• Journal of Power System Engineering
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• v.18 no.1
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• pp.135-139
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• 2014

We propose some properties for fuzzy hypothesis test by fuzzy significance probability. First, we define fuzzy number data and fuzzy significance probability for repeatedly observed data with alternated error term. By the agreement index, we compare fuzzy significance probability with significance level and drawing conclusions the degree of acceptance and rejection by agreement index.

• Communications for Statistical Applications and Methods
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• v.19 no.1
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• pp.147-155
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• 2012

We propose some properties for a fuzzy correlation test by reduced-spread fuzzy variance for sample fuzzy data. First, we define the condition of fuzzy data for repeatedly observed data or that which includes error term data. By using the average of spreads for fuzzy numbers, we reduce the spread of fuzzy variance and define the agreement index for the degree of acceptance and rejection. Given a non-normal random fuzzy sample, we have bivariate normal distribution by apply Box-Cox power fuzzy transformation and test the fuzzy correlation for independence between the variables provided by the agreement index.

• Economic and Environmental Geology
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• v.41 no.6
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• pp.763-771
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• 2008

Uncertainties are pervasive in engineering geological problems. Therefore, the presence of uncertainties and their significance in analysis and design of slopes have been recognized. Since the uncertainties cannot be taken into account by the conventional deterministic approaches in slope stability analysis, the probabilistic analysis has been considered as the primary tool for representing uncertainties in mathematical models. However, some uncertainties are caused by incomplete information due to lack of information, and those uncertainties cannot be handled appropriately by the probabilistic approach. For those uncertainties, the theory of fuzzy sets is more appropriate. Therefore, in this study, fuzzy reliability analysis has been proposed in order to deal with the uncertainties which cannot be quantified in the probabilistic analysis due to the limited information. For the practical example, a slope is selected in this study and both the probabilistic analysis and the fuzzy reliability analysis have been carried out for planar failure. In the fuzzy reliability analysis, the dip angle and internal friction angle of discontinuity are considered as triangular fuzzy numbers since the random properties of the variables cannot be obtained completely under the conditions of limited information. In the study, the fuzzy reliability index and the probabilities of failure are evaluated from fuzzy arithmetic and compared to those from the probabilistic approach using Monte Carlo simulation and point estimate method. The analysis results show that the fuzzy reliability analysis is more appropriate for the condition that the uncertainties arise due to incomplete information.