Normal and exponential fuzzy probability for generalized trigonometric fuzzy sets

Yun Dong Jo(조윤동),Yong Sik Yun(윤용식) 한국지능시스템학회 2014 한국지능시스템학회논문지 Vol.24 No.4

일반화된 삼각함수 퍼지집합은 삼각함수 퍼지수의 일반화이다. Zadeh([7])는 확률을 이용하여 퍼지이벤트에 대한 확률을 정의하였다. 우리는 정규분포와 지수분포를 각각 이용하여 실수 ? 위에서 정규퍼지확률과 지수퍼지확률을 정의하고, 일반화된 삼각함수 퍼지집합에 대하여 정규퍼지확률과 지수퍼지확률을 계산하였다. 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 ? using the normal and exponential distribution, respectively, and we calculate the normal and exponential fuzzy probability for generalized trigonometric fuzzy sets.

Normal and exponential fuzzy probability for generalized trigonometric fuzzy sets

조윤동,윤용식,Jo, Yun Dong,Yun, Yong Sik Korean Institute of Intelligent Systems 2014 한국지능시스템학회논문지 Vol.24 No.4

일반화된 삼각함수 퍼지집합은 삼각함수 퍼지수의 일반화이다. Zadeh([7])는 확률을 이용하여 퍼지이벤트에 대한 확률을 정의하였다. 우리는 정규분포와 지수분포를 각각 이용하여 실수 $\mathbb{R}$ 위에서 정규퍼지확률과 지수퍼지확률을 정의하고, 일반화된 삼각함수 퍼지집합에 대하여 정규퍼지확률과 지수퍼지확률을 계산하였다. 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.

The Binomial Distribution with Fuzzy Valued Probability

강만기,서현아,박영래,최규탁 한국지능시스템학회 2008 한국지능시스템학회 학술발표 논문집 Vol.18 No.1

We introduce some properties for fuzzy binomial distributions with fuzzy valued probability. First we define fuzzy type Ⅰ error and type Ⅱ error for fuzzy relative frequency and agreement index. And we show that an fuzzy power function and fuzzy binomial frequency function for binomial proportion test.

Fuzzy Hypothesis Test by Significance Probability

강만기,서현아,정지영,최규탁 한국지능시스템학회 2010 한국지능시스템학회 학술발표 논문집 Vol.20 No.1

반복적인 실험에서 관측된 데이터가 구간으로 관측되거나 오차항올 포함한 데이터가 퍼지 데이터로서의 조건을 정의하고, 퍼지 확률에 의한 퍼지 유의확률을 정리하여 유의수준과 검정통계량으로 유의확률을 동의지수법으로 비교하여 가설을 검정하는 방법을 제시하고 예증한다. We propose some properties for fuzzy hypothesis test by fuzzy significance probability. First, we define fuzzy 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.

Fuzzy-technique-based expert elicitation on the occurrence probability of severe accident phenomena in nuclear power plants

Suh, Young A,Song, Kiwon,Cho, Jaehyun Korean Nuclear Society 2021 Nuclear Engineering and Technology Vol.53 No.10

The objective of this study is to estimate the occurrence probabilities of severe accident phenomena based on a fuzzy elicitation technique. Normally, it is difficult to determine these probabilities due to the lack of information on severe accident progression and the highly uncertain values currently in use. In this case, fuzzy set theory (FST) can be best exploited. First, questions were devised for expert elicitation on technical issues of severe accident phenomena. To deal with ambiguities and the imprecision of previously developed (reference) probabilities, fuzzy aggregation methods based on FST were employed to derive the occurrence probabilities of severe accidents via four phases: 1) choosing experts, 2) quantifying weighting factors for the experts, 3) aggregating the experts' opinions, and 4) defuzzifying the fuzzy numbers. In this way, this study obtained expert elicitation results in the form of updated occurrence probabilities of severe accident phenomena in the OPR-1000 plant, after which the differences between the reference probabilities and the newly acquired probabilities using fuzzy aggregation were compared, with the advantages of the fuzzy technique over other approaches explained. Lastly, the impact of applying the updated severe accident probabilities on containment integrity was quantitatively investigated in a Level 2 PSA model.

The Fuzzy Power Function of a Test

강만기,정지영,박영례,최규탁 한국지능시스템학회 2007 한국지능시스템학회 학술발표 논문집 Vol.17 No.2

We introduction some properties for fuzzy power function of performance of a test. First we define fuzzy type I error and type II error for the probability of the two types of error. And we show that an fuzzy error probability of one kind can only be reduced at cost of increasing the other fuzzy error probability.

NORMAL FUZZY PROBABILITY FOR GENERALIZED QUADRATIC FUZZY SETS

김창일,윤용식 충청수학회 2012 충청수학회지 Vol.25 No.2

A generalized quadratic fuzzy set is a generalization of a quadratic fuzzy number. Zadeh dees the probability of the fuzzy event using the probability. We dee the normal fuzzy prob-ability on R using the normal distribution. And we calculate the normal fuzzy probability for generalized quadratic fuzzy sets.

무선 센서 네트워크에서 동적 여과를 위한 퍼지 기반 확률 조절 기법

한만호,이해영,조대호 한국정보통신설비학회 2008 한국정보통신설비학회 학술대회 Vol.2008 No.1

Generally, sensor nodes can be easily compromised and seized by an adversary because sensor nodes are hostile environments after dissemination. An adversary may be various security attacks into the networks using compromised node. False data injection attack using compromised node, it may not only cause false alarms, but also the depletion of the severe amount of energy waste. Dynamic en-route scheme for Filtering False Data Injection (DEF) can detect and drop such forged report during the forwarding process. In this scheme, each forwarding nodes verify reports using a regular probability. In this paper, we propose verification probability adjustment scheme of forwarding nodes though a fuzzy rule-base system for the Dynamic en-route filtering scheme for Filtering False Data Injection in sensor networks. Verification probability determination of forwarding nodes use false traffic rate and distance form source to base station.

Stability and Stabilization for Discrete-time Markovian Jump Fuzzy Systems with Time-varying Delays: Partially Known Transition Probabilities Case

송민국,박진배,주영훈 제어·로봇·시스템학회 2013 International Journal of Control, Automation, and Vol.11 No.1

This paper focuses on the stability analysis and the stabilization problem for a discrete-time Markovian jump fuzzy systems (MJFSs) with time-varying delays and partially known transition probabilities. These systems are made more general, by relaxing the traditional assumption in MJFSs that all the transition probabilities must be completely known. The class of MJFSs considered is described by a fuzzy model composed of two levels: a crisp level that represents the jumps and a fuzzy level that represents the system nonlinearities. Based on a stochastic Lyapunov function, stability and stabilization conditions for the MJFSs with time-varying delays are derived in both the case of completely known transition probabilities and the case of partially known transition probabilities. The derived conditions are represented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is used to illustrate the effectiveness of the proposed theorem.

Normal fuzzy probability for generalized triangular fuzzy sets

강철,윤용식,Kang, Chul,Yun, Yong-Sik Korean Institute of Intelligent Systems 2012 한국지능시스템학회논문지 Vol.22 No.2

확률공간 (${\Omega}$, $\mathfrak{F}$, $P$) 위에 정의된 퍼지집합을 퍼지이벤트라 한다. Zadeh는 확률 $P$를 이용하여 퍼지이벤트 $A$에 대한 확률을 정의하였다. 우리는 일반화된 삼각퍼지집합을 정의하고 거기에 확장된 대수적 작용소를 적용하였다. 일반화된 삼각퍼지집합은 대칭적이지만 함숫값으로 1을 갖지 않을 수 있다. 두 개의 일반화된 삼각퍼지집합 $A$와 $B$에 대하여 $A(+)B$와 $A(-)B$는 일반화된 사다리꼴퍼지집합이 되었지만, $A({\cdot})B$와 $A(/)B$는 일반화된 삼각퍼지집합도 되지 않았고 일반화된 사다리꼴퍼지집합도 되지 않았다. 그리고 정규분포를 이용하여 $\mathbb{R}$위에서 정규퍼지확률을 정의하였다. 그리고 일반화된 삼각퍼지집합에 대한 정규퍼지확률을 계산하였다. 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.