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A Fuzzy Set Theoretic Foundation for Vagueness in Uncertainty Analysis

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  • Stephen D. Unwin

Abstract

We emphasize the distinction between two forms of uncertainty that arise in risk and reliability analyses: (1) that due to the randomness inherent in the system under investigation and (2) that due to the vagueness inherent in the assessor's perception and judgement of that system. It is proposed that whereas the probabilistic approach to the former variety of uncertainty is an appropriate one, the same may not be true of the latter. Through seeking to quantify the imprecision that characterizes our linguistic description of perception and comprehension, fuzzy set theory provides a formal framework for the representation of vagueness. In connection with the second form of uncertainty, fuzzy sets and the associated theory of “possibility” are considered as a basis upon which to model the imprecision and vagueness attached to the expert judgement of event likelihood (e.g. component failure). It is noted that from the perspective of the technical complexity of propagation, the possibilistic treatment of uncertainty compares favorably with the more familiar Bayesian approach.

Suggested Citation

  • Stephen D. Unwin, 1986. "A Fuzzy Set Theoretic Foundation for Vagueness in Uncertainty Analysis," Risk Analysis, John Wiley & Sons, vol. 6(1), pages 27-34, March.
    • Handle: RePEc:wly:riskan:v:6:y:1986:i:1:p:27-34
    DOI: 10.1111/j.1539-6924.1986.tb00191.x
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    1. Stanley Kaplan, 1981. "On The Method of Discrete Probability Distributions in Risk and Reliability Calculations–Application to Seismic Risk Assessment," Risk Analysis, John Wiley & Sons, vol. 1(3), pages 189-196, September.
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    Cited by:

    1. Tzu Yang Loh & Mario P. Brito & Neil Bose & Jingjing Xu & Kiril Tenekedjiev, 2020. "Fuzzy System Dynamics Risk Analysis (FuSDRA) of Autonomous Underwater Vehicle Operations in the Antarctic," Risk Analysis, John Wiley & Sons, vol. 40(4), pages 818-841, April.
    2. Majda Ćesić & Katarina Rogulj & Jelena Kilić Pamuković & Andrija Krtalić, 2024. "A Systematic Review on Fuzzy Decision Support Systems and Multi-Criteria Analysis in Urban Heat Island Management," Energies, MDPI, vol. 17(9), pages 1-41, April.
    3. Roger Flage & Piero Baraldi & Enrico Zio & Terje Aven, 2013. "Probability and Possibility‐Based Representations of Uncertainty in Fault Tree Analysis," Risk Analysis, John Wiley & Sons, vol. 33(1), pages 121-133, January.
    4. Roger Flage & Terje Aven & Enrico Zio & Piero Baraldi, 2014. "Concerns, Challenges, and Directions of Development for the Issue of Representing Uncertainty in Risk Assessment," Risk Analysis, John Wiley & Sons, vol. 34(7), pages 1196-1207, July.
    5. Tzu Yang Loh & Mario P. Brito & Neil Bose & Jingjing Xu & Kiril Tenekedjiev, 2019. "A Fuzzy‐Based Risk Assessment Framework for Autonomous Underwater Vehicle Under‐Ice Missions," Risk Analysis, John Wiley & Sons, vol. 39(12), pages 2744-2765, December.

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