, though, to highlight that the result of the MBMs were in balance with those of the IMO Expert Group study. This generally confirms that the output variables were effectively manipulated, and represented the variations of the input variables as expected.

The limitations derive from the fact that past data were used and were extrapolated into the future. This is especially the case for the variables related to future extra efficiency and abatement cost. However, the aim of our model is to improve understanding regarding the variable behavior, rather than achieving precision. That being said, we believe that the model could have a wider application in any sector seeking to achieve emission mitigation, and this is part of our future work.

In conclusion, though more exhaustive work is needed, it can be said that our application is able to give high qualitative information about the proposed MBMs.