Optimal Fuel Selection Using a Hybrid VIKOR-TOPSIS Approach: A Comprehensive Analysis of Environmental Regulations and Road Transport Pollutant Emissions

This study employs a hybrid MCDM approach that integrates three well-established techniques: Criteria Importance Through Inter-Criteria Correlation (CRITIC), ViseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR), and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) [16-18]. As illustrated in Figure 1, the methodology follows a structured sequence of steps to evaluate and rank six fuel alternatives based on performance and environmental indicators.

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Figure 1. Hybrid MCDM methodology overview

The hybrid MCDM approach used in this study is based on a unique integration of CRITIC, VIKOR, and TOPSIS. Initially, CRITIC is applied to assign objective weights to the criteria based on their variability and inter-criteria correlation. These weights are then used in the VIKOR and TOPSIS methods to rank the alternatives. The novelty of this approach lies in the sequencing of these methods, ensuring that the most important criteria, as identified by CRITIC, are given the highest priority in the ranking process. Additionally, a new aggregation method is employed that combines both utility and regret measures from VIKOR and TOPSIS, offering a more comprehensive decision-making framework than traditional methods.

2.1 Data collection

The experimental data are based on Hoseinpour et al. [13], who tested six fuel configurations on a naturally aspirated, four-cylinder, water-cooled, direct-injection (DI) diesel engine. The engine was operated under various loads, 25%, 50%, and 75% of full brake mean adequate pressure (BMEP) and at two speeds (1,300 rpm and 2,000 rpm). The fuel cases tested include:

Performance criteria included:

• Brake Thermal Efficiency (BTE)
• Exhaust Gas Temperature (EGT)
• Base Fuel Flow Rate (Gb)
• Gasoline Flow Rate (Gf)
• Air/Fuel Ratio (AFR)

2.2 CRITIC method for weight assignment

The CRITIC method assigns objective weights to each criterion by combining variability (standard deviation) and conflict (correlation between criteria) [19-22].

Step 1: Normalize the decision matrix using Eq. (1):

$a_{i j}^{+}=\frac{a_{i j}-a_j^{\min }}{a_j^{\max }-a_j^{\min }}$          (1)

Step 2: Compute the amount of information (C_j) using Eq. (2):

$C_j=\sigma_j \cdot \sum_{k=1}^n\left(1-r_{j k}\right)$          (2)

Step 3: Determine objective weights (w_j) using Eq. (3):

$w_j=\frac{C_j}{\sum_{j=1}^m C_j}$          (3)

This ensures that criteria with high variability and low correlation are assigned greater weights.

2.3 VIKOR method for ranking

The VIKOR method ranks alternatives based on their proximity to the ideal solution, considering both utility and regret measures.

Step 1: Normalize the decision matrix (same as CRITIC).

Step 2: Identify best and worst values using Eqs. (4) and (5):

$\begin{gathered}f_j^*=\operatorname{Max}_i f_{i j}, f_j^{-}=\operatorname{Min}_i f_{i j} \\ j=1,2 \ldots, n\end{gathered}$          (4)

$\begin{gathered}f_j^*=\operatorname{Min}_i f_{i j}, f_j^{-}=\operatorname{Max}_i f_{i j} \\ j=1,2 \ldots, n\end{gathered}$          (5)

Eqs. (4) and (5) were revised to properly define benefit and cost criteria. Eq. (4) now defines the benefit criteria with the max operator, and Eq. (5) defines the cost criteria with the min operator. This ensures consistency in how benefit and cost criteria are treated in the ranking process.

Step 3: Calculate S and R values using Eqs. (6) and (7):

$S_i=\sum_j w_j \cdot \frac{f_j^*-f_{i j}}{f_j^*-f_j^{-}}$          (6)

$R_i=\max _j\left[w_j \cdot \frac{f_j^*-f_{i j}}{f_j^*-f_j^{-}}\right]$          (7)

Step 4: Compute VIKOR index (Q_i) using Eq. (8):

$Q_i=v \cdot \frac{S_i-S^*}{S^{-}-S^*}+(1-v) \cdot \frac{R_i-R^*}{R^{-}-R^*}$          (8)

where,

$\begin{gathered}S^*=\operatorname{Min}_i\left\{S_i\right\} ; S^{-}=\operatorname{Max}_i\left\{S_i\right\} ; \\ R^*=\operatorname{Min}_i\left\{R_i\right\} ; R^{-}=\operatorname{Max}_i\left\{R_i\right\} .\end{gathered}$

v=0.5 is for balanced decision-making.

Step 5: Rank alternatives in ascending order by Q_i values.

2.4 TOPSIS method for final evaluation

The TOPSIS method identifies the alternative closest to the positive ideal solution and farthest from the negative ideal.

Step 1: Create a normalized matrix using Eq. (9):

$f_{i j}(\mathrm{x})=\frac{x_{i j}}{\sqrt{\sum_{i=1}^m x_{i j}^2}}$          (9)

Step 2: Determine the weighted normalized matrix using Eq. (10):

$V_{i j}=r_{i j} \times W_j$          (10)

where, W_j are the weights of the criteria and are given by the entropy method.

Step 3: Obtain the maximum z⁺ and minimum scores z^- for each column using Eqs. (11)-(14):

$Z^{+}=\underbrace{\max }_n\left\{V_{i j}\right\}=\left\{Z_1^{+}, Z_2^{+}, Z_3^{+}\right\}$          (11)

$Z^{-}=\underbrace{\min }_n\left\{V_{i j}\right\}=\left\{Z_1^{-}, Z_2^{-}, Z_3^{-}\right\}$          (12)

$\alpha_n^{+}=\sqrt{\left(V_{i 1}-Z_1^{+}\right)^2+\left(V_{i 2}-Z_2^{+}\right)^2+\left(V_{i 3}-Z_3^{+}\right)^2}$          (13)

$\begin{gathered}\alpha_n^{-}=\sqrt{\left(V_{i 1}-Z_1^{-}\right)^2+\left(V_{i 2}-Z_2^{-}\right)^2+\left(V_{i 3}-Z_3^{-}\right)^2} \\ i=1,2 \ldots, n\end{gathered}$          (14)

Step 4: The final ranking index should be created.

The FRIn [23-28] is a credible ranking index that defines the basis for the ultimate ranking. For MCDM techniques, we consider the separation distance, which can be defined as the distance between the positive ideal solution and the negative ideal solution for the ranking index in the proposed model.

Eq. (15) (FRIn) offers a unique aggregation formula compared to the traditional TOPSIS relative closeness formula, $C_i=a_n^{-} /\left(a_n^{-}+a_n^{+}\right)$. The main advantage of using FRIn is its ability to combine both utility and regret measures from VIKOR and TOPSIS, providing a more comprehensive decision-making framework. Unlike the traditional TOPSIS formula, which primarily focuses on the relative closeness of each alternative to the ideal solution, the FRIn formula allows for a more nuanced ranking, incorporating both the utility of preferred criteria and the regret associated with non-preferred criteria. This enhances the precision and robustness of the decision-making process, making it more applicable to complex problems with multiple conflicting criteria.

$\begin{aligned} F R I_n= & \alpha_n^{-} n=1 {man}-\left(\frac{\alpha_n^{+}}{\sum_{n=1}^m \alpha_n^{+}}\right) \\ & -1 \leq F R I_n \leq 1\end{aligned}$          (15)

Alternatives are ranked in descending order of C_i.

This methodology enables systematic evaluation and comparison of fuel alternatives by integrating performance data, statistical weighting, compromise solutions, and proximity to ideal values.

In this study, a comprehensive MCDM approach, incorporating the CRITIC, VIKOR, and TOPSIS methods, was employed to evaluate the performance of six alternative fuel types in a 4-cylinder automotive diesel engine. The analysis was based on five key performance indicators: gasoline mass flow rate (Gf), base fuel flow rate (Gb), air/fuel ratio (RAF), exhaust gas temperature (Teg), and brake thermal efficiency (Ebt). The experimental data used in this study were sourced from references [13, 25-31].

4.1 Decision matrices for different engine conditions

We constructed decision matrices to evaluate the performance of each fuel type under varying engine operating conditions. These matrices represent key criteria across six test cases (RC1 to RC6) as shown in Table 1, providing a comprehensive view of fuel performance. The matrices were used to calculate the weights for each criterion using the CRITIC method, ensuring an unbiased evaluation based on the relative importance of each criterion.

Table 1. Decision matrix for case 1 (N = 1300 rpm, Load = 25%, BMEP = 2.1 bar)

4.2 CRITIC method for weight estimation

The CRITIC method was used to assign weights to each criterion based on its variability and correlation with other criteria. The results, shown in Table 2, indicate that the gasoline mass flow rate (Gf) and exhaust gas temperature (Teg) are the most influential parameters, given their high variability across the different fuel types.

Table 2. Weights using the CRITIC method

The significant variation in weights across different cases is due to load and speed dependencies. For example, at higher engine loads, Gf becomes more critical as it directly influences combustion efficiency and emissions. Similarly, Teg varies with engine speed, highlighting its importance in controlling thermal efficiency and emissions.

4.3 Ranking using CRITIC and VIKOR methods

We ranked fuel types using VIKOR after applying CRITIC for weight determination. Table 3 shows that Fuel 3 (D+FG2) performs best in most tests, followed by Fuel 6 (B20+FG2) and Fuel 2 (D+FG1).

Table 3. Results and rankings according to CRITIC and VIKOR methods

Figure 3 compares performance across different cases (RC1–RC6), highlighting D+FG2 as the top performer. This chart illustrates the optimal fuels based on VIKOR rankings and performance across conditions.

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Figure 3. Bar chart for fuel comparison (RAF, Gf, Gb, Teg, Ebt)

4.4 Final ranking using TOPSIS and VIKOR methods

After integrating the TOPSIS and VIKOR methods, the final ranking of the fuel types was determined, as shown in Table 4. Fuel 3 (D+FG2) emerges as the optimal fuel, followed by Fuel 6 (B20+FG2) and Fuel 2 (D+FG1). These results validate the importance of combining diesel with gasoline fumigation and biodiesel to achieve higher engine performance and lower emissions.

Table 4. Final ranking using TOPSIS and VIKOR

4.5 Visual representation of fuel performance

Figure 4 below compares the air/fuel ratio (RAF) across the six fuel types. This provides insight into how the different fuels impact the combustion process and fuel efficiency.

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Figure 4. Bar chart for fuel comparison (RAF)

Figure 5 illustrates the final ranking of the fuels based on the integrated TOPSIS and VIKOR methods. It clearly shows the proportion of each fuel's performance in the overall ranking.

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Figure 5. Final fuel ranking distribution (TOPSIS and VIKOR)

Figure 6 shows the variation in brake thermal efficiency (Ebt) across the different fuel types. The chart highlights the consistent superior performance of D+FG2 and B20+FG2 in all cases.

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Figure 6. Performance variation (brake thermal efficiency) across cases

Figure 7 shows the relationship between gasoline mass flow rate (Gf) and brake thermal efficiency (Ebt) for different fuels. The size of the bubbles reflects the fuel's performance, providing a clear comparison.

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Figure 7. Relationship between Gf and Ebt for different fuels

The integration of CRITIC, VIKOR, and TOPSIS in this study provides a novel and robust framework for fuel selection. Unlike conventional methods, the sequencing of CRITIC for weighting followed by VIKOR and TOPSIS for ranking allows for more precise decision-making. This approach ensures that the most relevant criteria have the greatest influence on the ranking process. Furthermore, the use of a new aggregation method that combines utility and regret measures from both VIKOR and TOPSIS contributes to the uniqueness of this study, providing a more comprehensive and accurate evaluation compared to traditional single-method approaches.

4.6 Discussion of results

The results demonstrate that D+FG2 (Fuel 3) consistently ranks as the highest-performing fuel in most test cases. It consistently ranks as the highest-performing fuel in terms of both thermal efficiency and emission reduction. This aligns with existing literature, which highlights the positive impact of biodiesel blends and gasoline fumigation on reducing emissions and improving engine performance [13, 14].

The MCDM results show that D+FG2 ranks highest due to its enhanced combustion efficiency and reduced CO emissions. B20+FG2 ranks second, demonstrating a significant reduction in PM and CO emissions, highlighting the role of biodiesel blends in improving environmental performance.

We collected emission data for key pollutants—NOx, PM, and CO—across each of the fuel alternatives tested. The results showed that D+FG2 significantly reduced NOx emissions by 18%, PM emissions by 20%, and CO emissions by 15%. These findings align with the observed trends in engine performance, where the optimized combustion process contributes to reduced pollutant emissions while maintaining high thermal efficiency.

B20+FG2 (Fuel 6) also shows excellent performance, ranking second across most test cases. Its environmental benefits are significant, as it achieves higher fuel efficiency and lower emissions than pure diesel. This suggests that biodiesel blends are a viable alternative to pure diesel, offering the dual benefits of reducing carbons and improving engine performance.

The reduction in CO, PM, and NOx emissions from D+FG2 and B20+FG2 can significantly improve air quality and reduce respiratory and cardiovascular diseases.

Challenges to adopting D+FG2 and B20+FG2 include the need for modified fueling infrastructure, higher biodiesel production costs, and compatibility with existing engines.

B20 demonstrated a significant reduction in emissions of NOx, PM, and CO when compared to traditional diesel, indicating its potential as a more suitable option for areas with high pollution levels, especially in regions prioritizing emission control.

Fuel 2 (D+FG1) shows moderate performance but lags behind D+FG2 and B20+FG2 in several key parameters. The lower gasoline mass flow rate (Gf) in D+FG1 results in lower thermal efficiency and higher exhaust temperatures. However, D+FG1 still performs better than pure diesel (Fuel 1) in terms of emissions, particularly in terms of NOx and CO.

The D+GF mixture was shown to reduce CO emissions by 15% relative to conventional diesel, based on emission testing, highlighting its capability to contribute to improved air quality.

In comparison, B20 (Fuel 4) and B20+FG1 (Fuel 5) rank lower due to higher exhaust temperatures and less efficient combustion. The high air/fuel ratio (RAF) in these fuels indicates that the combustion process is less optimized, leading to higher emissions and lower engine efficiency.

These findings suggest that while biodiesel offers environmental benefits, its combustion characteristics require further optimization for improved fuel economy and performance.

Diesel (Fuel 1), while still widely used, consistently ranks the lowest across most test cases, indicating its inefficiency and high emissions. The high exhaust gas temperature and low thermal efficiency make diesel a less favorable option as global emission standards continue to tighten.

This study highlights the potential for alternative fuels, such as D+FG2 and B20+FG2, to not only meet emission reduction goals but also provide superior engine performance, aligning with global efforts to reduce the environmental impact of road transportation.

This integrated analysis of fuel types using MCDM methods supports the shift toward more sustainable fuels, such as gasoline-fueled biodiesel blends, which offer improved performance and reduced emissions. It also suggests that further work is needed to optimize fuel mixtures and explore emission control technologies to meet increasingly stringent environmental standards.

The study confirms the efficacy of an integrated MCDM approach to evaluate and rank alternative fuels for diesel engines. D+FG2 (Fuel 3) is identified as the most optimal fuel, offering the best balance between engine performance and environmental sustainability. These results provide valuable insights into the future of cleaner fuels and their role in meeting global emission standards.