Fuzzy Fault Trees: the Fast and the Formal

Thi Kim Nhung Dang; Benedikt Peterseim; Milan Lopuhaä-Zwakenberg; Mariëlle Stoelinga

doi:10.48550/arXiv.2507.02886

Fuzzy Fault Trees: the Fast and the Formal

Thi Kim Nhung Dang
, Benedikt Peterseim
, Milan Lopuhaä-Zwakenberg
, Mariëlle Stoelinga

Research output: Working paper › Preprint › Academic

61 Downloads (Pure)

Abstract

We provide a rigorous framework for handling uncertainty in quantitative fault tree analysis based on fuzzy theory. We show that any algorithm for fault tree unreliability analysis can be adapted to this framework in a fully general and computationally efficient manner. This result crucially leverages both the alpha-cut representation of fuzzy numbers and the coherence property of fault trees. We evaluate our algorithms on an established benchmark of synthetic fault trees, demonstrating their practical effectiveness.

Original language	English
Publisher	ArXiv.org
DOIs	https://doi.org/10.48550/arXiv.2507.02886
Publication status	Published - 19 Jun 2025

Keywords

math.GM

Access to Document

10.48550/arXiv.2507.02886Licence: CC BY

2507.02886v1Final published version, 1.59 MBLicence: CC BY

Fuzzy Fault Trees: The Fast and the Formal
Dang, T. K. N., Peterseim, B., Lopuhaä-Zwakenberg, M. & Stoelinga, M. I. A., 2 Oct 2025, Quantitative Evaluation of Systems and Formal Modeling and Analysis of Timed Systems : Second International Joint Conference, QEST+FORMATS 2025, Aarhus, Denmark, August 26–28, 2025, Proceedings. Prabhakar, P. & Vandin, A. (eds.). Cham: Springer, p. 256-274 19 p.
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Cite this

@techreport{9434f3cc0b7a40c39a6484fc8f0f7de0,

title = "Fuzzy Fault Trees: the Fast and the Formal",

abstract = "We provide a rigorous framework for handling uncertainty in quantitative fault tree analysis based on fuzzy theory. We show that any algorithm for fault tree unreliability analysis can be adapted to this framework in a fully general and computationally efficient manner. This result crucially leverages both the alpha-cut representation of fuzzy numbers and the coherence property of fault trees. We evaluate our algorithms on an established benchmark of synthetic fault trees, demonstrating their practical effectiveness. ",

keywords = "math.GM",

author = "Dang, \{Thi Kim Nhung\} and Benedikt Peterseim and Milan Lopuha{\"a}-Zwakenberg and Mari{\"e}lle Stoelinga",

note = "Accepted for the proceedings of the International Conference on the Quantitative Evaluation of Systems (QEST); this preprint contains an appendix with proofs",

year = "2025",

month = jun,

day = "19",

doi = "10.48550/arXiv.2507.02886",

language = "English",

publisher = "ArXiv.org",

type = "WorkingPaper",

institution = "ArXiv.org",

}

TY - UNPB

T1 - Fuzzy Fault Trees

T2 - the Fast and the Formal

AU - Dang, Thi Kim Nhung

AU - Peterseim, Benedikt

AU - Lopuhaä-Zwakenberg, Milan

AU - Stoelinga, Mariëlle

N1 - Accepted for the proceedings of the International Conference on the Quantitative Evaluation of Systems (QEST); this preprint contains an appendix with proofs

PY - 2025/6/19

Y1 - 2025/6/19

N2 - We provide a rigorous framework for handling uncertainty in quantitative fault tree analysis based on fuzzy theory. We show that any algorithm for fault tree unreliability analysis can be adapted to this framework in a fully general and computationally efficient manner. This result crucially leverages both the alpha-cut representation of fuzzy numbers and the coherence property of fault trees. We evaluate our algorithms on an established benchmark of synthetic fault trees, demonstrating their practical effectiveness.

AB - We provide a rigorous framework for handling uncertainty in quantitative fault tree analysis based on fuzzy theory. We show that any algorithm for fault tree unreliability analysis can be adapted to this framework in a fully general and computationally efficient manner. This result crucially leverages both the alpha-cut representation of fuzzy numbers and the coherence property of fault trees. We evaluate our algorithms on an established benchmark of synthetic fault trees, demonstrating their practical effectiveness.

KW - math.GM

U2 - 10.48550/arXiv.2507.02886

DO - 10.48550/arXiv.2507.02886

M3 - Preprint

BT - Fuzzy Fault Trees

PB - ArXiv.org

ER -

Fuzzy Fault Trees: the Fast and the Formal

Abstract

Keywords

Access to Document

Fingerprint

Research output

Fuzzy Fault Trees: The Fast and the Formal

Cite this