• East Asian mathematical journal
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• v.29 no.3
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• pp.269-278
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• 2013

A fuzzy set A defined on a probability space (${\Omega}$, $\mathfrak{F}$, P) is called a fuzzy event. Zadeh defines the probability of the fuzzy event A using the probability P. We define the normal fuzzy probability on $\mathbb{R}$ using the normal distribution. We calculate the normal fuzzy probability for generalized trapezoidal fuzzy sets and give some examples.

• Journal of the Korean Institute of Intelligent Systems
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• v.24 no.4
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• pp.398-402
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• 2014

A generalized trigonometric fuzzy set is a generalization of a trigonometric fuzzy number. Zadeh([7]) defines the probability of the fuzzy event using the probability. We define the normal and exponential fuzzy probability on $\mathbb{R}$ using the normal and exponential distribution, respectively, and we calculate the normal and exponential fuzzy probability for generalized trigonometric fuzzy sets.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.217-225
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• 2012

A generalized quadratic fuzzy set is a generalization of a quadratic fuzzy number. Zadeh defines the probability of the fuzzy event using the probability. We define the normal fuzzy probability on $\mathbb{R}$ using the normal distribution. And we calculate the normal fuzzy probability for generalized quadratic fuzzy sets.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.2
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• pp.212-217
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• 2012

A fuzzy set $A$ defined on a probability space ${\Omega}$, $\mathfrak{F}$, $P$ is called a fuzzy event. Zadeh defines the probability of the fuzzy event $A$ using the probability $P$. We define the generalized triangular fuzzy set and apply the extended algebraic operations to these fuzzy sets. A generalized triangular fuzzy set is symmetric and may not have value 1. For two generalized triangular fuzzy sets $A$ and $B$, $A(+)B$ and $A(-)B$ become generalized trapezoidal fuzzy sets, but $A({\cdot})B$ and $A(/)B$ need not to be a generalized triangular fuzzy set or a generalized trapezoidal fuzzy set. We define the normal fuzzy probability on $\mathbb{R}$ using the normal distribution. And we calculate the normal fuzzy probability for generalized triangular fuzzy sets.

• Journal of the Korean Statistical Society
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• v.21 no.2
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• pp.111-125
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• 1992

Since Zadeh's definition for probability of fuzzy event is presented, alternative definitions for probability of fuzzy event is suggested. Also various properties of these new definitions have been presented. In this paper it is our purpose to show the works continued by finding a natural definition of a fuzzy probability measure on an arbitrary fuzzy measurable space. Thus, the main process is to observe fuzzy probability measure to be qualified by weak axioms of boundary condition, monotonicity and continuity suggested by Klir (1988). Especially, we will show that these axioms are satisfied through in succession of modifications from the Yager's method.

• Ocean Systems Engineering
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• v.8 no.1
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• pp.41-55
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• 2018

Accidental oil and gas leak is a critical concern for the offshore industry because it can lead to severe consequences and as a result, it is imperative to evaluate the probabilities of occurrence of the consequences of the leakage in order to assess the risk. Event Tree Analysis (ETA) is a technique to identify the consequences that can result from the occurrence of a hazardous event. The probability of occurrence of the consequences is evaluated by the ETA, based on the failure probabilities of the sequential events. Conventional ETA deals with events with crisp failure probabilities. In offshore applications, it is often difficult to arrive at a single probability measure due to lack of data or imprecision in data. In such a scenario, fuzzy set theory can be applied to handle imprecision and data uncertainty. This paper presents fuzzy ETA (FETA) methodology to compute the probability of the outcomes initiated due to oil/gas leak in an actual offshore-onshore installation. Post FETA, sensitivity analysis by Fuzzy Weighted Index (FWI) method is performed to find the event that has the maximum contribution to the severe sequences. It is found that events of 'ignition', spreading of fire to 'equipment' and 'other areas' are the highest contributors to the severe consequences, followed by failure of 'leak detection' and 'fire detection' and 'fire water not being effective'. It is also found that the frequency of severe consequences that are catastrophic in nature obtained by ETA is one order less than that obtained by FETA, thereby implying that in ETA, the uncertainty does not propagate through the event tree. The ranking of severe sequences based on their probability, however, are identical in both ETA and FETA.

• Nuclear Engineering and Technology
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• v.29 no.1
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• pp.25-34
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• 1997

This study presents a new approach for expert opinion elicitation process to assess an uncertainty inherent in accident management. The need to work with rare event and limited data in accident management leads analysis to use expert opinions extensively. Unlike the conventional approach using point-valued probabilities, the study proposes the concept of fuzzy probability to represent expert opinion. The use of fuzzy probability has an advantage over the conventional approach when an expert's judgment is used under limited dat3 and imprecise knowledge. The study demonstrates a method of combining and propagating fuzzy probabilities. finally, the proposed methodology is applied to the evaluation of the probability of a bottom head failure for the flooded case in the Peach Bottom BWR nuclear power plant.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.17 no.31
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• pp.177-186
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• 1994

Most causes of accidents are due to physical unsafety conditions and human unsafety actions. The design of safety work by ergonomics method is one of the methodes which effectively reduce these unsafety conditions and unsafety actions. This paper presents considerations in design of safety work. And when we try to analyze the accident event by means of probability, there exist some problems because of fuzziness in physical unsafety conditions' components and human unsafety actions' components which are the causes of basic event. For this reason, it is impossible for input probability of basic event to define a crisp value. In consideration of the uncertain probability of components, this paper deals with the Fuzzy set theory by membership value and suggests calculation procedure and analysis of disaster event.

• Journal of Korean Society for Quality Management
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• v.20 no.2
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• pp.44-54
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• 1992

In conventional fault-tree analysis, the failure probabilities of components of a system are treated as exact values in estimating the failure probability of the top event. For the plant layout and systems of the products, however, it is often difficult to evaluate the failure probabilities of components from past occurences, because the environments of the systems change. Furthermore, it might be necessary to consider possible failure of components of the systems even if they have never failed before. In the paper, instead of the probability of failure, we propose the possibility of failure, viz, a fuzzy set defined in probability space. Thus, in this paper based on a fuzzy fault-tree model, the maximum possibility of system failure is determined from the possibility of failure of each component within the system according to the extension principle.

• Journal of the Korean Institute of Intelligent Systems
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• v.7 no.1
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• pp.5-15
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• 1997

This paper mentions a fault tree analysis using not probability but natural language and fuzzy theory, Reliability estimate of each basic event and dependence level estimate among subsystems are expressed by linguistic terms. Analysis results are also expressed by natural language. The meaning of linguistic terms is expressed by a fuzzy set. In the presented analysis approach parametrized operations of fuzzy sets are considered so that analyst's subjectivity can be introduced into the analysis. This paper gives the Chernobyl accident as an example of the fuzzy fault tree analysis using linguistic terms.