• 대한수학회논문집
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• 제21권2호
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• pp.385-395
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• 2006

We study the exponential fuzzy probability for quadratic fuzzy number and trigonometric fuzzy number defined by quadratic function and trigonometric function, respectively. And we calculate the exponential fuzzy probabilities for fuzzy numbers driven by operations.

• 충청수학회지
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• 제25권2호
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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.

• Coupled systems mechanics
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• 제2권3호
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• pp.255-269
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• 2013

This paper targets to investigate the solution of fuzzy quadratic Riccati differential equations with various types of fuzzy environment using Homotopy Perturbation Method (HPM). Fuzzy convex normalized sets are used for the fuzzy parameter and variables. Obtained results are depicted in term of plots to show the efficiency of the proposed method.

• East Asian mathematical journal
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• 제36권5호
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• pp.561-570
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• 2020

We compute the extended four operations of the 2-dimensional quadratic fuzzy numbers. Then we calculate the intersection between a plane perpendicular to the x-axis, which passes through each vertex, and the resulting 2-dimensional quadratic fuzzy number. We confirm that the equations of the two intersections acquired in this way and the graphs are actually identical, respectively.

• 한국지능시스템학회논문지
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• 제15권3호
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• pp.277-281
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• 2005

2차 곡선들에 의해 정의되는 두 개의 2차 퍼지수의 연산들에 대하여 연구하였다. 그리고 그 연산들에 의하여 생성되는 퍼지수들에 대한 정규 퍼지 확률을 계산하였다.

• 충청수학회지
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• 제27권1호
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• pp.123-132
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• 2014

In this paper, we investigate the following form of a certain class of quadratic functional equations and its fuzzy stability. $$f(kx+y)+f(kx-y)=f(x+y)+f(x-y)-2(1-k^2)f(x)$$ where k is a fixed rational number with $k{\neq}1$, -1, 0.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권3호
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• pp.247-263
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• 2016

Let $M_{1}f(x,y):=\frac{3}{4}f(x+y)-\frac{1}{4}f(-x-y)+\frac{1}{4}f(x-y)+\frac{1}{4}f(y-x)-f(x)-f(y)$, $M_{2}f(x,y):=2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})-f(x)-f(y)$. Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) $N(M_{1}f(x,y),t){\geq}N({\rho}M_{2}f(x,y),t)$ where ρ is a fixed real number with |ρ| < 1, and (0.2) $N(M_{2}f(x,y),t){\geq}N({\rho}M_{1}f(x,y),t)$ where ρ is a fixed real number with |ρ| < $\frac{1}{2}$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권2호
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• pp.163-179
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• 2016

Let $M_1f(x,y):=\frac{3}{4}f(x+y)-\frac{1}{4}f(-x-y)+\frac{1}{4}(x-y)+\frac{1}{4}f(y-x)-f(x)-f(y)$, $M_2f(x,y):=2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})-f(x)-f(y)$ Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) $N(M_1f(x,y)-{\rho}M_2f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$ and (0.2) $N(M_2f(x,y)-{\rho}M_1f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$ in fuzzy Banach spaces, where ρ is a fixed real number with ρ ≠ 1.

• 전기학회논문지
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• 제59권5호
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• pp.981-989
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• 2010

In this study, we introduce a new architecture of fuzzy inference system. In the fuzzy inference system, we use Fuzzy C-Means clustering algorithm to form the premise part of the rules. The membership functions standing in the premise part of fuzzy rules do not assume any explicit functional forms, but for any input the resulting activation levels of such radial basis functions directly depend upon the distance between data points by means of the Fuzzy C-Means clustering. As the consequent part of fuzzy rules of the fuzzy inference system (being the local model representing input output relation in the corresponding sub-space), four types of polynomial are considered, namely constant, linear, quadratic and modified quadratic. This offers a significant level of design flexibility as each rule could come with a different type of the local model in its consequence. Either the Least Square Estimator (LSE) or the weighted Least Square Estimator (WLSE)-based learning is exploited to estimate the coefficients of the consequent polynomial of fuzzy rules. In fuzzy modeling, complexity and interpretability (or simplicity) as well as accuracy of the obtained model are essential design criteria. The performance of the fuzzy inference system is directly affected by some parameters such as e.g., the fuzzification coefficient used in the FCM, the number of rules(clusters) and the order of polynomial in the consequent part of the rules. Accordingly we can obtain preferred model structure through an adjustment of such parameters of the fuzzy inference system. Moreover the comparative experimental study between WLSE and LSE is analyzed according to the change of the number of clusters(rules) as well as polynomial type. The superiority of the proposed model is illustrated and also demonstrated with the use of Automobile Miles per Gallon(MPG), Boston housing called Machine Learning dataset, and Mackey-glass time series dataset.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 학술대회 논문집 정보 및 제어부문
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• pp.337-339
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• 2004

In this paper, we discuss optimal design of Fuzzy Polynomial Neural Networks by means of Genetic Algorithms(GAs). Proceeding the layer, this model creates the optimal network architecture through the selection and the elimination of nodes by itself. So, there is characteristic of flexibility. We use a triangle and a Gaussian-like membership function in premise part of rules and design the consequent structure by constant and regression polynomial (linear, quadratic and modified quadratic) function between input and output variables. GAs is applied to improve the performance with optimal input variables and number of input variables and order. To evaluate the performance of the GAs-based FPNNs, the models are experimented with the use of Medical Imaging System(MIS) data.