• Journal of the Korean Data and Information Science Society
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• v.14 no.1
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• pp.131-141
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• 2003

In this paper, we prove that multi-variate fuzzy polynomials are universal approximators for multi-variate fuzzy functions which are the extension principle of continuous real-valued function under $T_W-based$ fuzzy arithmetic operations for a distance measure that Buckley et al.(1999) used. We also consider a class of fuzzy polynomial regression model. A mixed non-linear programming approach is used to derive the satisfying solution.

• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.695-705
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• 2003

In this article, we propose a regression and correlation analysis via dynamic graphs and implement them in Java Web Start. For the polynomial relations between dependent and independent variables, dynamic graphics are implemented for both polynomial regression and spline estimates for an instant model selection. The results include basic statistics. They are available both as a web-based service and an application.

• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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• pp.1289-1295
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• 2008

We find the generalized characteristic polynomial of graphs G($F_{1},F_{2},{\cdots},F_{v}$) the semi-zigzag product of G and ${\{F_{i}\}^{v}_{i=1}$ obtained from G by replacing vertices by circulant graphs of vertices and joining $F_{i}$'s along the edges of G. These graphs contain discrete tori and are key examples in the study of network model.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.6
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• pp.415-424
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• 2004

In this paper, we introduce and investigate a new category of rule-based fuzzy inference system based on Information Granulation(IG). The proposed rule-based fuzzy modeling implements system structure and parameter identification in the efficient form of “If..., then...” statements, and exploits the theory of system optimization and fuzzy implication rules. The form of the fuzzy rules comes with three types of fuzzy inferences: a simplified one that involves conclusions that are fixed numeric values, a linear one where the conclusion part is viewed as a linear function of inputs, and a regression polynomial one as the extended type of the linear one. By the nature of the rule-based fuzzy systems, these fuzzy models are geared toward capturing relationships between information granules. The form of the information granules themselves becomes an important design features of the fuzzy model. Information granulation with the aid of HCM(Hard C-Means) clustering algorithm hell)s determine the initial parameters of rule-based fuzzy model such as the initial apexes of the membership functions and the initial values of polynomial function being used in the Premise and consequence Part of the fuzzy rules. And then the initial Parameters are tuned (adjusted) effectively with the aid of the improved complex method(ICM) and the standard least square method(LSM). In the sequel, the ICM and LSM lead to fine-tuning of the parameters of premise membership functions and consequent polynomial functions in the rules of fuzzy model. An aggregate objective function with a weighting factor is proposed in order to achieve a balance between performance of the fuzzy model. Numerical examples are included to evaluate the performance of the proposed model. They are also contrasted with the performance of the fuzzy models existing in the literature.

• Animal Bioscience
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• v.37 no.8
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• pp.1333-1344
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• 2024

Objective: Litter size and piglet loss at birth significantly impact piglet production and are closely associated with sow parity. Understanding how these traits vary across different parities is crucial for effective herd management. This study investigates the patterns of the number of born alive piglets (NBA), number of piglet losses (NPL), and the proportion of piglet losses (PPL) at birth in Landrace sows under tropical conditions. Additionally, it aims to identify the most suitable model for describing these patterns. Methods: A dataset comprising 2,322 consecutive reproductive records from 258 Landrace sows, spanning parities from 1 to 9, was analyzed. Modeling approaches including 2nd and 3rd degree polynomial models, the Wood gamma function, and a longitudinal model were applied at the individual level to predict NBA, NPL, and PPL. The choice of the best-fitting model was determined based on the lowest mean and standard deviation of the difference between predicted and actual values, Akaike information criterion (AIC), and Bayesian information criterion (BIC). Results: Sow parity significantly influenced NBA, NPL, and PPL (p<0.0001). NBA increased until the 4th parity and then declined. In contrast, NPL and PPL decreased until the 2nd parity and then steadily increased until the 8th parity. The 2nd and 3rd degree polynomials, and longitudinal models showed no significant differences in predicting NBA, NPL, and PPL (p>0.05). The 3rd degree polynomial model had the lowest prediction standard deviation and yielded the smallest AIC and BIC. Conclusion: The 3rd degree polynomial model offers the most suitable description of NBA, NPL, and PPL patterns. It holds promise for applications in genetic evaluations to enhance litter size and reduce piglet loss at birth in sows. These findings highlight the importance of accounting for sow parity effects in swine breeding programs, particularly in tropical conditions, to optimize piglet production and sow performance.

• Journal of the Korean Institute of Intelligent Systems
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• v.7 no.2
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• pp.96-105
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• 1997

In this paper, A new design method of fuzzy modeling is presented for the model identification of nonlinear complex systems. The proposed FPNN(Fuzzy Polynomial Neural Network) modeling implements system structure and parameter identification using GMDH(Group Method of Data Handling) method and linguistic fuzzy implication rules from input and output data of processes. In order to identify premise structure and parameter of fuzzy implication rules, GMDH method and regression polynomial fuzzy reasoning method are used and the least square method is utilized for the identification of optimum consequence parameters. Time series data for gas furnace and those for wastewater treatment process are used for the purpose of evaluating the performance of the proposed FPNN modeling. The results show that the proposed method can produce the fuzzy model with higher accuracy than other works achieved previously.

• Proceedings of the KIEE Conference
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• 2003.07d
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• pp.2627-2629
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• 2003

In this paper, we propose a new architecture of Genetic Algorithms(GAs)-based Self-Organizing Polynomial Neural Networks(SOPNN). The conventional SOPNN is based on the extended Group Method of Data Handling(GMDH) method and utilized the polynomial order (viz. linear, quadratic, and modified quadratic) as well as the number of node inputs fixed (selected in advance by designer) at Polynomial Neurons (or nodes) located in each layer through a growth process of the network. Moreover it does not guarantee that the SOPNN generated through learning has the optimal network architecture. But the proposed GA-based SOPNN enable the architecture to be a structurally more optimized networks, and to be much more flexible and preferable neural network than the conventional SOPNN. An aggregate performance index with a weighting factor is proposed in order to achieve a sound balance between approximation and generalization (predictive) abilities of the model. To evaluate the performance of the GA-based SOPNN, the model is experimented with using nonlinear system data.

• Geomechanics and Engineering
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• v.30 no.6
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• pp.551-564
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• 2022

Fragmenting the rock mass is considered as the most important work in open-pit mines. Ground vibration is the most hazardous issue of blasting which can cause critical damage to the surrounding structures. This paper focuses on developing an explicit model to predict the ground vibration through an multi objective evolutionary polynomial regression (MOGA-EPR). To this end, a database including 79 sets of data related to a quarry site in Malaysia were used. In addition, a gene expression programming (GEP) model and several empirical equations were employed to predict ground vibration, and their performances were then compared with the MOGA-EPR model using the mean absolute error (MAE), root mean square error (RMSE), mean (𝜇), standard deviation of the mean (𝜎), coefficient of determination (R²) and a20-index. Comparing the results, it was found that the MOGA-EPR model predicted the ground vibration more precisely than the GEP model and the empirical equations, where the MOGA-EPR scored lower MAE and RMSE, 𝜇 and 𝜎 closer to the optimum value, and higher R² and a20-index. Accordingly, the proposed MOGA-EPR model can be introduced as a useful method to predict ground vibration and has the capacity to be generalized to predict other blasting effects.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.5 no.1
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• pp.43-48
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• 1987

The terrain is classified by the parameters-gradient, curuature, bump frequency and the ratio of the surface area to the corresponding planar area- that indicate the quantitative measurement of the terrain roughness, and the terrain is fitted to the polynomial function. According to the terrain roughness, the flat terrain, the gently undulating terrain, the rough terrain are classified The flat terrain, the gently undulating terrain and the rough terrain are fitted to the plane function, the 3th or 5th polynomial function and the 5th polynomial function, respectively.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2006.05a
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• pp.113-116
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• 2006

본 논문은 소프트웨어 공정에 대하여 기호코팅을 이용한 유전자 알고리즘 기반 퍼지 다항식 뉴럴 네트워크 (Genetic Algorithms-based Fuzzy Polynomial Neural Networks ; gFPNN)의 모델을 제안한다. 유전자 알고리즘에는 이진코딩, 기호코팅, 실수코딩이 있다. 제안된 모델은 스트링의 길이에 따른 해밍절벽을 기호코딩으로 극복하였다. gFPNN에 전반부 멤버쉽 함수는 삼각형과 가우시안형의 멤버쉽 함수가 사용된다. 그리고 규칙의 후반부는 간략, 선형, 이차식 그리고 변형된 이차식 함수에 의해 설계된다. 실험적 예제를 통하여 제안된 모델의 성능이 근사화 능력과 일반화 능력이 우수함을 보인다.