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Robustness of sustainable aviation fuel supplier rankings under alternative fuzzy representations and MCDM methods

This study validates the robustness of SAF1 as the top-ranked sustainable aviation fuel supplier across various fuzzy representations and MCDM methods, while highlighting that although the leading candidate remains consistent, the complete supplier ordering varies and should be treated as a priority for further due diligence rather than an automatic selection.

Original authors: Büşra ALTINKAYNAK

Published 2026-08-13

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Büşra ALTINKAYNAK

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are the captain of a massive airline fleet, and your mission is to switch from burning dirty fossil fuels to a cleaner, greener alternative called Sustainable Aviation Fuel (SAF). But here's the catch: you can't just pick a fuel supplier at random. You have to choose the best one out of a handful of options, and you have to weigh dozens of different factors at once. Some factors are about money (how much does it cost?), some are about the planet (how much pollution does it save?), and others are about logistics (can they deliver on time?). This is a classic "multi-criteria decision" problem, which is just a fancy way of saying, "How do you make a perfect choice when every option has good points and bad points?"

In the real world, we rarely have perfect, crystal-clear numbers. We often have to rely on human experts saying things like "High," "Medium," or "Very High" instead of exact dollar amounts. To handle this fuzziness, scientists use special math tools called "fuzzy logic" and "uncertainty analysis." Think of these tools as a way to turn vague guesses into a range of possibilities, like drawing a target with a thick marker instead of a tiny dot. The big question for airlines is: if we change how we draw that target, or if we change the rules for how we count the points, does our choice of the "best" supplier stay the same, or does it flip upside down?

This is exactly what Büşra Altınkaynak's study investigates. The author takes a previously published ranking of three SAF suppliers—let's call them SAF1, SAF2, and SAF3—and puts them through a rigorous "stress test." Imagine you have a recipe for a cake that everyone agrees is the best. But what if you change the type of flour, the way you mix the batter, or the oven temperature? Does the cake still taste the same, or does it become a completely different dessert?

In this study, the "recipe" is the mathematical model used to pick the winner. The original study (by Ecer et al.) had already picked a winner, but Altınkaynak wanted to see if that winner was truly robust or just lucky because of the specific math used. She re-ran the entire selection process using different versions of the "fuzzy" math, different ways of weighing the importance of criteria, and different ranking algorithms.

Here is what she found:

First, the "winner" actually changed immediately. The original study said SAF2 was the best. However, as soon as Altınkaynak switched the math to a different type of fuzzy number (turning the vague "High" and "Low" into specific triangular shapes) and analyzed the uncertainty, the new math declared SAF1 the winner. This happened right at the very first step of her re-calculation.

Once SAF1 took the top spot, it stayed there. No matter how she tweaked the other parts of the math—whether she used a different method to calculate the importance of the criteria (switching from one method to another called MEREC) or used different ranking formulas (like MARCOS, CRADIS, TOPSIS, or COPRAS)—SAF1 remained the number one choice.

However, the story gets a little more complicated when looking at the runners-up. While everyone agreed SAF1 was the best, the methods disagreed on who came in second and third.

Two of the methods (MARCOS and CRADIS) agreed perfectly on the whole list: SAF1, then SAF2, then SAF3.
Another method (TOPSIS) agreed that SAF1 was first, but it flipped the order of the other two, putting SAF3 ahead of SAF2.
A fourth method (COPRAS) went back to the original order: SAF1, SAF2, SAF3.

The study also tested how "tough" these rankings were. They simulated small changes in the importance of the criteria (like saying "cost is 10% more important than usual") to see if the rankings would collapse. The results showed that the order of the suppliers was quite stable; the rankings didn't flip-flop just because the weights changed slightly.

So, what does this mean for the airline captain? The study suggests that SAF1 is a very strong candidate and should be the priority for further investigation. The math is surprisingly consistent about SAF1 being the best, even when the rules of the game change. However, the study also warns that we shouldn't be too confident about the exact order of the second and third suppliers. The "fuzziness" of the data and the choice of math method can change who comes in second.

In short, the paper concludes that while SAF1 looks like the clear front-runner, airlines shouldn't just sign a contract immediately based on a single computer ranking. Instead, they should treat SAF1 as the top choice to investigate further, while keeping SAF2 and SAF3 in the running until they have more concrete, real-world data to decide between them. The study proves that while the "best" choice can be robust, the "second best" choice is often a matter of perspective.

Technical Summary: Robustness of Sustainable Aviation Fuel Supplier Rankings

Problem Statement
The selection of Sustainable Aviation Fuel (SAF) suppliers is a complex multi-criteria group decision-making (MCDM) problem involving conflicting economic, environmental, social, technical, and delivery criteria. While previous studies, such as Ecer et al. (2025), have proposed integrated models for SAF supplier selection, there is limited explicit attention paid to tracing where a published supplier recommendation first changes when the core components of the decision model—uncertainty representation, criterion weighting, and ranking procedures—are modified sequentially. Furthermore, existing comparisons often rely on final rankings, potentially obscuring the distinction between agreement on the leading supplier versus agreement on the complete ordering of all alternatives. This study addresses the need to evaluate the robustness of SAF supplier rankings under alternative fuzzy representations and MCDM methods to determine if a published reference ranking is stable or sensitive to methodological choices.

Methodology
The study employs a sequential methodological comparison using the decision problem reported by Ecer et al. (2025) as a published benchmark. The dataset comprises 39 criteria, three SAF suppliers, and four equally weighted decision makers. The methodology proceeds through five experimental configurations (E1–E5):

Data Representation: The original linguistic assessments from the benchmark study are ordinally re-encoded as Triangular Fuzzy Numbers (TFNs) rather than Interval-Valued Fuzzy Neutrosophic Numbers (IVFNNs). Two group aggregation rules are applied: a "min–mean–max" rule (retaining minimum lower and maximum upper bounds while averaging modal values) and a standard "TFN arithmetic mean."
Uncertainty Propagation: Pointwise crisp decision matrices are generated within $\alpha$ -cut intervals ( $\alpha = 0, 0.1, \dots, 1$ ) to propagate uncertainty without collapsing TFNs into single representative values immediately.
Weighting:
- E2: Uses reconstructed LOPCOW-derived weights (fixed based on the benchmark).
- E3–E5: Replaces fixed weights with classical MEREC (Method based on the Removal Effects of Criteria) weights, recalculated for each pointwise realization.
Ranking Procedures:
- E2 & E3: MARCOS (Measurement Alternatives and Ranking according to COmpromise Solution).
- E4: CRADIS (Compromise Ranking of Alternatives from Distance to Ideal Solution).
- E5: TOPSIS and COPRAS for cross-method comparison.
Robustness Analysis: The study calculates rank frequencies (interpreted as scenario frequencies) to determine rank acceptability. It assesses agreement via Spearman's rank correlation, exact-order frequency, and winner agreement. Additionally, local sensitivity is tested via $\pm 10\%$ one-at-a-time and simultaneous weight perturbations.

Key Results

Shift in Leading Supplier: The most significant finding is that the leading supplier changes between the published benchmark (E1: SAF2 > SAF3 > SAF1) and the first recalculated configuration (E2: SAF1 > SAF2 > SAF3). This reversal occurs when ordinal TFN re-encoding and $\alpha$ -cut analysis are introduced, even before changing the weighting or ranking methods.
Stability of the Core Winner: Once SAF1 is established as the leader in E2, all subsequent configurations (E3–E5) retain SAF1 as the first-ranked supplier at $\alpha = 1$ .
Methodological Sensitivity:
- Weighting: Replacing LOPCOW weights with MEREC did not alter the core ordering at $\alpha = 1$ but significantly affected rank acceptability. Under min–mean–max aggregation, SAF1's rank-1 frequency decreased; under arithmetic-mean aggregation, it increased.
- Ranking Methods: MARCOS and CRADIS produced identical rankings across all $\alpha$ levels and aggregation rules when fed the same inputs. However, TOPSIS and COPRAS, while agreeing on SAF1 as the winner, reversed the positions of SAF2 and SAF3.
Agreement vs. Robustness: The study demonstrates that agreement on the leading supplier can coexist with disagreement on the complete ordering. At $\alpha = 1$ , TOPSIS and COPRAS showed a Spearman correlation of 0.500 and zero exact-order agreement due to the reversal of the second and third ranks, despite 100% winner agreement.
Sensitivity: All methods preserved their baseline ordering under $\pm 10\%$ weight perturbations at $\alpha = 1$ , indicating local stability regarding criterion weights, though this does not account for the broader variation observed across the uncertainty region.

Significance and Claims
The paper claims that its primary contribution is identifying the specific stage at which a published supplier ordering departs from a reference result and distinguishing between the robustness of the "core winner" and the "complete ordering."

The study concludes that while there is consistent support for prioritizing SAF1 for subsequent commercial, technical, and operational due diligence, the evidence does not support a fixed, deterministic ordering of the remaining suppliers (SAF2 and SAF3). The author argues that for airline procurement, SAF1 should be treated as the priority candidate for further investigation rather than an automatically selected supplier. The findings suggest that decision-makers should evaluate core rankings, $\alpha$ -cut rank acceptability, and cross-method agreement collectively, rather than relying on a single deterministic ordering derived from one specific model specification. The study emphasizes that an unchanged core ranking does not imply unchanged robustness across the wider uncertainty region.

Technical Summary: Robustness of Sustainable Aviation Fuel Supplier Rankings

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