A ranking supplied by ten experts cannot tell a trader anything about returns. Liu, Shen, Dinçer, Yüksel and Eti place an elaborate uncertainty framework over their ordering of five sustainable-finance product categories, yet the final decision never moves. Table 17 reports the same order across all 50 ranking columns. That invariance is the paper's most revealing number, and it cuts against the authors' interpretation.
Five products inside a large machine
The underlying decision problem is compact. The five ESG criteria are carbon impact (CRBN), resource efficiency (RSCR), social responsibility (SOCR), ethical practices (ETHP), and compliance with sustainable regulations (STRG). The five alternatives are green tokenized assets (GTA), biodiversity conservation funds (IFBC), ESG-linked fintech platforms (EFP), circular-economy venture capital (CEVC), and sustainability-based loans (SBL).
Ten experts, each with 21 to 28 years of experience, assess both matrices using a nine-point linguistic scale running from extremely low to extremely high. The paper is direct about the source material: "No data is used in the analysis."
Each linguistic label becomes a five-component fuzzy number. The representation, called dynamic multi-facet fuzzy sets (DMFFS), combines base membership with four derived degrees: non-membership, entropy-based hesitation, engagement, and resistance. Four control parameters (a, b, c, d) determine those degrees. The authors fix them at four settings, each intended to describe a behavioural scenario: negative (10, 5, 1, 1), positive (1, 1, 5, 1), unstable (1, 2, 1, 10), and natural (1, 1, 1, 1). These four settings come from the authors. A statistics-driven route for setting the parameters also appears in Eqs. (49) to (52), though the study does not use it.
Criterion weights begin with an expert-scored directed dependency matrix. The authors defuzzify it, normalise the results into probability-like vectors, and apply Shannon entropy and information gain. Every criterion has baseline entropy of ln(5) = 1.609. In the overall case in Table 8, social responsibility produces the highest information gain, 0.636, and receives a weight of 0.273. Ethical practices follows with 0.538 and 0.231. Carbon impact finishes last in that case, with information gain of 0.313 and a weight of 0.134.
Alternatives are then scored through principal component ranking optimization (PCRO). The authors use that name for a procedure that extracts the dominant eigenvector from the covariance of the weighted decision matrix, using power iteration over six steps.
The resulting order is clear. Sustainability-based loans rank first with a global score of 3.226. ESG-linked fintech platforms are second at 2.007, circular-economy VC is third at 0.223, biodiversity funds are fourth at -2.299, and green tokenized assets finish last at -3.156.
Reproduction stops at the inputs
The study never defines a universe of tradeable instruments. Its five alternatives are sustainable-finance categories rather than tickers. The abstract also advertises AI-assisted amplification of expert opinion, while the Analysis section supplies only the consensus matrices from ten experts in Tables 2 and 3. No reproducible augmentation procedure appears, and the individual assessments remain unavailable.
Any attempted recreation would therefore require a new input matrix. Testing that matrix would say nothing about the reported result.
Why do all 50 columns agree?
The benchmark uses extended TOPSIS, a distance-to-ideal ranking rule, alongside a five-case sensitivity analysis. For that analysis, the same five weights (0.1340, 0.2111, 0.2724, 0.2304, 0.1520) are rotated cyclically across the five criteria. Each method contributes five reported columns, comprising the four behavioural scenarios and the overall case. Five permutation cases across two ranking methods produce 50 columns. All 50 give the same order: sustainability-based loans, ESG-linked fintech, circular-economy VC, biodiversity funds, and green tokenized assets.
The paper presents this agreement as validation. The result reads differently once the movement in the inputs is considered. Under the negative case, weights range from 0.116 for carbon impact to 0.310 for social responsibility. The positive case compresses them to a band from 0.178 through 0.237, leaving them close to uniform. Criterion ranks also change. In the positive scenario, carbon impact moves from 5th to 4th, resource efficiency falls from 3rd to 5th, and sustainable regulations rises from 4th to 3rd.
Still, the alternatives never reorder. A weight vector shifts from near-uniform to a near-threefold spread, while the five-facet fuzzy structure uses parameters ranging from 1 to 10. Every route reaches the same ordinal answer. The assessment matrix appears so heavily dominance-ordered that the surrounding machinery becomes decorative.
The authors state the limits of their sensitivity design carefully. The invariance "should be interpreted as evidence that the obtained ranking is stable under the specified cyclic permutation design, not as evidence that PCRO rankings must remain invariant under any arbitrary weight change." That caveat is correct and appears in the paper. They also address the repeated result directly, writing that the identical rankings "should not be interpreted as a repeated or unchanged computation" because each case applies a different cyclic permutation of the Table 16 weights.
The computations may differ. The decision does not. Ordinal ranking is the output, and recomputed scores that never change the order leave that output untouched.
A similar qualification accompanies the benchmark. The authors say PCRO/TOPSIS agreement "is interpreted as a consistency check for the DMFFS-based inputs and the information-gain-derived weights, not as a universal claim that PCRO is superior." Yet the section continues to frame the agreement as validation.
The PCA step raises a separate concern. A five-by-five decision matrix offers little basis for statistically meaningful covariance estimation. Table 13 reports every entry of the unstable-scenario covariance matrix as 0.0000. In the negative scenario, the SBL row contains the weighted decision matrix values (0.090, 0.180, 0.242, 0.083, 0.114) rather than covariances. The row looks mislabelled.
Consensus hides the disagreement
The panel has relevant credentials and spans commercial banking risk, ESG consulting, academia, asset management, fintech strategy, governance advisory, regulatory advisory, and audit. Nine of the ten experts have international ESG exposure. According to the paper, individual assessments were followed by moderated discussion of divergent judgments within a structured consensus process.
No formal inter-expert reliability test was performed. The authors describe their dispersion review as "a procedural screening mechanism rather than as a separate statistical hypothesis test." The disclosure is welcome, but Tables 2 and 3 ultimately show only one consolidated linguistic matrix. Readers cannot inspect how far the ten experts initially disagreed, who changed position during moderation, or whether removing any panellist would alter the conclusion. Moderated consensus can manufacture correlated judgment.
Carbon impact provides the substantive result worth challenging. In the overall case it ranks last among five criteria, with a weight of 0.134. The authors themselves call this counterintuitive. Their explanation is that governance credibility acts as a precondition for credible environmental transition, allowing social and ethical criteria to carry more informational weight. They also observe that most panellists work in emerging markets, where regional enforcement conditions may shape the result.
Neither explanation is tested.
The claim remains a hypothesis drawn from ten people's priors and wrapped in entropy arithmetic. Another result receives no real explanation: green tokenized assets finish last at -3.156, while ESG-linked fintech platforms take second place at 2.007. Both belong to digital sustainable finance. The Discussion credits the fintech result to the digital transformation of sustainable finance, yet that account cannot explain why the other digital category sits at the bottom.
The manuscript changes its claim halfway through
The abstract and methodology use careful language. Weighting is repeatedly described as "an information-gain-based dependency-weighting procedure" rather than a learned Bayesian Network. The methodology adds an explicit boundary: "no sparse DAG structure or conditional probability table is learned from observational data."
PCRO receives the same caution. The paper says it "does not eliminate correlation from the original ESG criteria, nor does this study provide a formal proof that PCRO minimizes multicollinearity relative to TOPSIS, VIKOR, or other MCDM methods."
The Discussion then opens with a different account: "The Bayesian Network provides probabilistic weighting by capturing causal interdependencies among ESG criteria." In the same paragraph, PCRO "enhances robustness by minimizing multicollinearity." The Conclusion repeats the Bayesian claim and describes the model as integrating "Bayesian probabilistic weighting."
Those statements conflict with the limitations established earlier in the manuscript. The front half appears to have been revised while the back half retained older claims. A practitioner who reads only the Conclusion would leave with a Bayesian-network interpretation that the method itself does not support.
Nothing here is priced
The five-facet fuzzy construction contains genuine engineering. Its parameter interpretation gives a behavioural meaning to each control: a for decisiveness, b for ambiguity amplification, c for engagement, and d for cognitive inertia. The authors also reasonably propose that future work integrate real ESG performance datasets and examine predictive validity.
Until such evidence exists, placing sustainability-based loans first says nothing about returns, spreads, default behaviour, or portfolio contribution.
Two independently recruited panels could change the assessment. If the same protocol leaves all 50 columns in agreement for both, the elicitation may be capturing something structural. If the rankings separate, the invariance came from this panel rather than the method.