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Kaimen Rigor review

Evaluate teaching quality of physical education using a hybrid multi-criteria decision-making framework

Chen Z, Luo S.

DOI: 10.1371/journal.pone.0280845
Record issued: 2026-08-05
Engine: 7.15.0
Exported: 2026-09-19

Prepared by Alpha1. This document is confidential: it is intended for the recipient it was shared with and must not be redistributed. The live record at alpha1science.com/verify/a632bdfc-71b4-4117-b76f-e45ea9c04d7d is authoritative.

Kaimen Rigor review

Kaimen Rigor reviewed

3.25 / 5

Adequate — real issues to address

Computational Study

Critical

High-priority

How this rating was calculated

Started at 5★ — deductions

IntegrityIntegrity concern ×3−1.5★
ReportingStudy design partially met−0.25★

Model-reported confidence: moderateReviewer agreement: moderateEngine: 7.15.0Source: full text

Not verified in this report

Statistics were not checked: no recomputable values were found in this text — no test statistic reported with its degrees of freedom, no effect estimate printed with both a 95% CI and a p-value, and no percentage printed with both its count and its denominator.
No data or code availability links were detected to verify.

Biggest issues

01Internal contradictions in the reported numbers
mediumArithmeticreviewer-assessedFull detail
At ζ=0.6 in Table 9, the reported RI values (A1≈0.260, A2≈0.257, A3≈-0.327, A4≈-0.843) imply ranking A1≻A2≻A3≻A4 under the paper's rule that larger RI means better, yet the table lists A3 as the best college with ranking A3≻A1≻A2≻A4.
“ζ = 0.6 | (0.216,0.273, 0.165,0.158, 0.188) | RI ( A 1 ) ≈ 0.260, RI ( A 2 ) ≈ 0.257, RI ( A 3 ) ≈ -0.327, RI ( A 4 ) ≈ -0.843. | A 3 ≻ A 1 ≻ A 2 ≻ A 4 | A 3”
Table 9

Findings by category

101ArithmeticNumerical inconsistencies 102OverreachOverstated conclusions 03AuthenticityNone found 104DisclosureReporting gaps 05AvailabilityNone found · partly checked 106CopyeditCopyediting

This Kaimen Rigor review uses Kaimen Rigor reviewers trained on a curated corpus of high-fidelity and retracted papers, with expert supervision and curation. It can still make mistakes; verify each finding against the source before relying on it.

The paper proposes a novel hybrid MCDM framework with a clear scientific premise and adequate reporting transparency, but it is undermined by unresolved internal contradictions in key tables (Table 9 and Table 10) and a lack of code sharing, which limit reproducibility and trust in the illustrative results.

The three independent reviewers largely agreed on the strong dimensions (scientific premise, reporting transparency) and N/A designations, but diverged on study design (N/A vs. warn) and key resources/data code availability (N/A vs. fail/warn). The synthesized judgment follows the scoring rules strictly, resolving the N/A cases, and the warnings reflect the most impactful gaps. The statistics component verified no inferential tests. The citation check found no retracted or missing references.

Numerical inconsistencies

1 finding · worst medium

Values that contradict each other or are impossible for the stated sample: recomputed p-values and test statistics, GRIM/GRIMMER checks on summary numbers, percentages against their own counts, totals against their parts, and estimates against their own confidence intervals.

Internal contradictions in the reported numbersAssessed

mediuminternal contradiction
At ζ=0.6 in Table 9, the reported RI values (A1≈0.260, A2≈0.257, A3≈-0.327, A4≈-0.843) imply ranking A1≻A2≻A3≻A4 under the paper's rule that larger RI means better, yet the table lists A3 as the best college with ranking A3≻A1≻A2≻A4.
“ζ = 0.6 | (0.216,0.273, 0.165,0.158, 0.188) | RI ( A 1 ) ≈ 0.260, RI ( A 2 ) ≈ 0.257, RI ( A 3 ) ≈ -0.327, RI ( A 4 ) ≈ -0.843. | A 3 ≻ A 1 ≻ A 2 ≻ A 4 | A 3”
Table 9
lowinternal contradiction
The Total gap (TG) values in Table 10 do not consistently follow the stated formula TG = ∑|h_i - H_i|/H_i. For example, for Approach 1 (A4≻A1≻A2≻A3) versus the optimal order A1≻A2≻A4≻A3, the formula yields approximately 2.17, not 4.00; several other rows also appear inconsistent.
T G = ∑ i = 1 m | h i − H i H i | ... Approach 1 ... 4.00
Table 10reviewer’s wording
lowinternal contradiction
Criterion C4 is named 'Teaching effect' in Table 1 but is referred to as 'teaching link' in the case study text, which is inconsistent.
“they recognize the most important criterion C 2 and the least important criterion C 4”
Case study, Illustration, paragraph 2

Overstated conclusions

1 finding · worst low

Conclusions that reach past what the paper's own results support — including a significance claim that no longer holds when the statistic is recomputed, and efficacy resting on an unvalidated surrogate endpoint.

Conclusions only partially backed by the presented evidenceAssessed

9 major claims checked against the paper's own evidence: all adequately supported.

partialReviewers 1, 3
The proposed MAIRCA-ELECTRE approach is feasible and the most appropriate among these approaches.
The comparison supports feasibility and superiority on this single illustrative dataset, but 'most appropriate' is a generalization from one example, and the Table 10 Total gap values are not consistently reproduced from Eq. (17).
Evidence: Table 10 compares seven approaches; the proposed method's ranking matches the aggregate optimal ranking and has the smallest reported Total gap (0.00).
“Overall, results show that the proposed MAIRCA-ELECTRE approach is feasible and the most appropriate among these approaches.”
Discussions
partialReviewers 1, 3
The main advantage of the approach is that it can properly deal with non-compensatory criteria.
The paper argues that ELECTRE handles non-compensatory criteria, but it does not provide a direct test or demonstration of this property beyond the design rationale.
Evidence: The discussion states that ELECTRE can effectively handle non-compensatory criteria, but no dedicated experiment isolates this behavior.
“The main advantage of such approach is that it can properly deal with non-compensatory criteria during the teaching quality evaluation process.”
Discussions, paragraph 1
supportedReviewers 1, 3
The proposed approach is practicable and can provide instructions for teaching-quality evaluation of physical education.
The illustrative case and sensitivity/comparison analyses provide adequate evidence that the algorithm is operable and yields a coherent ranking.
Evidence: A worked case study (Section 4) with four alternatives and five criteria, plus sensitivity and comparison analyses (Section 5), demonstrates the algorithm's applicability.
“Results show that our approach is practicable and can provide instructions for the teaching quality evaluation of physical education.”
Abstract
supportedReviewer 1
MAIRCA has neither been extended in a picture fuzzy environment nor utilized for teaching-quality evaluation.
The literature review provides reasonable support for the claimed gap based on the cited works.
Evidence: The introduction lists numerous MAIRCA extensions (rough, hesitant-fuzzy, fuzzy, intuitionistic-fuzzy) and none in a picture-fuzzy or teaching-quality context.
“However, the MAIRCA has neither been extended in a picture fuzzy environment, nor been utilized to deal with teaching quality evaluation issues.”
Introduction
supportedReviewer 2
The proposed hybrid MAIRCA-ELECTRE method is feasible for evaluating teaching quality of physical education.
The paper presents a detailed case study with four alternatives and five criteria, demonstrating the step-by-step application of the method and obtaining a ranking order, which supports feasibility.
Evidence: Section 4, Case study, Tables 2-8 and ranking results.
“In this section, a case of teaching quality evaluation of physical education is investigated.”
Section 4, Case study, paragraph 1
supportedReviewer 2
The method can handle non-compensatory criteria during the evaluation process.
The ELECTRE method, which is designed for non-compensatory criteria, is used in Phase IV. The paper explicitly states this advantage and the comparison analyses show that other methods (which assume compensation) yield different results.
Evidence: Section 3, Phase IV: 'The ELECTRE III method is adopted for obtaining the alternatives’ ranks.'; Section 5.2: 'Approach 1, 2, 3, 4 and 6 cannot deal with the situation where evaluation criteria are not compensatory.'
“In this phase, the ELECTRE III method is adopted for obtaining the alternatives’ ranks.”
Section 3, Phase IV
supportedReviewer 2
The proposed MAIRCA-ELECTRE approach outperforms other existing methods in terms of total gap from the optimal ranking.
The comparison analysis shows that the proposed method has the smallest total gap (TG=0.00) compared to six other approaches, as shown in Table 10.
Evidence: Table 10, last column: Total gap TG values.
“Our approach (MAIRCA-ELECTRE) achieves the smallest gap, followed by Approach 6.”
Table 10
supportedReviewer 2
Picture fuzzy numbers can accommodate diverse viewpoints and describe decision makers’ ambiguity, uncertainty, and inconsistency sufficiently.
The paper uses PFNs to represent evaluation data (Table 2) and explains that PFNs have four membership functions to capture different attitudes. The case study illustrates this by showing how decisions are aggregated.
Evidence: Section 2, Definition 1 and Section 4, Step 1: 'PFNs are finally used to describe the evaluation results.'
“The most obvious feature of PFNs is it that it contains four different membership functions, which can accommodate diverse viewpoints and describe decision makers’ ambiguity, uncertainty and inconsistency sufficiently.”
Section 2, Definition 1
supportedReviewer 3
The proposed MAIRCA-ELECTRE approach is more pertinent than six other approaches in handling teaching quality evaluation issues.
The comparison analysis shows that the proposed method's ranking matches the optimal ranking order derived from a scoring mechanism, and it has the smallest total gap.
Evidence: Table 10 lists ranking orders of six approaches and the proposed method; the scoring mechanism yields the optimal ranking A1≻A2≻A4≻A3, which matches the proposed method.
“It is clear that the ranking order with MAIRCA-ELECTRE approach is the same with the optimal ranking order.”
Comparison analyses, paragraph 2

Data authenticity concerns

None found

An adversarial read for patterns associated with data that may not be genuine: results that look too clean, implausibly large effects, duplicated data or images, and methods that do not match the results reported.

Checked — nothing surfaced.

Reporting gaps

1 finding · worst medium

Required detail the manuscript never states — study design, biological variables, ethics approval and consent, key resources, statistical reporting, data and code availability, and overall transparency.

Study-design details incomplete (controls, blinding, power)Assessed

Eight Dimensions3 pass · 1 warn

The introduction cites multiple relevant studies on physical education teaching quality evaluation and picture fuzzy decision-making. It acknowledges limitations such as qualitative methods or information loss, and explains how the hybrid MAIRCA-ELECTRE method with PFNs addresses these gaps. The rationale logically links the premise to the study objectives.

Sub-criteria

prior work citedADEQUATE

premise rationaleADEQUATE

limitations addressedADEQUATE

Per reviewer (3) — the votes behind the verdict

PASSReviewer 1· 90% conf

The paper clearly establishes a research gap and rationale: MAIRCA has not been extended to picture-fuzzy environments or applied to teaching-quality evaluation, and prior MCDM methods suffer identified weaknesses.

Evidence

“However, these methods are qualitative or applied only to certain decision-making environments.”

Introduction ¶2

“However, they may lead to information loss or distortion during the aggregation process.”

Introduction ¶3

“Nevertheless, the classical MAIRCA approach with exact numbers cannot capture decision makers’ ambiguity and vagueness.”

Introduction ¶4

PASSReviewer 2· 95% conf

The paper clearly establishes its scientific foundation by citing prior work on teaching quality evaluation and MCDM methods, providing a logical rationale for the proposed approach, and addressing limitations of existing methods.

Evidence

paraphrase[Introduction, paragraph 1-3]

“Some researchers have focused on the teaching quality evaluation of physical education. ... However, these methods are qualitative or applied only to certain decision-making environments.”

paraphrase[Introduction, paragraph 4]

“PFNs (picture fuzzy numbers) are suggested to describe uncertain evaluation information... The most obvious feature of PFNs is it that it contains four different membership functions, which can accommodate diverse viewpoints.”

paraphrase[Introduction, paragraph 5-6]

“However, they may lead to information loss or distortion during the aggregation process... the classical MAIRCA approach with exact numbers cannot capture decision makers’ ambiguity and vagueness.”

PASSReviewer 3· 90% conf

The paper clearly establishes the scientific foundation, reviews prior work extensively, and articulates the rationale and limitations motivating the proposed framework.

Evidence

“However, these methods are qualitative or applied only to certain decision-making environments.”

Introduction ¶2

“The major innovation and contribution are: First, PFNs are utilized to depict complex and fuzzy evaluation information.”

Introduction ¶4

“However, the MAIRCA has neither been extended in a picture fuzzy environment, nor been utilized to deal with teaching quality evaluation issues.”

Introduction ¶3

The four phases of the proposed framework are fully described. Sensitivity analysis and comparison with six alternative approaches serve as an adequate baseline/ablation analogue. However, the case study is introduced as a 'Suppose' scenario with no rationale for choosing four colleges, five criteria, and ten decision makers, and no data-curation or inclusion/exclusion criteria are reported. Randomization and blinding are not applicable to a computational illustration.

Sub-criteria

controlsADEQUATE

power analysisNOT REPORTED

blinding levelsN/A

outlier handlingN/A

randomization unitN/A

inclusion exclusionN/A

randomization methodN/A

replicate distinctionN/A

independent replicationN/A

Per reviewer (3) — the votes behind the verdict

WARNReviewer 1· 75% conf

The methodological pipeline is clearly specified, but the illustrative case study lacks justification for the dataset size, criteria set, and decision-maker panel, and no analogue of a power/dataset-selection analysis is provided.

Evidence

“Suppose there are four physical education colleges { A 1 , A 2 , A 3 , A 4 }, the proposed methodology in Section 4 is adopted to evaluate their teaching quality.”

Section 4, Illustration

“ten decision makers (including four government representatives related to physical education, four professionals and scholars in the field of physical education, and two sports practitioners) are organized to make assessments”

Section 4, Illustration

paraphrase[Section 5]

“Sensitivity analysis varies criteria weights and six alternative approaches are compared against the proposed method.”

N/AReviewer 2· 90% conf

The study is a computational/methodological paper with no experimental design; only one sub-criterion (controls via comparison analyses) is applicable and reported adequately.

Evidence

paraphrase[Section 5.2, Comparison analyses]

“The paper compares the proposed MAIRCA-ELECTRE approach with six other decision-making methods (Approach 1-6) using the same case study data.”

WARNReviewer 3· 70% conf

The method is validated through comparison with six approaches and sensitivity analysis, but the illustrative dataset selection is not justified.

Evidence

“To testify the sensitivity of the proposed method, the variations of ranking results are analyzed by changing the criteria weights”

Analyses and discussions, Sensitivity a…

“Several different decision-making approaches are applied to deal with the teaching quality evaluation of physical education.”

Comparison analyses, paragraph 1

paraphrase[Case study, Illustration]

“Paraphrase: The paper states 'Suppose there are four physical education colleges' without explaining why four alternatives, five criteria, or ten decision makers were chosen.”

The paper is a computational MCDM framework applied to a hypothetical teaching quality evaluation problem. It does not involve any animals, human subjects, or biological materials. Therefore, all sub-criteria are not applicable.

Sub-criteria

demographicsN/A

sex reportedN/A

sex justifiedN/A

age weight healthN/A

housing conditionsN/A

species strain sourceN/A

Per reviewer (3) — the votes behind the verdict

N/AReviewer 1· 95% conf

No biological subjects, samples, or animal/human physiological data are involved; the case study concerns educational institutions.

Evidence

absence[Whole paper]

No biological or physiological data are reported.

N/AReviewer 2· 100% conf

No biological subjects or variables are involved; the study uses a synthetic illustrative case.

N/AReviewer 3· 95% conf

No biological or subject-level data are used; the study is purely computational.

The study does not involve any human participants, animals, or non-public subject-level data. It is a purely computational methodology paper with a synthetic illustrative example. Therefore, all ethical approval sub-criteria are not applicable.

Sub-criteria

iacuc statementN/A

informed consentN/A

irb ethics statementN/A

regulatory complianceN/A

Per reviewer (3) — the votes behind the verdict

N/AReviewer 1· 85% conf

The case study is an illustrative numerical example ('Suppose there are four physical education colleges...'), not a study on non-public subject-level data; no ethics approval is required.

Evidence

paraphrase[Section 4, Illustration]

“Suppose there are four physical education colleges { A 1 , A 2 , A 3 , A 4 }...”

absence[Whole paper]

No ethics approval or consent statement appears.

N/AReviewer 2· 100% conf

No human or animal subjects, tissues, or non-public identifiable data are used; ethical approval is not required.

N/AReviewer 3· 95% conf

No human or animal subjects are involved; the decision makers are hypothetical and no non-public data are used.

The paper proposes a mathematical framework and does not report any antibodies, cell lines, organisms, reagents, or custom software. The methods are described algorithmically, but no specific software tool is identified. Since no key biological or chemical resources are used, the dimension is not_applicable.

Sub-criteria

mycoplasma testingN/A

reagents identifiedN/A

organisms identifiedN/A

antibodies identifiedN/A

cell line authenticationN/A

software tools identifiedN/A

Per reviewer (3) — the votes behind the verdict

N/AReviewer 1· 60% conf

No bench reagents, organisms, cell lines, antibodies, or investigational products are used, and no software implementation is reported.

Evidence

absence[Methods and Case study]

No software or bench resources are identified.

N/AReviewer 2· 95% conf

No biological or chemical resources are used; the study is entirely computational and does not require software identification.

FAILReviewer 3· 70% conf

The paper does not identify any software, code, or other key resources used to implement the computational method.

Evidence

absence[Entire manuscript]

No software, version, or code repository is mentioned anywhere in the paper.

There are no hypothesis tests, p-values, confidence intervals, or effect-size estimates. Spearman's rho is computed only as a descriptive similarity measure (λ and ℏ) without a test, so this dimension is not applicable.

Sub-criteria

tests namedN/A

exact p valuesN/A

effect sizes ciN/A

data presentationN/A

software identifiedN/A

assumptions verifiedN/A

mathematical plausibilityN/A

Per reviewer (3) — the votes behind the verdict

N/AReviewer 1· 90% conf

No inferential statistics are reported; the study uses deterministic multi-criteria computations and descriptive rank-correlation coefficients without p-values.

Evidence

absence[Whole paper]

No hypothesis tests or p-values are reported.

“the Spearman’s rank-correlation test [] is adopted with the following two parameters: ƛ = 1 − 6 ⋅ ∑ i = 1 m ( d i s ( A i ) ) 2 m ( m 2 − 1 )”

Section 5, Sensitivity analyses

N/AReviewer 2· 90% conf

No inferential statistics are used; the analysis is deterministic and descriptive.

Evidence

paraphrase[Section 4, Case study (Tables 2-8)]

“The initial evaluation matrix, theoretical assessment matrix, real assessment matrix, difference matrix, concordance degree, credibility degree, and ranking indices are all presented in tabular form.”

N/AReviewer 3· 90% conf

The study performs no inferential statistics; it reports deterministic ranking indices and comparisons without p-values, confidence intervals, or hypothesis tests.

The paper includes a data availability statement stating that all relevant data are within the manuscript. The data used in the case study are fully presented in tables. No additional repository deposit or code sharing is applicable since the data are fully included and no custom code was developed (the method is described mathematically).

Sub-criteria

code sharingN/A

accession numbersN/A

repository depositN/A

data availability statementADEQUATE

Per reviewer (3) — the votes behind the verdict

PASSReviewer 1· 70% conf

A data availability statement is present and all relevant data are contained in the manuscript; no external repository deposit, accession numbers, or code sharing apply.

Evidence

“Data Availability All relevant data are within the manuscript.”

Data availability

absence[Whole paper]

No external repository or code is provided.

PASSReviewer 2· 85% conf

The data availability statement is present and adequate (data are within the manuscript); no repository or code is required.

Evidence

“Data Availability All relevant data are within the manuscript.”

Data availability

WARNReviewer 3· 80% conf

A data availability statement is present and adequate, but no code is shared.

Evidence

“Data Availability All relevant data are within the manuscript.”

Data availability

absence[Entire manuscript]

No code or software repository is mentioned.

The methods are described comprehensively in Sections 3 and 4. The case study is presented with all steps and tables. Limitations are discussed in the conclusion (e.g., equal expert weights, complete rationality). The conclusions are proportional to the evidence. Funding sources and a competing interests statement are provided. Trial registration is not applicable.

Sub-criteria

funding coiADEQUATE

trial registrationN/A

reporting guidelineN/A

methods completenessADEQUATE

all outcomes reportedADEQUATE

limitations discussedADEQUATE

conclusions proportionalADEQUATE

Per reviewer (3) — the votes behind the verdict

PASSReviewer 1· 85% conf

Methods are fully specified, limitations and funding/COI are disclosed, and conclusions track the presented comparisons.

Evidence

“experts are assumed to have equal weights, which may be not appropriate in some cases.”

Conclusion

“The authors have declared that no competing interests exist.”

Funding

PASSReviewer 2· 90% conf

The manuscript reports methods in detail, includes funding and competing interests, and discusses limitations proportionally.

Evidence

paraphrase[Section 3, Hybrid multi-criteria decision-making framework]

“The methodology is presented with four phases: establishment of assessment matrix, determination of criteria weights using modified SWARA, construction of difference matrix using extended MAIRCA, and acquisition of ranking orders using ELECTRE III.”

“One limitation of the model may be that all decision makers are assumed to have complete rationality and equal weights, which should be overcome by introducing other theories in the future.”

Conclusion

paraphrase[Funding statement and Competing Interests]

“Competing Interests: The authors have declared that no competing interests exist. ... This work was supported by Teaching Reform Research Project of Hunan Provincial Education Department (HNJG-2021-0305)...”

PASSReviewer 3· 85% conf

The paper provides complete methods, reports all results, discusses limitations, and includes funding and competing interests statements.

Evidence

“However, there are still some limitations of the proposed methodology.”

Conclusion

“The authors have declared that no competing interests exist.”

Funding

Broken references and links

None found · partly checked

References checked against Crossref, OpenAlex and Retraction Watch for retractions and resolvability, plus declared data and code links probed for whether they resolve to content matching the paper.

Nothing surfaced — but not everything feeding this category ran (missing: data/code link verification), so read this as a partial clean bill.

Checked 41 references by DOI: 3 verified — 38 no DOI (shown, not verified).

NO DOI
Assessment for learning in physical education: The what, why and how
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Integrating assessment into physical education teaching
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Evaluation of physical education teaching quality in colleges based on the hybrid technology of data mining and hidden Markov model
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Research on teaching quality evaluation model of physical education based on simulated annealing algorithm
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Evaluation of physical education teaching based on web embedded system and virtual reality
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Combining psychology, a Game Sense Approach and the Aboriginal game Buroinjin to teach quality physical education
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Evaluation of teaching quality of public physical education in colleges based on the fuzzy evaluation theory
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Intuitionistic fuzzy similarity and information measures with physical education teaching quality assessment
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Research on the teaching quality evaluation of physical education with intuitionistic fuzzy TOPSIS method
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Picture fuzzy sets
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Likelihood-based hybrid ORESTE method for evaluating the thermal comfort in underground mines
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Picture fuzzy aggregation operators and their application to multiple attribute decision making
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Picture fuzzy Dombi aggregation operators: application to MADM process
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Some picture fuzzy Bonferroni mean operators with their application to multicriteria decision making
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Picture fuzzy tensor and its application in multi-attribute decision making
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Interval-valued picture fuzzy Maclaurin symmetric mean operator with application in multiple attribute decision-making
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
An integrated EDAS-ELECTRE method with picture fuzzy information for cleaner production evaluation in gold mines
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
A multi-criteria decision-making framework for risk ranking of energy performance contracting project under picture fuzzy environment
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Different approaches to multi-criteria group decision making problems for picture fuzzy environment
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
An extended bidirectional projection method for picture fuzzy MAGDM and its application to safety assessment of construction project
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Hybrid PSO-WDBA method for the site selection of tailings pond
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Evaluating public transport service quality using picture fuzzy analytic hierarchy process and linear assignment model
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
ERP selection using picture fuzzy CODAS method
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
A fuzzy-multi attribute decision making approach for efficient service selection in cloud environments
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Evaluating the satisfaction level of citizens in municipality services by using picture fuzzy VIKOR method: 2014–2019 period analysis
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Selection of railway level crossings for investing in security equipment using hybrid DEMATEL-MARICA model
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
New hybrid multi-criteria decision-making DEMATELMAIRCA model: sustainable selection of a location for the development of multimodal logistics centre
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Evaluating the performance of suppliers based on using the R’AMATEL-MAIRCA method for green supply chain implementation in electronics industry
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
An integrated MC-HFLTS&MAIRCA method and application in cargo distribution companies
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
An integrated approach for fuzzy failure modes and effects analysis using fuzzy AHP and fuzzy MAIRCA
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Implementation of MCDM-based integrated approach to identifying the uncertainty factors on the constructional project
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
A fuzzy AHP-MAIRCA Model for overtourism assessment: The Case of Malaga Province
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Evaluating biological inspiration for biologically inspired design: An integrated DEMATEL‐MAIRCA based on fuzzy rough numbers
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
An aggregation technique for optimal decision-making in materials selection
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
A neutrosophic normal cloud and its application in decision-making
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Sustainable supplier selection in healthcare industries using a new MCDM method: Measurement of alternatives and ranking according to COmpromise solution (MARCOS)
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
A novel IMF SWARA-FDWGA-PESTEL analysis for assessment of healthcare system
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).
NO DOI
Impact of the number of vehicles on traffic safety: multiphase modeling
No DOI in the reference — shown for manual review; not independently verifiable (not a fabrication signal).

Copyediting

1 finding · worst low

Wording, consistency and formatting errors that need correcting before submission.

Wording or formatting errors that need correctingAssessed

12 copyedit issues flagged (2 major): mostly typo, other, consistency.

MAJORotherReferences section, trailing line
“t of alternatives and ranking according to COmpromise solution (MARCOS) . Computers & Industrial Engineering , 140 , 106231 .”
→ Restore the full reference title; likely 'Technique of alternatives and ranking according to COmpromise solution (MARCOS)'.
The reference appears truncated/garbled, making it unverifiable.
MAJORconsistencyCase study, Illustration, paragraph 2
“they recognize the most important criterion C 2 and the least important criterion C 4”
→ they recognize the most important criterion C 2 and the least important criterion C 5
C4 is 'Teaching effect', not 'Teaching link' (C5). The naming is inconsistent with Table 1.
MINORtypoIntroduction, Williams et al. sentence
“discussed the teach quality of physical education”
→ change 'teach quality' to 'teaching quality'
Simple typo in a key term.
MINORtypoIntroduction, Gireesha et al. sentence
“to assess could service”
→ change 'could service' to 'cloud service'
Context indicates 'cloud service'.
MINORgrammarDiscussions
“can effectively handle evaluation criteria with non-compensate.”
→ change 'with non-compensate' to 'with non-compensatory criteria'
Incomplete grammatical phrase.
MINORtypoSection 5, Sensitivity analyses
“Toss explore the relationship between ranking orders under different ζ valuesss”
→ change 'Toss' to 'To' and 'valuesss' to 'values'
Typo in section heading/introductory sentence.
MINORtypoSection 5, Approach 6 description
“the better the physical education college A iss”
→ change 'A iss' to 'A i'
Corrupted subscript in text.
MINORtypoSection 5.1, Sensitivity analyses, paragraph beginning 'Toss explore'
“Toss explore the relationship between ranking orders...”
→ Change to 'To explore the relationship between ranking orders...'
Typo: 'Toss' should be 'To'.
MINORotherSection 5.1, Sensitivity analyses, last line of text before references
“sss”
→ Remove extraneous 'sss'
Appears to be a stray character.
MINORconsistencySection 2, Preliminaries, Definition 6
“d ( α 1 , α 2 ) = ( | a 1 − a 2 | 2 + | b 1 − b 2 | 2 + | c 1 − c 2 | 2 + | e 1 − e 2 | 2 ) .”
→ Add square root symbol: d ( α 1 , α 2 ) = sqrt( | a 1 − a 2 |^2 + | b 1 − b 2 |^2 + | c 1 − c 2 |^2 + | e 1 − e 2 |^2 ).
The formula is missing the square root; can be clarified.
MINORclaritySection 5.1, Sensitivity analyses, Table 9 footnote
“ƛ and ℏ values are computed...”
→ Define ƛ and ℏ in the text before the table, or in the legend.
The symbols are defined in equations (15)-(16) but not in the table caption.
MINORtypoSensitivity analyses, paragraph 3
“Toss explore the relationship”
→ To explore the relationship
Typo: 'Toss' should be 'To'.

Kaimen Rigor Action ItemsFinal pass before journal submission

This published paper has significant internal contradictions in its main results tables that warrant a correction or erratum. An informed reader should withhold trust in the illustrative rankings until the authors explain or correct the inconsistencies in Table 9 (ζ=0.6 row) and Table 10 (Total gap values). The absence of shared code also hinders independent verification. The paper's methodological framework remains of interest, but the numerical demonstration is unreliable in its current form.

1.
HIGHrigor
Correct the internal contradiction in Table 9 at ζ=0.6: the reported RI values (A1≈0.260, A2≈0.257, A3≈-0.327, A4≈-0.843) imply ranking A1≻A2≻A3≻A4, but the table lists A3 as the best. Recompute the RI values or re-rank and update the sensitivity discussion.
This inconsistency undermines the credibility of the sensitivity analysis and the main illustrative results.
2.
HIGHrigor
Recompute the Total gap (TG) values in Table 10 using Eq. (17) and correct entries that are inconsistent with the formula (e.g., Approach 1 should yield ~2.17, not 4.00).
The TG values are central to the comparison analysis; incorrect values misrepresent the relative performance of competing methods.
3.
HIGHreporting
Issue a correction or erratum to address the two internal contradictions above (Table 9 and Table 10) and clarify which values are correct.
Published results with clear numerical errors require formal correction to maintain scientific integrity.
4.
HIGHdata code
Deposit the code or a detailed spreadsheet implementing the MAIRCA-ELECTRE calculations in a public repository (e.g., Zenodo, GitHub) and update the data availability statement to include the repository link.
Reproducibility of the numerical results is impossible without the computational steps; code sharing is expected for a computational method paper.
5.
HIGHreporting
Add a justification for the choice of 4 alternatives, 5 criteria, and 10 decision makers in the case study, or explicitly state that the example is purely illustrative and the numbers are arbitrary.
The lack of rationale for the dataset dimensions leaves the reader wondering whether the results are sensitive to these choices.
6.
HIGHreporting
Correct the garbled MARCOS reference in the References section (missing title) and ensure all references are complete and verifiable.
An unverifiable reference is a citation integrity concern and may indicate sloppy proofreading.
7.
MEDIUMcopyedit
Fix the typo 'teach quality' to 'teaching quality' in the Introduction.
Standard copyedit issue; the key term is misspelled.
8.
MEDIUMcopyedit
Fix 'could service' to 'cloud service' in the Introduction (Gireesha et al. sentence).
Contextually clear typo that should be corrected for clarity.
9.
MEDIUMcopyedit
Fix 'non-compensate' to 'non-compensatory criteria' in the Discussions section.
Incomplete grammatical phrase hinders readability.
10.
MEDIUMcopyedit
Fix 'Toss explore' to 'To explore' and 'valuesss' to 'values' in Section 5.1 (Sensitivity analyses).
Multiple typos in the same sentence suggest a need for thorough proofreading.
11.
MEDIUMcopyedit
Remove the stray 'sss' at the end of the Sensitivity analyses section before the references.
Likely a copy-paste artifact that should be deleted.
12.
MEDIUMother
Confirm criterion C4 name: Table 1 lists 'Teaching effect' but the case study text refers to it as 'teaching link'; use consistent terminology throughout.
Inconsistent naming confuses the reader and may indicate a deeper error in the criteria set.
13.
LOWreporting
Add a statement clarifying whether the decision makers are real or hypothetical; if hypothetical, remove the implication of empirical recruitment that would require ethics approval.
Avoids any ambiguity about the nature of the case study.
14.
LOWreporting
Consider adding a reporting guideline checklist (e.g., a general transparency checklist) for computational methods, or state that none is applicable.
Enhances completeness, though not strictly required for a methodological paper.

Full text (41,504 chars)Analyzed: Aug 5, 2026

RigorReviewer 1

RigorReviewer 2

RigorReviewer 3

RigorPre-Submission Reviewer

CopyeditAgent Scribe

CitationsCitation Integrity

StatisticsStatistics Consistency

PreregistrationDeterministic check· no model (rule-based)

The star rating is the report’s one-glance summary. Every paper starts at 5★ and loses stars for the concrete problems the review finds — so a rating is never a vague average, it’s a running total you can read line by line under “How this rating was calculated.”

How stars are deducted

Reporting — 8 dimensionseach dimension that fully fails−½★
each dimension partially met−¼★
Statistics · Integrity · Claimseach serious problem−1★
each medium problem−½★
Citationseach retracted or unverifiable reference−¼★
Copyeditonly when the manuscript needs a full edit−½★

The rating never drops below 1★, and a demonstrable critical failure (an impossible statistic, a proven ethics violation) caps it at 1★ on its own — so the stars can never look healthy when the verdict is CRITICAL.

The rating draws on a panel of agents. Three independent Kaimen Rigor reviewers grade the eight dimensions below across several independent passes (the shown verdict is their majority vote — steadier than any single run), isolate the paper’s major claims and check its own evidence backs them, and flag integrity concerns. Alongside them, a citation agent resolves every reference against Crossref, OpenAlex, and Retraction Watch; a statistics agent recomputes reported tests; and rule-based checks verify that declared data/code links actually resolve. Full text is required — an abstract-only submission is not analyzed.

The eight reporting dimensions

Scientific PremisePrior work, rationale, and how it addresses gaps.

Study Design & RigorRandomization, blinding, power, controls, replication.

Biological VariablesSex, age, species/strain, housing, demographics.

Ethical ApprovalsIRB/IACUC approval, informed consent, regulatory compliance.

Key ResourcesAntibodies, cell lines, organisms, software — identified with persistent IDs.

Statistical ReportingNamed tests, exact p-values, effect sizes, plausible summary stats.

Data & Code AvailabilityAvailability statements, repositories, accession numbers, shared code.

Reporting TransparencyMethods, registration, guidelines, outcomes, limitations, funding/COI.

Graded against NIH, MDAR, ARRIVE 2.0, CONSORT, EQUATOR, and RRID guidelines. A dimension that doesn’t apply to the study type is skipped, never penalized.

This Kaimen Rigor review is model-assisted and is not a substitute for formal expert review. It complements human evaluation by surfacing potential methodological concerns — verify each finding against the source.

Evaluate teaching quality of physical education using a hybrid multi-criteria decision-making framework

Chen Z, Luo S.

DOI

10.1371/journal.pone.0280845

Record issued

2026-08-05

Engine

7.15.0

Exported

2026-09-19