• 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 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 applied mathematics & informatics
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• v.19 no.1_2
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• pp.513-520
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• 2005

We calculate the normal fuzzy probability for trigonometric fuzzy numbers defined by trigonometric functions. And we study the normal probability for some operations of two trigonometric fuzzy numbers. Furthermore, we calculate the normal fuzzy probability for some fuzzy numbers generated by operations.

• 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 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 Institute of Intelligent Systems
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• v.15 no.3
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• pp.277-281
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• 2005

We study some operations of two quadratic fuzzy numbers defined by quadratic curves. And we calculate the normal fuzzy probability for fuzzy numbers generated by the operations.

• 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.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.843-856
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• 2009

In possibility framework, we propose two risk measures named Fuzzy Value-at-Risk and Fuzzy Conditional Value-at-Risk, based on Credibility measure. Two portfolio optimization models for fuzzy portfolio selection problems are formulated. Then a chaos genetic algorithm based on fuzzy simulation is designed, and finally computational results show that the two risk measures can play a role in possibility space similar to Value-at-Risk and Conditional Value-at-Risk in probability space.

• Journal of Information Processing Systems
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• v.16 no.2
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• pp.318-328
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• 2020

Letter of Credit (L/C) is currently a very popular international settlement method frequently used in international trade processes amongst countries around the globe. Compared with other international settlement methods, however, L/C has some obvious shortcomings. Firstly, it is not easy to use due to the sophisticated processes its usage involves. Secondly, it is sometimes accompanied by a few risks and some uncertainty. Thus, highly efficient methods need to be used to assess and control these risks. To begin with, FAHP and KMV methods are used to resolve the problem of incomplete information associated with L/C and then, on this basis, Bayesian game theory is used in order to make more scientific and reasonable decisions with respect to international trade.

• Nuclear Engineering and Technology
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• v.28 no.5
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• pp.431-439
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• 1996

In the process of simplifying the complex fate of the plant into a binary state, the information loss is inevitable. To minimize the information loss, the quantification of plant safety status has been formulated through the combination of the probability density function arising from the sensor measurement and the membership function representing the expectation of the state of the system. Therefore, in this context, the safety index is introduced in an attempt to quantify the plant status from the perspective of safety. The combination of probability density function and membership function is achieved through the integration of the fuzzy intersection of the two functions, and it often is not a simple task to integrate the fuzzy intersection due to the complexity that is the result of the fuzzy intersection. Therefore, a methodology based on the Algebra of Logic is used to express the fuzzy intersection and the fuzzy union of the arbitrary functions analytically. These exact analytical expressions are then numerically integrated by the application of Monte Carlo method. The benchmark tests for rectangular area and both fuzzy intersection and union of two normal distribution functions have been performed. Lastly, the safety index was determined for the Core Reactivity Control of Yonggwang 3&4 using the presented methodology.