• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2006년도 춘계학술대회 학술발표 논문집 제16권 제1호
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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.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.15-15
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• 2000

In the past couple of years, there has been increasing interest in the fusion of neural networks and fuzzy logic. Most of the existing fused models have been proposed to implement different types of fuzzy reasoning mechanisms and inevitably they suffer from the dimensionality problem when dealing with complex real-world problem. To overcome the problem, we propose the self-organizing networks with activation nodes based on fuzzy inference and polynomial function. The proposed model consists of two parts, one is fuzzy nodes which each node is operated as a small fuzzy system with fuzzy implication rules, and its fuzzy system operates with Gaussian or triangular MF in Premise part and constant or regression polynomials in consequence part. the other is polynomial nodes which several types of high-order polynomials such as linear, quadratic, and cubic form are used and are connected as various kinds of multi-variable inputs. To demonstrate the effectiveness of the proposed method, time series data for gas furnace process has been applied.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2005년도 제36회 하계학술대회 논문집 D
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• pp.2873-2875
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• 2005

The optimal structure of the conventional Fuzzy Polynomial Neural Networks (FPNN)[3] depends on experience of designer. For the conventional Fuzzy Polynomial Neural Networks, input variable number, number of input variable, number of Membership Functions(MFs) and consequence structures are selected through the experience of a model designer iteratively. In this paper, we propose the new design methodology to find the optimal structure of Fuzzy Polymomial Neural Network by using Genetic Algorithms(GAs)[4, 5]. In the sequel, It is shown that the proposed Advanced Genetic Algorithms based Fuzzy Polynomial Neural Network(Advanced GAs-based FPNN) is more useful and effective than the existing models for nonlinear process. We used Medical Imaging System(MIS)[6] data to evaluate the performance of the proposed model.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1998년도 제13차 학술회의논문집
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• pp.254-259
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• 1998

A new design methology is proposed to identify the structure and parameters of fuzzy model using PNN and a fuzzy inference method. The PNN is the extended structure of the GMDH(Group Method of Data Handling), and uses several types of polynomials such as linear, quadratic and cubic besides the biquadratic polynomial used in the GMDH. The FPNN(Fuzzy Polynomial Neural Networks) algorithm uses PNN(Polynomial Neural networks) structure and a fuzzy inference method. In the fuzzy inference method, the simplified and regression polynomial inference methods are used. Here a regression polynomial inference is based on consequence of fuzzy rules with a polynomial equations such as linear, quadratic and cubic equation. Each node of the FPNN is defined as fuzzy rules and its structure is a kind of neuro-fuzzy architecture. In this paper, we will consider a model that combines the advantage of both FPNN and PNN. Also we use the training and testing data set to obtain a balance between the approximation and generalization of process model. Several numerical examples are used to evaluate the performance of the our proposed model.

• 전기학회논문지
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• 제64권1호
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• pp.128-135
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• 2015

In this study, we develop the very short-term precipitation forecasting model as well as classifier based on polynomial radial basis function neural networks by using AWS(Automatic Weather Station) and KLAPS(Korea Local Analysis and Prediction System) meteorological data. The polynomial-based radial basis function neural networks is designed to realize precipitation forecasting model as well as classifier. The structure of the proposed RBFNNs consists of three modules such as condition, conclusion, and inference phase. The input space of the condition phase is divided by using Fuzzy C-means(FCM) and the local area of the conclusion phase is represented as four types of polynomial functions. The coefficients of connection weights are estimated by weighted least square estimation(WLSE) for modeling as well as least square estimation(LSE) method for classifier. The final output of the inference phase is obtained through fuzzy inference method. The essential parameters of the proposed model and classifier such ad input variable, polynomial order type, the number of rules, and fuzzification coefficient are optimized by means of Particle Swarm Optimization(PSO) and Differential Evolution(DE). The performance of the proposed precipitation forecasting system is evaluated by using KLAPS meteorological data.

• 전기학회논문지
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• 제66권12호
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• pp.1772-1781
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• 2017

In this study, the design methodology for alleviating the overfitting problem of Polynomial Neural Networks(PNN) is realized with the aid of two kinds techniques such as L2 regularization and Sum of Squared Coefficients (SSC). The PNN is widely used as a kind of mathematical modeling methods such as the identification of linear system by input/output data and the regression analysis modeling method for prediction problem. PNN is an algorithm that obtains preferred network structure by generating consecutive layers as well as nodes by using a multivariate polynomial subexpression. It has much fewer nodes and more flexible adaptability than existing neural network algorithms. However, such algorithms lead to overfitting problems due to noise sensitivity as well as excessive trainning while generation of successive network layers. To alleviate such overfitting problem and also effectively design its ensuing deep network structure, two techniques are introduced. That is we use the two techniques of both SSC(Sum of Squared Coefficients) and $L_2$ regularization for consecutive generation of each layer's nodes as well as each layer in order to construct the deep PNN structure. The technique of $L_2$ regularization is used for the minimum coefficient estimation by adding penalty term to cost function. $L_2$ regularization is a kind of representative methods of reducing the influence of noise by flattening the solution space and also lessening coefficient size. The technique for the SSC is implemented for the minimization of Sum of Squared Coefficients of polynomial instead of using the square of errors. In the sequel, the overfitting problem of the deep PNN structure is stabilized by the proposed method. This study leads to the possibility of deep network structure design as well as big data processing and also the superiority of the network performance through experiments is shown.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2004년도 추계학술대회 학술발표 논문집 제14권 제2호
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• pp.433-436
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• 2004

In this paper, we introduce a new Fuzzy Polynomial Neural Networks (FPNNS)-like structure whose neuron is based on the Fuzzy Set-based Fuzzy Inference System (FS-FIS) and is different from that of FPNNS based on the Fuzzy relation-based Fuzzy Inference System (FR-FIS) and discuss the ability of the new FPNNS-like structure named Fuzzy Set-based Polynomial Neural Networks (FSPNN). The premise parts of their fuzzy rules are not identical, while the consequent parts of the both Networks (such as FPNN and FSPNN) are identical. This difference results from the angle of a viewpoint of partition of input space of system. In other word, from a point of view of FS-FIS, the input variables are mutually independent under input space of system, while from a viewpoint of FR-FIS they are related each other. The proposed design procedure for networks architecture involves the selection of appropriate nodes with specific local characteristics such as the number of input variables, the order of the polynomial that is constant, linear, quadratic, or modified quadratic functions being viewed as the consequent part of fuzzy rules, and a collection of the specific subset of input variables. On the parameter optimization phase, we adopt Information Granulation (IC) based on HCM clustering algorithm and a standard least square method-based learning. Through the consecutive process of such structural and parametric optimization, an optimized and flexible fuzzy neural network is generated in a dynamic fashion. To evaluate the performance of the genetically optimized FSPNN (gFSPNN), the model is experimented with using the time series dataset of gas furnace process.

• 전기학회논문지
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• 제60권4호
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• pp.862-870
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• 2011

In this paper, we introduce a new topology of Radial Basis Function-based Polynomial Neural Networks (RPNN) that is based on a genetically optimized multi-layer perceptron with Radial Polynomial Neurons (RPNs). This study offers a comprehensive design methodology involving mechanisms of optimization algorithms, especially Fuzzy C-Means (FCM) clustering method and Particle Swarm Optimization (PSO) algorithms. In contrast to the typical architectures encountered in Polynomial Neural Networks (PNNs), our main objective is to develop a design strategy of RPNNs as follows : (a) The architecture of the proposed network consists of Radial Polynomial Neurons (RPNs). In here, the RPN is fully reflective of the structure encountered in numeric data which are granulated with the aid of Fuzzy C-Means (FCM) clustering method. The RPN dwells on the concepts of a collection of radial basis function and the function-based nonlinear (polynomial) processing. (b) The PSO-based design procedure being applied at each layer of RPNN leads to the selection of preferred nodes of the network (RPNs) whose local characteristics (such as the number of input variables, a collection of the specific subset of input variables, the order of the polynomial, and the number of clusters as well as a fuzzification coefficient in the FCM clustering) can be easily adjusted. The performance of the RPNN is quantified through the experimentation where we use a number of modeling benchmarks - NOx emission process data of gas turbine power plant and learning machine data(Automobile Miles Per Gallon Data) already experimented with in fuzzy or neurofuzzy modeling. A comparative analysis reveals that the proposed RPNN exhibits higher accuracy and superb predictive capability in comparison to some previous models available in the literature.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1999년도 하계학술대회 논문집 G
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• pp.2856-2858
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• 1999

In this paper, the FPNN(Fuzzy Polynomial Neural Networks) algorithm with multi-layer fuzzy inference structure is proposed for the model identification of a complex nonlinear system. The FPNN structure is generated from the mutual combination of PNN (Polynomial Neural Network) structure and fuzzy inference method. The PNN extended from the GMDH(Group Method of Data Handling) uses several types of polynomials such as linear, quadratic and modifled quadratic besides the biquadratic polynomial used in the GMDH. In the fuzzy inference method, simplified and regression polynomial inference method which is based on the consequence of fuzzy rule expressed with a polynomial such as linear, quadratic and modified quadratic equation are used Each node of the FPNN is defined as a fuzzy rule and its structure is a kind of fuzzy-neural networks. Gas furnace data used to evaluate the performance of our proposed model.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제13권7호
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• pp.3690-3713
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• 2019

According to the main group key management schemes logical key hierarchy (LKH), exclusion basis systems (EBS) and other group key schemes are limited in network structure, collusion attack, high energy consumption, and the single point of failure, this paper presents a group key management scheme for wireless sensor networks based on Lagrange interpolation polynomial characteristic (AGKMS). That Chinese remainder theorem is turned into a Lagrange interpolation polynomial based on the function property of Chinese remainder theorem firstly. And then the base station (BS) generates a Lagrange interpolation polynomial function f(x) and turns it to be a mix-function f(x)' based on the key information m(i) of node i. In the end, node i can obtain the group key K by receiving the message f(m(i))' from the cluster head node j. The analysis results of safety performance show that AGKMS has good network security, key independence, anti-capture, low storage cost, low computation cost, and good scalability.