2018
DOI: 10.1515/jisys-2018-0159
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A Novel Weakest t-norm based Fuzzy Fault Tree Analysis Through Qualitative Data Processing and Its Application in System Reliability Evaluation

Abstract: Abstract The quantification of the fuzzy fault tree analysis (FFTA) is based on fuzzy arithmetic operations. It is well known that the weakest t-norm (Tw)-based fuzzy arithmetic operations have some advantages. The Tw-based fuzzy arithmetic operations provide fuzzy results with less fuzziness and preserve the shape of fuzzy numbers. The purpose of this study is to develop a Tw-based fuzzy fault tree analysis (TBFFTA… Show more

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Cited by 7 publications
(5 citation statements)
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“…e membership value, as the function value of μ A (X)A, indicates the degree of accuracy that x is a constituent of fuzzy set A. It is supposed that μ A : X ∈ [0.1], where μ A (X) � 0 means that x is belonged to A but not to the fuzzy set A [26,31,32] (2) Triangular Fuzzy Number. A triangular fuzzy number N is referred to as a triplet (l • m • u), and the membership function μ N (x) can be illustrated by equation (1) as follows:…”
Section: Basic Definitions and Preliminariesmentioning
confidence: 99%
“…e membership value, as the function value of μ A (X)A, indicates the degree of accuracy that x is a constituent of fuzzy set A. It is supposed that μ A : X ∈ [0.1], where μ A (X) � 0 means that x is belonged to A but not to the fuzzy set A [26,31,32] (2) Triangular Fuzzy Number. A triangular fuzzy number N is referred to as a triplet (l • m • u), and the membership function μ N (x) can be illustrated by equation (1) as follows:…”
Section: Basic Definitions and Preliminariesmentioning
confidence: 99%
“…proposed fuzzy probability‐based FTA (FPFTA) to evaluate the lower bound, upper bound and best estimate of system failure probability when quantitative data are not available precisely and only qualitative data are available. Kumar 21 utilized the concept of weakest t‐norm‐based fuzzy arithmetic operations incorporating fuzzy FTA and evaluated the lower bound, upper bound and the best estimate of system failure probability using qualitative data processing. The absolute errors between the results from all these approaches and established data are calculated and shown in Table 9.…”
Section: Case Studiesmentioning
confidence: 99%
“…introduced a probability‐based FFTA, where triangular fuzzy numbers (TFNs) are used for the quantification of BEs failure possibilities. Kumar 21 integrated the concept of weakest triangular norm (Tw$T_{w}$) with FFTA for system reliability evaluation. Purba et al 22 .…”
Section: Introductionmentioning
confidence: 99%
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“…Zadeh [35] introduced the concept of fuzzy set theory. Fuzzy set theory has been applied in different areas such as inventory modeling, reliability engineering, decision-making problems and statistics [6,7,[18][19][20]34]. Initially, Vujošević et al [32] developed an EOQ formula by taking fuzzy inventory costs.…”
Section: Introductionmentioning
confidence: 99%