Pith. sign in

REVIEW 4 major objections 5 minor 42 references

Interval-Valued Fuzzy Fault Tree Analysis through Qualitative Data Processing and its Applications in Marine Operations

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Interval-valued fuzzy fault tree analysis converts qualitative expert judgments into top-event failure probabilities and criticality rankings for marine operations.

desk verdict 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. read the letter →

arxiv 2411.15249 v1 pith:G5WS72RZ submitted 2024-11-22 stat.AP math.PR

Hitesh Khungla , Kulbir Singh , Mohit Kumar This is my paper · ORCID
classification stat.APmath.PR MSC 03E7290B25
keywords interval-valuedfuzzyfaulttreeanalysiscargocontaminationchemicaltankersshipsteeringabilityreliabilityexpertjudgmentaggregationsimilaritymethodbest-worst
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

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).

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 (4)
  1. [Section 3, Step 2.5, Eq. (2)] 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.
  2. [Section 3, Step 4 and Sections 4.1, 4.3] 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.
  3. [Sections 4.2 and 4.4] 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.
  4. [Section 4.2] 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.
minor comments (5)
  1. [Section 1, Introduction] The sentence "FTA is a powerful to calculate the FP" is ungrammatical; it should read "FTA is a powerful tool to calculate the FP."
  2. [Section 2, Definition 2.3] 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.
  3. [Sections 4.1-4.4] 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.
  4. [Section 3, Step 1.3] 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).
  5. [Sections 4.1 and 4.3] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the probability and ranking outputs are computed from fixed inputs and external formulas, with validation against external benchmarks rather than fitted parameters.

full rationale

The derivation chain is a fixed computation: expert linguistic ratings are the inputs; SAM aggregation with BWM-derived expert weights, defuzzification, the Yu et al. CFP-to-FP conversion, and standard FTA gate equations are all applied as given formulas. No parameter in the paper is calibrated to the validation benchmarks (Senol et al. and Gurgen et al.), so the reported top-event probabilities and FVI rankings are not forced by construction. The authors cite several of their own earlier fuzzy FTA papers, but those citations appear in background and methodological lists and do not carry the central claim; the load-bearing external inputs are the fault tree structures, expert judgments, and the Yu et al. conversion, none of which are derived from the paper's outputs. The Yu et al. mapping's transferability from FPSO mooring to the two studied cases is a genuine correctness and sensitivity concern, but it is not circularity because the mapping is an external assumption, not a fitted or self-referential result. Similarly, the apparent typo in the aggregation equation (2) is a data-integrity concern about whether a product or weighted sum was actually computed, not a case of the conclusion being equivalent to its premises. No specific reduction of a prediction to its inputs can be exhibited, so the honest finding is no significant circularity.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. Its numerical outputs rest on several subjective choices: the linguistic-to-IVTFN mapping, the SAM relaxation factor, BWM preference values, expert weighting scores, and the defuzzification rule. It also depends on the transferability of an external CFP-to-FP conversion function and on the correctness of reused fault trees.

free parameters (5)
  • Beta relaxation factor = 0.5
    Chosen in Step 2.4 to give equal weight to expert opinion and SAM agreement. It directly changes consensus coefficients and therefore the aggregated fuzzy numbers and final probabilities.
  • Linguistic-to-IVTFN scale = Not fully specified in the text
    Seven linguistic terms (VL to VH) are mapped to interval-valued triangular fuzzy numbers, but the complete numerical intervals are not all recoverable from the text. This scale determines every defuzzified value and probability.
  • BWM criteria preference values = 7, 4, 2
    Decision-maker pairwise preferences in Section 4.1 produce the criteria weights (0.1000, 0.7146, 0.1854). Different preferences would change expert weights and the final results.
  • Expert weighting scores (WS) = Matrices in Sections 4.1 and 4.3
    Subjectively assigned scores for designation, experience, and qualification are multiplied by criteria weights to produce expert weights. These scores are choices, not measured quantities.
  • Defuzzification weights = b weighted 4, a, c, e, h weighted 1
    The formula A* = (4b + a + c + e + h)/8 is used in Step 3 without derivation or citation for this exact weighting. Different defuzzification choices would change all crisp failure possibilities.
assumptions (5)
  • standard math IVTFN arithmetic operations from Definition 2.3 are valid and applicable to the expert opinion aggregation.
    Addition, subtraction, multiplication, division, and scalar multiplication of interval-valued triangular fuzzy numbers are taken from [33] and used throughout the case studies.
  • domain assumption The Yu et al. CFP-to-FP conversion function transfers from its original FPSO context to chemical cargo contamination and ship steering loss.
    Step 4 applies the piecewise conversion function without recalibration or justification that the mapping is valid in the new application domains.
  • domain assumption The fault tree structures from Senol et al. and Gurgen et al. accurately and completely represent the two real-world scenarios.
    Both case studies reuse published fault trees. Missing or incorrectly specified gates or basic events would change the top-event probability and the FVI rankings.
  • domain assumption Basic events are statistically independent.
    The AND and OR gate probability formulas in Step 5 require independence of basic events, which is not justified from the case study data.
  • domain assumption Expert linguistic judgments are reliable, non-redundant, and representative of the actual failure behavior.
    The entire quantitative output rests on expert elicitation with no ground-truth failure data or validation of expert accuracy.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Interval-Valued Fuzzy Fault Tree Analysis through Qualitative Data Processing and its Applications in Marine Operations." pith.science (2026). https://pith.science/paper/G5WS72RZ

@misc{pith2026241115249,
  author       = {Pith},
  title        = {Pith review of: Interval-Valued Fuzzy Fault Tree Analysis through Qualitative Data Processing and its Applications in Marine Operations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/G5WS72RZ}},
  note         = {Machine review of arXiv:2411.15249}
}
read the original abstract

Marine accidents highlight the crucial need for human safety. They result in loss of life, environmental harm, and significant economic costs, emphasizing the importance of being proactive and taking precautionary steps. This study aims to identify the root causes of accidents, to develop effective strategies for preventing them. Due to the lack of accurate quantitative data or reliable probability information, we employ qualitative approaches to assess the reliability of complex systems. We collect expert judgments regarding the failure likelihood of each basic event and aggregate those opinions using the Similarity-based Aggregation Method (SAM) to form a collective assessment. In SAM, we convert expert opinions into failure probability using interval-valued triangular fuzzy numbers. Since each expert possesses different knowledge and various levels of experience, we need to assign weights to their opinions to reflect their relative expertise. We employ the Best-Worst Method (BWM) to calculate the weights of each criterion, and then use the weighting scores to determine the weights of each expert. Ranking of basic events according to their criticality is a crucial step, and in this study, we use the FVI measure to prioritize and rank these events according to their criticality level. To demonstrate the effectiveness and validity of our proposed methodology, we apply our method to two case studies: (1) chemical cargo contamination, and (2) the loss of ship steering ability. These case studies serve as examples to illustrate the practicality and utility of our approach in evaluating criticality and assessing risk in complex systems.

Figures

Figures reproduced from arXiv: 2411.15249 by the authors.

Figure 1
Figure 1. Visual representation of an IVTFN Definition 2.3. Fuzzy Arithmetic Operations for IVTFN [33] The fuzzy arithmetic operations for an IVTFN are defined as follows: Let A˜ = [(a1, b1, c1),(e1, b1, h1)], B˜ = [(a2, b2, c2),(e2, b2, h2)] be two IVTFN and k be any positive scalar then, (1) A˜ + B˜ = [(a1 + a2, b1 + b2, c1 + c2),(e1 + e2, b1 + b2, h1 + h2)] (2) A˜ − B˜ = [(|a1 − c2|, |b1 − b2|, |c1 − a2|),(|e1 − h2|, |b1 −… view at source ↗
Figure 2
Figure 2. Fault tree of top event chemical cargo contamination [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Fault tree for event A of chemical cargo contamination 11 [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Fault tree for event B of chemical cargo contamination [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: Fault tree for event C of chemical cargo contamination 12 [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: Fault tree for event D of chemical cargo contamination Step.1 Experts Judgements To evaluate the possibilities of BEs, a group of three experts is chosen. Experts’ opinions about the likelihood of BEs occurring can be subjective due to variations in their levels of kno…
Figure 7
Figure 7. Figure 7: FVI measure of each BE 4.2. Results and discussion Using the proposed approach, FP of TE after applying IVFFTA is 2.834E − 04. If a company has 10 chemical tankers, each conducting 6 cargo operations monthly, resulting in a total of 60 cargo operations per month. It me…
Figure 8
Figure 8. Figure 8: Fault tree of top event loss of ship steering ability [PITH_FULL_IMAGE:figures/full_fig_p021_8.png]
Figure 9
Figure 9. Figure 9: FVI measure of each BE 4.4. Results and discussion The probability of the TE, as calculated by S. Gurgen et al.[14], is 4.86E-02, while our proposed approach produces a slightly higher value 5.4E − 02. The ranking of events based on both methods is provided in [PITH_F…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

42 extracted references · 42 canonical work pages

  1. [18]

    Fuzzy system reliability analysis based on level (λ,1) interval-valued fuzzy numbers,

    C.-F. Fuh, R. Jea, and J.-S. Su, “Fuzzy system reliability analysis based on level (λ,1) interval-valued fuzzy numbers,” Information Sciences , vol. 272, pp. 185–197, 2014

    work page 2014

  2. [19]

    Fuzzy fault tree analysis using level (λ,ρ) interval-valued fuzzy numbers,

    P. KUMAR and S. SINGH, “Fuzzy fault tree analysis using level (λ,ρ) interval-valued fuzzy numbers,” Mathematical Theory and Modeling , vol. 2, pp. 136–142, 2015

    work page 2015

  3. [1]

    An extension to fuzzy developed failure mode and effects analysis (fdfmea) application for aircraft landing system,

    M. Yazdi, S. Daneshvar, and H. Setareh, “An extension to fuzzy developed failure mode and effects analysis (fdfmea) application for aircraft landing system,” Safety Science, vol. 98, pp. 113–123, 2017. 27

    work page 2017

  4. [2]

    Launch control safety study,

    H. A. Watson et al. , “Launch control safety study,” Bell labs , 1961

    work page 1961

  5. [3]

    Fault-tree analysis by fuzzy probability,

    H. Tanaka, L. T. Fan, F. S. Lai, and K. Toguchi, “Fault-tree analysis by fuzzy probability,” IEEE Transactions on Reliability , vol. R-32, no. 5, pp. 453–457, 1983

    work page 1983

  6. [4]

    Fuzzy fault tree analysis for fire and explosion of crude oil tanks,

    D. Wang, P. Zhang, and L. Chen, “Fuzzy fault tree analysis for fire and explosion of crude oil tanks,” Journal of Loss Prevention in the Process Industries , vol. 26, 11 2013

    work page 2013

  7. [5]

    An extension to fuzzy fault tree analysis (ffta) application in petrochemical process industry,

    S. Lavasani, A. Zendegani, and M. Celik, “An extension to fuzzy fault tree analysis (ffta) application in petrochemical process industry,” Process Safety and Environ- mental Protection, vol. 93, 05 2014

    work page 2014

  8. [6]

    Assessment of gas and dust explosion in coal mines by means of fuzzy fault tree analysis,

    S. Shi, B. Jiang, and X. Meng, “Assessment of gas and dust explosion in coal mines by means of fuzzy fault tree analysis,” International Journal of Mining Science and Technology, vol. 28, no. 6, pp. 991–998, 2018

    work page 2018

Show all 42 references
  1. [7]

    Reliability assessment of solar photovoltaic systems based on fuzzy fault tree analysis,

    S. Parveen, H. Ashfaq, and M. Asjad, “Reliability assessment of solar photovoltaic systems based on fuzzy fault tree analysis,” Life Cycle Reliability and Safety Engi- neering, vol. 8, 11 2018

    2018

  2. [8]

    Fuzzy fault tree analysis for coal burst occurrence prob- ability in underground coal mining,

    A. Mottahedi and M. Ataei, “Fuzzy fault tree analysis for coal burst occurrence prob- ability in underground coal mining,” Tunnelling and Underground Space Technology, vol. 83, pp. 165–174, 2019

    2019

  3. [9]

    An application of fuzzy fault tree analysis for spread mooring systems,

    A. Mentes and I. Helvacioglu, “An application of fuzzy fault tree analysis for spread mooring systems,” Ocean Engineering - OCEAN ENG, vol. 38, pp. 285–294, 02 2011

    2011

  4. [10]

    Fault tree analysis of chemical cargo contamination by using fuzzy approach,

    Y. E. Senol, Y. V. Aydogdu, B. Sahin, and I. Kilic, “Fault tree analysis of chemical cargo contamination by using fuzzy approach,” Expert Systems with Applications , vol. 42, no. 12, pp. 5232–5244, 2015

    2015

  5. [11]

    Failure probability analysis by employing fuzzy fault tree analysis,

    M. N. Mohammad Yazdi, Farzaneh Nikfar, “Failure probability analysis by employing fuzzy fault tree analysis,” International Journal of System Assurance Engineering and Management , 2017

    2017

  6. [12]

    A fuzzy bayesian network approach for risk analysis in process industries,

    M. Yazdi and S. Kabir, “A fuzzy bayesian network approach for risk analysis in process industries,” Process Safety and Environmental Protection, vol. 111, pp. 507– 519, 2017

    2017

  7. [13]

    Application of fuzzy fault tree analysis (ffta) to maritime industry: A risk analysing of ship mooring operation,

    A. Kuzu, E. Akyuz, and O. Arslan, “Application of fuzzy fault tree analysis (ffta) to maritime industry: A risk analysing of ship mooring operation,” Ocean Engineering, vol. 179, 03 2019

    2019

  8. [14]

    Fuzzy fault tree analysis for loss of ship steering ability,

    S. G¨ urgen, D. Yazır, and O. Konur, “Fuzzy fault tree analysis for loss of ship steering ability,” Ocean Engineering, vol. 279, p. 114419, 2023. 28

    2023

  9. [15]

    An α-cut interval based if-importance measure for intu- itionistic fuzzy fault tree analysis of subsea oil and gas production system,

    M. Kaushik and M. Kumar, “An α-cut interval based if-importance measure for intu- itionistic fuzzy fault tree analysis of subsea oil and gas production system,” Applied Ocean Research, vol. 125, p. 103229, 2022

    2022

  10. [16]

    An integrated approach of intuitionistic fuzzy fault tree and bayesian network analysis applicable to risk analysis of ship mooring operations,

    M. Kaushik and M. Kumar, “An integrated approach of intuitionistic fuzzy fault tree and bayesian network analysis applicable to risk analysis of ship mooring operations,” Ocean Engineering, vol. 269, p. 113411, 2023

    2023

  11. [17]

    Fuzzy logic = computing with words,

    L. Zadeh, “Fuzzy logic = computing with words,” IEEE Transactions on Fuzzy Sys- tems, vol. 4, no. 2, pp. 103–111, 1996

    1996

  12. [20]

    Aggregation of fuzzy opinions under group de- cision making,

    Hsi-Mei Hsu and Chen-Tung Chen, “Aggregation of fuzzy opinions under group de- cision making,” Fuzzy Sets and Systems , vol. 79, no. 3, pp. 279–285, 1996

    1996

  13. [21]

    Combining probability distributions from experts in risk analysis.,

    Clemen, R. T. and Winkler, R. L, “Combining probability distributions from experts in risk analysis.,” Risk analysis, vol. 19, pp. 187–203, 1999

    1999

  14. [22]

    Consistency control and expert consistency prioritization for ffta by using extent analysis method of trapezoidal fahp,

    B. Sahin, “Consistency control and expert consistency prioritization for ffta by using extent analysis method of trapezoidal fahp,” Applied Soft Computing, vol. 56, pp. 46– 54, 2017

    2017

  15. [23]

    Fuzzy fault tree analysis of chlorine gas release hazard in chlor-alkali industry using α-cut interval-based similarity aggregation method.,

    Kumar, M. and Singh, K., “Fuzzy fault tree analysis of chlorine gas release hazard in chlor-alkali industry using α-cut interval-based similarity aggregation method.,” Applied Soft Computing , vol. 125, 2022

    2022

  16. [24]

    Best-worst multi-criteria decision-making method: Some properties and a linear model,

    J. Rezaei, “Best-worst multi-criteria decision-making method: Some properties and a linear model,” Omega, vol. 64, pp. 126–130, 2016

    2016

  17. [25]

    Defuzzification in fuzzy controllers,

    H. Hellendoorn and C. Thomas, “Defuzzification in fuzzy controllers,” Journal of Intelligent and Fuzzy Systems , 1993

    1993

  18. [26]

    A fuzzy extension of saaty’s priority theory,

    Van Laarhoven, P. J. and Pedrycz, W., “A fuzzy extension of saaty’s priority theory,” Fuzzy sets and Systems , vol. 11, pp. 229–241, 1983

    1983

  19. [27]

    A fuzzy programming method for deriving priorities in the analytic hi- erarchy process,

    L. Mikhailov, “A fuzzy programming method for deriving priorities in the analytic hi- erarchy process,” Journal of the Operational Research Society, vol. 51, no. 3, pp. 341– 349, 2000

    2000

  20. [28]

    Deriving priorities from fuzzy pairwise comparison judgements,

    L. Mikhailov, “Deriving priorities from fuzzy pairwise comparison judgements,”Fuzzy Sets and Systems , vol. 134, no. 3, pp. 365–385, 2003. 29

    2003

  21. [29]

    Application of fuzzy fault tree analysis on oil and gas offshore pipelines,

    M. Lavasani, J. Wang, Z. Yang, and J. Finlay, “Application of fuzzy fault tree analysis on oil and gas offshore pipelines,” International Journal of Materials Science and Engineering, vol. 1, pp. 29–42, 01 2011

    2011

  22. [30]

    Risk assessment of the ship steering gear failures using fuzzy-bayesian networks,

    O. Y¨ uksel, B. Goksu, and C. Sakar, “Risk assessment of the ship steering gear failures using fuzzy-bayesian networks,” Ocean Engineering, vol. 274, 04 2023

    2023

  23. [31]

    G. J. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications . Prentice-Hall, 2015

    2015

  24. [32]

    Zimmermann, Fuzzy Set Theory — and Its Applications

    H. Zimmermann, Fuzzy Set Theory — and Its Applications . Springer Dordrecht, 2001

    2001

  25. [33]

    Extension of the aras method for decision-making problems with interval-valued triangular fuzzy numbers,

    D. Stanujkic, “Extension of the aras method for decision-making problems with interval-valued triangular fuzzy numbers,”Informatica, vol. 26, pp. 335–355, 06 2016

    2016

  26. [34]

    Fuzzy tempo- ral fault tree analysis of dynamic systems,

    S. Kabir, M. Walker, Y. Papadopoulos, E. R¨ ude, and P. Securius, “Fuzzy tempo- ral fault tree analysis of dynamic systems,” International Journal of Approximate Reasoning, vol. 77, pp. 20–37, 2016

    2016

  27. [35]

    Similarity measure of the interval-valued fuzzy num- bers and its application in risk analysis in paddy cultivation,

    M. K. Gogoi and R. Chutia, “Similarity measure of the interval-valued fuzzy num- bers and its application in risk analysis in paddy cultivation,” Journal of Ambient Intelligence and Humanized Computing , vol. 13, p. 1829–1852, 2022

    2022

  28. [36]

    Defuzzification in fuzzy controllers,

    H. Hellendoorn and C. Thomas, “Defuzzification in fuzzy controllers,” Journal of Intelligent & Fuzzy Systems , vol. 1, no. 2, pp. 109–123, 1993

    1993

  29. [37]

    Ranking and defuzzification methods based on area compensation,

    P. Fortemps and M. Roubens, “Ranking and defuzzification methods based on area compensation,” Fuzzy Sets and Systems , vol. 82, no. 3, pp. 319–330, 1996

    1996

  30. [38]

    Defuzzification: criteria and classification,

    W. V. Leekwijck and E. E. Kerre, “Defuzzification: criteria and classification,” Fuzzy Sets and Systems , vol. 108, no. 2, pp. 159–178, 1999

    1999

  31. [39]

    Defuzzification within a multicriteria decision model,

    S. OPRICOVIC and G.-H. TZENG, “Defuzzification within a multicriteria decision model,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Sys- tems, vol. 11, no. 05, pp. 635–652, 2003

    2003

  32. [40]

    An approach to human reliability in man-machine systems using error possibility,

    T. Onisawa, “An approach to human reliability in man-machine systems using error possibility,” Fuzzy Sets and Systems , vol. 27, no. 2, pp. 87–103, 1988

    1988

  33. [41]

    A novel risk analysis approach for fpso single point mooring system using bayesian network and interval type-2 fuzzy sets,

    J. Yu, H. Ding, Y. Yu, S. Wu, Q. Zeng, and W. Ma, “A novel risk analysis approach for fpso single point mooring system using bayesian network and interval type-2 fuzzy sets,” Ocean Engineering, vol. 266, pp. 113–144, 2022

    2022

  34. [42]

    M. R. Arnljot Hoyland, System reliability theory: models and statistical methods . New Jersey: John Wiley & Sons, 2009. 30

    2009

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.