{"id":"2efde6d6-0607-4d96-949b-e98e095706b3","arxiv_id":"2411.15249","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"An interval-valued fuzzy fault tree analysis pipeline estimates top-event probabilities and critical event rankings for chemical cargo contamination and loss of ship steering ability.","lead":"This paper combines interval-valued fuzzy numbers with fault tree analysis, expert opinion aggregation, and the Best-Worst Method to estimate failure probabilities and rank critical causes in two maritime scenarios. It offers risk analysts a practical recipe for working when quantitative failure data are missing.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Top-event probabilities depend entirely on the Yu et al. CFP-to-FP mapping; its transfer from FPSO mooring to cargo contamination and steering loss is unvalidated and is the key load-bearing assumption.","rationale":"The reader's weakest assumption correctly identifies the Yu et al. CFP-to-FP conversion as the most load-bearing vulnerability. The paper's entire probability scale, including the top-event probabilities that are compared to Senol et al. and Gurgen et al., flows through this mapping. Since the mapping was originally calibrated for FPSO single-point-mooring risk, its use in two different maritime domains is an external validity assumption that is neither justified nor tested. The concern is not an internal inconsistency; the methodology is clearly described and the two case studies are useful demonstrations. However, the central claim of 'valid' failure probabilities cannot be accepted without testing this transferability. A recalibration test using domain-specific anchor probabilities would settle whether the mapping is neutral or whether the reported probabilities are artifacts. Since the reader already returned a conditional verdict, and this concern reinforces that conditionality rather than overturning the paper's contribution, the verdict should remain conditional. I therefore recommend no change.","tokens_in":11148,"tokens_out":4731,"duration_ms":47614,"concrete_test":"Recompute both case studies using the paper's reported expert opinions and fault trees, replacing the Yu et al. piecewise mapping with a domain-calibrated mapping fit to two anchor probabilities: chemical cargo contamination frequency (e.g., ~0.25/year per fleet of 10 tankers with 6 operations/month, as the paper's own cadence claim implies) and steering gear failure rate from class society or port state control data. Re-run the FTA to obtain TE probabilities and FVI rankings under the recalibrated mapping. If either TE probability changes by more than 10×, or if the top-ranked basic event changes, the Yu et al. conversion is not transferable and the reported closeness is not a valid confirmation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative outputs—TE probabilities 2.834E−04 and 5.4E−02, and the implied ~4y10m contamination period—are produced after applying the Yu et al. (2022) piecewise CFP-to-FP conversion in Step 4. That mapping's coefficients were calibrated for FPSO single-point-mooring risk (Ref. [41]); no justification is given for transferring it to chemical cargo contamination or ship steering loss, and no sensitivity analysis is provided. The mapping is nonlinear with three regimes, so a small calibration error can change basic-event FPs by orders of magnitude, and TE probabilities inherit that sensitivity. The paper's validation in §4.2 compares its TE probability to Senol et al.'s observed cadence and ranking, but the cadence comparison depends on additional unstated fleet assumptions (10 tankers, 6 operations/month), and ranking correlation is insensitive to the probability scale. The aggregation equation (2) appears to be a typo—the reported CFP 0.4909 for BE53 is inconsistent with a product of three IVTFNs, suggesting a weighted sum was actually used—so the aggregation step is probably sound once corrected. The conversion, not the algebra, is the load-bearing external input.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops an interval-valued fuzzy fault tree analysis (IVFFTA) pipeline for fault tree analysis when quantitative basic-event failure probabilities are unavailable. Expert judgments are elicited as linguistic terms, converted to interval-valued triangular fuzzy numbers, aggregated with the Similarity Aggregation Method (SAM) using Best-Worst-Method-derived expert weights, defuzzified, mapped to failure probabilities with the Yu et al. (2022) CFP-to-FP conversion, and propagated through fault trees to obtain top-event probabilities and FVI criticality rankings. The method is applied to chemical cargo contamination, yielding a top-event probability of 2.834E-04, and to loss of ship steering ability, yielding 5.4E-02, with comparisons to Senol et al. (2015) and Gurgen et al. (2023).","tokens_in":11391,"tokens_out":6620,"duration_ms":65261,"significance":"If the pipeline is valid, the contribution is a potentially practical way to produce numerical failure probabilities and criticality rankings from qualitative maritime expert knowledge, with the interval-valued representation addressing uncertainty in membership functions. The paper is transparent in laying out each conversion step and attempts external validation against two published FFTA studies, which is a notable strength. The main value of the manuscript at this stage is as a methodological demonstration rather than a fully validated probability scale.","major_comments":[{"comment":"The aggregation formula is printed as a product over experts of CC(Eu) times R_u, but the surrounding text describes a weighted average, and the reported defuzzified CFP of 0.4909 for BE53 is inconsistent with a product of three IVTFNs whose membership values are bounded by 1. This is a load-bearing error in the central calculation chain; it should be corrected to a weighted sum (or otherwise justified), and the affected numerical results should be re-verified.","section":"Section 3, Step 2.5, Eq. (2)"},{"comment":"All reported top-event probabilities inherit the Yu et al. (2022) piecewise CFP-to-FP function, which was calibrated for an FPSO single point mooring system. The manuscript gives no domain-specific justification or recalibration for chemical cargo contamination or ship steering loss, and no sensitivity analysis around this mapping. Because K is piecewise and nonlinear, the top-event probabilities and the 4-year-10-month cadence claim are not robust against plausible changes in the conversion. The same absence of sensitivity analysis applies to the choice beta = 0.5 in Step 2.4; please add robustness checks and a transferability justification, or recalibrate the mapping.","section":"Section 3, Step 4 and Sections 4.1, 4.3"},{"comment":"The validation sections refer to ranking comparison tables that are not present in the manuscript: Section 4.2 says the ranking is in \"the following table\" and Section 4.4 refers to Table 22, but neither is included. The statements that the ranking \"closely aligns\" with Senol et al. and Gurgen et al. therefore cannot be checked; at minimum, the tables and a quantitative rank-correlation measure should be provided.","section":"Sections 4.2 and 4.4"},{"comment":"The single-point comparison between the computed 4 years 10 months and Senol et al.'s observed \"approximately four years\" is not a strong validation: it presupposes 10 tankers and 6 cargo operations per month without support, and it uses a point estimate with no uncertainty interval. The closeness of two point values does not validate the probability scale unless the fleet and operation-rate assumptions are justified and a range of plausible values is examined.","section":"Section 4.2"}],"minor_comments":[{"comment":"The sentence \"FTA is a powerful to calculate the FP\" is ungrammatical; it should read \"FTA is a powerful tool to calculate the FP.\"","section":"Section 1, Introduction"},{"comment":"The subtraction operation defined with absolute values is nonstandard and is not used later in the paper; either remove it or state why it is needed.","section":"Section 2, Definition 2.3"},{"comment":"Many referenced tables (e.g., Tables 3, 4, 5, 7-12, and 14-21) do not appear in the presented text; please ensure all supporting tables are included and numbered consistently.","section":"Sections 4.1-4.4"},{"comment":"The symbols a_bj and a_jw are not defined precisely enough; the indexing in the pairwise comparison vectors Ab and Aw should be aligned with the constraint equations in Eq. (1).","section":"Section 3, Step 1.3"},{"comment":"The paper should state explicitly whether the fault trees from Senol et al. and Gurgen et al. are used unchanged and whether any basic-event names or gate structures were modified.","section":"Sections 4.1 and 4.3"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a methodological application with a plausible pipeline, but the printed aggregation formula, the external CFP-to-FP mapping, and the absent validation tables are substantial issues that require revision. I do not see grounds for rejection: the errors appear fixable within the manuscript's scope. The editor may also want to check whether the missing tables are an artifact of the submission formatting; if not, they must be added before the paper can be assessed fairly."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a competent applied paper that puts an interval-valued fuzzy FTA pipeline through two maritime case studies. The intended method is coherent, but the headline probabilities rest on an unexamined transfer of a calibration curve, and one central equation looks misprinted. I would give it referee time, with major revision.\n\nWhat's new: not the components—IVTFNs, SAM, BWM, and FVI all exist in the literature—but the specific combination applied to chemical cargo contamination and loss of ship steering ability. That is a legitimate niche contribution for maritime reliability analysts who need a workflow from linguistic expert judgments to a probability and a priority list. The authors also compare against two prior fuzzy FTA studies, which is the right check for an applied paper of this type.\n\nSoft spots, in order of seriousness:\n\n1. Eq. (2) uses a product over CC(Eu) × R_u. The text describes a weighted average, and a product of three consensus coefficients (which sum to 1) would make the aggregate collapse. The reported defuzzified CFP for BE53 (0.4909) is consistent with a weighted sum, not a product. This is almost certainly a typo, but it is the aggregation step—the core of the method—so it must be fixed. If the product is literal, the aggregation is wrong.\n\n2. The Yu et al. CFP-to-FP conversion is adopted wholesale from FPSO mooring risk. It is nonlinear, with three regimes, and the paper gives no argument or sensitivity analysis for why it transfers to cargo contamination or steering loss. The closeness of 4y10m to Senol et al.'s \"about four years\" depends on extra assumptions (10 tankers, 6 operations/month), and ranking agreement is insensitive to the probability scale. The validation is suggestive, not strong.\n\n3. The introduction overstates novelty: \"no notable studies have employed interval-valued fuzzy numbers\" in FFTA sits awkwardly against refs [18] and [19], which use interval-valued fuzzy numbers for reliability. The real novelty is the specific pipeline, not the interval-valued representation.\n\n4. The full expert-judgment tables and IVTFN mappings are not provided in enough detail to reproduce the numbers independently.\n\nNone of this sinks the paper. Once Eq. (2) is corrected, the method is coherent, and the FVI rankings plus comparisons with earlier work give practitioners something usable.\n\nWho it's for: applied maritime reliability researchers, not fuzzy-set theoreticians. I would send it out for review, with a request to fix Eq. (2), run sensitivity on the CFP-to-FP mapping, and include the full data.","headline":"Competent application of interval-valued fuzzy FTA to two maritime cases, but the headline probabilities ride on an unvalidated calibration curve and one equation looks misprinted.","tokens_in":11915,"tokens_out":3552,"would_cite":false,"duration_ms":38465,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["03E72","90B25"],"pacs":[],"model":"deepseek-v4-flash","headline":"Interval-valued fuzzy fault tree analysis converts qualitative expert judgments into top-event failure probabilities and criticality rankings for marine operations.","keywords":["interval-valued fuzzy fault tree analysis","cargo contamination","chemical tankers","ship steering ability","reliability analysis","expert judgment aggregation","similarity aggregation method","best-worst method"],"falsifier":"Compare the computed recurrence interval against a fleet-wide incident database: if chemical tankers with roughly 720 cargo operations per year do not show contamination events about once every 4 years 10 months across a large sample, the conversion calibration is falsified. The steering-loss probability of $5.4\\times10^{-2}$ could likewise be checked against accident-report frequencies for ship steering failures.","tokens_in":10942,"feed_emoji":"⚓","tokens_out":11602,"duration_ms":96180,"temperature":0.7,"pith_summary":"The paper claims that interval-valued fuzzy fault tree analysis can turn qualitative expert linguistic ratings into quantitative failure probabilities and criticality rankings when numerical failure data are unavailable. The method aggregates expert opinions through the similarity aggregation method, weights experts through the best-worst method, defuzzifies interval-valued triangular fuzzy numbers, and converts failure possibility into failure probability with a piecewise function. Applied to two maritime cases, it reports a chemical cargo contamination top-event probability of $2.834\\times10^{-4}$ (a recurrence period of about 4 years 10 months) and a ship steering loss probability of $5.4\\times10^{-2}$, with basic-event rankings that closely match the earlier fault tree studies used as baselines. If the paper is right, maritime risk analysts can obtain failure probabilities and event prioritizations from subjective judgments alone when numerical data are missing.","feed_headline":"Fuzzy fault trees convert expert opinion into marine failure odds","feed_subtitle":"Linguistic judgments, not failure data, set cargo contamination odds and rank steering-loss risks.","key_machinery":"The central object is the interval-valued triangular fuzzy number (IVTFN), written $\\tilde{A}=[(a,b,c),(e,b,h)]$, whose lower and upper membership functions bracket the expert's uncertainty about failure possibility. The argument runs through a fixed chain: experts give linguistic ratings; the similarity aggregation method computes a consensus coefficient for each expert; the best-worst method derives criterion weights that are combined with weighting scores to get expert weights; the weighted fuzzy opinions are aggregated, defuzzified by $A^*=(4b+a+c+e+h)/8$, and converted to failure probability by the piecewise function $K=-0.72\\ln(CFP)+2.839$ for $0\\le CFP\\le0.2$, $K=4.523-3.287\\,CFP$ for $0.2\\le CFP\\le0.8$, and $K=3.705((1-CFP)/CFP)^{0.445}$ for $0.8\\le CFP\\le1$. OR and AND gate arithmetic then gives the top-event probability, and the FVI measure $FVI(BE_i)=(P_{TE}-P_{TE}(BE_i=0))/P_{TE}$ ranks basic events by criticality. The piecewise conversion is the step that turns fuzzy possibilities into probabilities, so the whole quantitative output depends on it.","core_discovery":"The paper's central claim is that interval-valued fuzzy numbers—triangular fuzzy numbers whose membership is an interval $[(a,b,c),(e,b,h)]$ bracketing the lower and upper membership functions—can be carried through the entire fault tree pipeline and produce defensible top-event probabilities and criticality rankings. For chemical cargo contamination the computed top-event probability is $2.834\\times10^{-4}$, which the paper associates with a recurrence cadence of roughly one contamination event per 4 years 10 months for a fleet operating 720 cargo operations per year. For loss of ship steering ability the computed probability is $5.4\\times10^{-2}$, close to the $4.86\\times10^{-2}$ obtained in the earlier study whose fault tree is used. The FVI importance measure ranks BE53 and BE6 as the most critical contamination events and BE13 as the dominant contributor to steering loss, and these rankings align with the earlier fault tree results. On the paper's own terms, this alignment and the closeness of the contamination cadence to observed practice are evidence that the interval-valued, expert-driven procedure is a valid extension of fuzzy fault tree analysis.","pith_inferences":["The absolute probabilities inherit the calibration of the adopted piecewise conversion; if that conversion is domain-specific, the reported values would shift, although a monotone conversion would leave the criticality rankings largely intact.","The practical value of the method may rest more on the relative FVI ranking than on the absolute top-event probability, because rankings are more stable under monotone transformations of the probability scale.","A natural testable extension is to recalibrate the conversion function with historical incident frequencies from chemical tanker fleets and then check whether the recurrence intervals and rankings still hold.","The same pipeline could be transferred to other qualitative risk settings, such as aviation or process safety, wherever expert linguistic ratings replace missing failure data."],"forward_implications":["For chemical cargo contamination, the method gives a top-event probability of $2.834\\times10^{-4}$, which the paper translates into a recurrence interval of about 4 years 10 months for 720 cargo operations per year.","For loss of ship steering ability, the method gives $5.4\\times10^{-2}$, close to the $4.86\\times10^{-2}$ reported by the fault tree study it builds on.","The FVI ranking marks BE53 and BE6 as the most critical contamination events and BE13 as the most critical steering-loss event, pointing inspection and maintenance effort at those basic events.","The pipeline works with linguistic expert ratings alone, so it can be applied where accident databases are sparse or nonexistent.","Interval-valued fuzzy numbers let the analysis represent uncertainty or disagreement in membership grades explicitly, which point-valued fuzzy numbers cannot."],"supporting_citations":[{"why":"Provides the piecewise crisp-failure-possibility to failure-probability conversion; every reported probability depends on it.","marker":"[41]"},{"why":"Supplies the chemical cargo contamination fault tree and the baseline ranking used for comparison.","marker":"[10]"},{"why":"Supplies the loss-of-ship-steering fault tree and the baseline probability and ranking used for comparison.","marker":"[14]"},{"why":"Provides the similarity aggregation method that combines expert opinions into a collective assessment.","marker":"[34]"},{"why":"Provides the best-worst method used to derive criterion weights and then expert weights.","marker":"[24]"},{"why":"Defines the interval-valued fuzzy number similarity measure on which the aggregation depends.","marker":"[35]"},{"why":"Defines arithmetic operations on interval-valued triangular fuzzy numbers used in aggregation and defuzzification.","marker":"[33]"},{"why":"Gives the OR and AND gate formulas that propagate basic-event probabilities to the top event.","marker":"[42]"}],"fun_headline_variants":["Interval fuzzy trees rank marine risks from expert say-so","Expert opinions feed fuzzy fault trees to set ship risk odds","No failure data? Fuzzy trees turn expert words into marine risk","Fuzzy logic plus expert opinion predicts cargo and steering loss","Qualitative data to marine risk: fuzzy fault tree analysis does it"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the piecewise conversion from failure possibility to failure probability, adopted from an offshore mooring risk study, transfers without recalibration to chemical cargo contamination and ship steering loss; if that mapping is not transferable, the reported absolute probabilities and their agreement with observed cadence no longer validate the method.","fun_headline_variants_meta":{"raw":{"variants":["Interval fuzzy trees rank marine risks from expert say-so","Expert opinions feed fuzzy fault trees to set ship risk odds","No failure data? Fuzzy trees turn expert words into marine risk","Fuzzy logic plus expert opinion predicts cargo and steering loss","Qualitative data to marine risk: fuzzy fault tree analysis does it"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000277,"raw_usage":{"total_tokens":1698,"prompt_tokens":1038,"completion_tokens":660,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":654,"completion_tokens_details":{"reasoning_tokens":577}},"tokens_in":654,"tokens_out":660,"duration_ms":7007,"temperature":1.0,"reasoning_tokens":577,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T14:53:48.263920+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compare the computed recurrence interval against a fleet-wide incident database: if chemical tankers with roughly 720 cargo operations per year do not show contamination events about once every 4 years 10 months across a large sample, the conversion calibration is falsified. The steering-loss probability of $5.4\\times10^{-2}$ could likewise be checked against accident-report frequencies for ship steering failures.","supporting_citations":[{"cited_title":"A novel risk analysis approach for fpso single point mooring system using bayesian network and interval type-2 fuzzy sets,","cited_arxiv_id":null,"evidence_quote":"Provides the piecewise crisp-failure-possibility to failure-probability conversion; every reported probability depends on it."},{"cited_title":"Fault tree analysis of chemical cargo contamination by using fuzzy approach,","cited_arxiv_id":null,"evidence_quote":"Supplies the chemical cargo contamination fault tree and the baseline ranking used for comparison."},{"cited_title":"Fuzzy fault tree analysis for loss of ship steering ability,","cited_arxiv_id":null,"evidence_quote":"Supplies the loss-of-ship-steering fault tree and the baseline probability and ranking used for comparison."},{"cited_title":"Fuzzy tempo- ral fault tree analysis of dynamic systems,","cited_arxiv_id":null,"evidence_quote":"Provides the similarity aggregation method that combines expert opinions into a collective assessment."},{"cited_title":"Best-worst multi-criteria decision-making method: Some properties and a linear model,","cited_arxiv_id":null,"evidence_quote":"Provides the best-worst method used to derive criterion weights and then expert weights."},{"cited_title":"Similarity measure of the interval-valued fuzzy num- bers and its application in risk analysis in paddy cultivation,","cited_arxiv_id":null,"evidence_quote":"Defines the interval-valued fuzzy number similarity measure on which the aggregation depends."},{"cited_title":"Extension of the aras method for decision-making problems with interval-valued triangular fuzzy numbers,","cited_arxiv_id":null,"evidence_quote":"Defines arithmetic operations on interval-valued triangular fuzzy numbers used in aggregation and defuzzification."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the OR and AND gate formulas that propagate basic-event probabilities to the top event."}],"review_version":1}