• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.9
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• pp.1055-1063
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• 1999

This paper present a conceptual possibilistic approach using fuzzy set theory to manage the uncertainties in the given reliability input date of the practical power system. In this paper, an algorithm is introduced to calculate the possibilstic reliability indices according to the degree of uncertainty in the given data. The probability distribution function can be transformed into an appropriate possibilstic representation using the probability-Possibility Consistency principle(PPCP) algorithm. In this the algorithm, the transformation is performation by making a compromise between the transformation consistency and the human updating experience. Fuzzy classifcation theory is applied to reduced the number of load data. The fuzzy classification method determines the closeness of load data points by assigning them to various clusters and then determening the distance between the clusters. The IEEE-RTS with 32-generating units is used to demonstrate the capability of the proposed algorithm.

• Journal of the Korean Geotechnical Society
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• v.23 no.11
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• pp.109-117
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• 2007

Uncertainty is pervasive in rock slope stability analysis due to various reasons and subsequently it may cause serious rock slope failures. Therefore, the importance of uncertainty has been recognized and subsequently the probability theory has been used to quantify the uncertainty since 1980's. However, some uncertainties, due to incomplete information, cannot be handled satisfactorily in the probability theory and the fuzzy set theory is more appropriate for those uncertainties. In this study the random variable is considered as fuzzy number and the fuzzy set theory is employed in rock slope stability analysis. However, the previous fuzzy analysis employed the approximate method, which is first order second moment method and point estimate method. Since previous studies used only the representative values from membership function to evaluate the stability of rock slope, the approximated analysis results have been obtained in previous studies. Therefore, the Monte Carlo simulation technique is utilized to evaluate the probability of failure for rock slope in the current study. This overcomes the shortcomings of previous studies, which are employed vertex method. With Monte Carlo simulation technique, more complete analysis results can be secured in the proposed method. The proposed method has been applied to the practical example. According to the analysis results, the probabilities of failure obtained from the fuzzy Monte Carlo simulation coincide with the probabilities of failure from the probabilistic analysis.

• Journal of Korean Tunnelling and Underground Space Association
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• v.12 no.1
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• pp.15-29
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• 2010

Spalling is a kind of instability phenomenon of surrounding rock around underground openings subjected to high in-situ stress according to the development of extension fractures. Three kinds of spalling criteria have been presented so far; however, all spalling criteria have the range of values so that the fuzziness and vagueness of spalling criterion cannot be avoided. In this study, a new fuzzy probability model is proposed to predict the probability of spalling in a systematic way by using fuzzy probability theory. Many of the underground opening projects worldwide are evaluated with the proposed method. Prediction results expressed as the spalling probability agree well with the in-situ observations. In particular, a new fuzzy probability model considering all three evaluation indices of spalling by adopting weighting factors based on relative reliability among three evaluation indices is able to resolve erroneous prediction of spalling by choosing only one prediction method. Moreover, the more reasonable value of spalling probability could have been obtained by adopting the modified damage index to the newly proposed fuzzy probability model.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.1
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• pp.46-51
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• 2007

In this paper, we propose a new data clustering method using local probability and hypothesis theory. To cluster the test data set we analyze the local area of the test data set using local probability distribution and decide the candidate class of the data set using mean standard deviation and variance etc. To decide each class of the test data, statistical hypothesis theory is applied to the decided candidate class of the test data set. For evaluating, the proposed classification method is compared to the conventional fuzzy c-mean method, k-means algorithm and Discriminator analysis algorithm. The simulation results show more accuracy than results of fuzzy c-mean method, k-means algorithm and Discriminator analysis algorithm.

• Geomechanics and Engineering
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• v.12 no.2
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• pp.269-294
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• 2017

This study aimed to realize the creation of fuzzy stochastic damage to describe reliability more essentially with the analysis of harmony of damage conception, probability and fuzzy degree of membership in interval [0,1]. Two kinds of fuzzy behaviors of damage development were deduced. Fuzzy stochastic damage models were established based on the fuzzy memberships functional and equivalent normalization theory. Fuzzy stochastic damage finite element method was developed as the approach to reliability simulation. The three-dimensional fuzzy stochastic damage mechanical behaviors of Jianshan mine slope were analyzed and examined based on this approach. The comprehensive results, including the displacement, stress, damage and their stochastic characteristics, indicate consistently that the failure foci of Jianshan mine slope are the slope-cutting areas where, with the maximal failure probability 40%, the hazardous Domino effects will motivate the neighboring rock bodies' sliding activities.

• Proceedings of the KIEE Conference
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• 1995.11a
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• pp.128-130
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• 1995

This paper presents the optimal operation scheduling on cogeneration systems connected with auxiliary equipment by using the possibility fuzzy theory. The probability fuzzy theory is a method to obtain the possibility of the solution from the fuzzification of coefficients. Simulation is carried out to obtain the boundary of heat production in each time interval. Simulation results shows effectively the flexible operation boundary to establish operation scheduling.

• Proceedings of the KSR Conference
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• 2007.11a
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• pp.1529-1532
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• 2007

Failure Mode, Effects, and Criticality Analysis (FMECA) is an extension of FMEA which includes a criticality analysis. The criticality analysis is used to chart the probability of failure modes against the severity of their consequences. The result highlights failure modes with relatively high probability and severity of consequences, allowing remedial effort to be directed where it will produce the greatest value. However, there are several limitations. Measuring severity of failure consequences is subjective and linguistic. Since The result of FMECA only gives qualitative and quantitative informations, it should be re-analysed to prioritize critical units. Fuzzy set theory has been introduced by Lotfi A. Zadeh (1965). It has extended the classical set theory dramatically. Based on fuzzy set theory, fuzzy logic has been developed employing human reasoning process. IF-THEN fuzzy rule based assessment approach can model the expert's decision logic appropriately. Fault tree analysis (FTA) is one of most common fault modeling techniques. It is widely used in many fields practically. In this paper, a simple fault tree analysis is proposed to measure the severity of components. Fuzzy rule based assessment method interprets linguistic variables for determination of critical unit priorities. An rail-way transforming system is analysed to describe the proposed method.

• Journal of the Korea institute for structural maintenance and inspection
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• v.2 no.2
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• pp.151-161
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• 1998

In this study, an attempt is made to apply the concept of fuzzy-bayesian theory to the integrity assessment of RC highway bridge, and uncertainty states are represented in terms of fuzzy sets which define several linguistic variables such as "very good", "good", "average", "poor", "very poor", etc. Especially, the concept of fuzzy conditional probability aids to derive a new reliability analysis which includes the subjective assessment of engineers without introducing any additional correction factors. The fuzzy concept are also used as reliability indexes for the condition assessment based on the proposed models, the proposed fuzzy theory-based approach with the results of visual inspection and extensive field load tests are applied to the integrity assessment of a new RC highway bridge, namely, Jichok bridge.

• Journal for History of Mathematics
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• v.25 no.1
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• pp.1-13
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• 2012

Possibility theory is a kind of mathematics of uncertainty for handling incomplete information. In this paper, we discuss vagueness and randomness as some causes of uncertainty and we introduce the possibility theory as a way of dealing with uncertainty, comparing it with the probability theory.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.3
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• pp.511-521
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• 2010

In this paper, we define the one-sided fuzzy set and we calculate the mean value and variance, defined by C. Carlsson and R. $Full{\acute{e}}r$, of this fuzzy set. And we obtain a result that, in some special case, the mean of the product of two fuzzy sets is the product of means of each fuzzy sets. This result can be considered as the similar result which is well-known in the independence of events in probability theory.