• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.7
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• pp.378-388
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• 2000

In this paper, we propose Fuzzy Polynomial Neural Networks(FPNN) based on Polynomial Neural Networks(PNN) and Fuzzy Neural Networks(FNN) for model identification of complex and nonlinear systems. The proposed FPNN is generated from the mutually combined structure of both FNN and PNN. The one and the other are considered as the premise part and consequence part of FPNN structure respectively. As the consequence part of FPNN, PNN is based on Group Method of Data Handling(GMDH) method and its structure is similar to Neural Networks. But the structure of PNN is not fixed like in conventional Neural Networks and self-organizing networks that can be generated. FPNN is available effectively for multi-input variables and high-order polynomial according to the combination of FNN with PNN. Accordingly it is possible to consider the nonlinearity characteristics of process and to get better output performance with superb predictive ability. As the premise part of FPNN, FNN uses both the simplified fuzzy inference as fuzzy inference method and error back-propagation algorithm as learning rule. The parameters such as parameters of membership functions, learning rates and momentum coefficients are adjusted using genetic algorithms. And we use two kinds of FNN structure according to the division method of fuzzy space of input variables. One is basic FNN structure and uses fuzzy input space divided by each separated input variable, the other is modified FNN structure and uses fuzzy input space divided by mutually combined input variables. In order to evaluate the performance of proposed models, we use the nonlinear function and traffic route choice process. The results show that the proposed FPNN can produce the model with higher accuracy and more robustness than any other method presented previously. And also performance index related to the approximation and prediction capabilities of model is evaluated and discussed.

• Proceedings of the KIEE Conference
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• 2003.07d
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• pp.2633-2635
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• 2003

In this study, we propose a fuzzy polynomial neural networks (FPNN) and a genetically optimized fuzzy polynomial neural networks(GoFPNN) for identification of non-linear system. GoFPNN architecture is designed by a FPNN based on fuzzy set and its structure and parameters are optimized by genetic algorithms. A fuzzy neural networks(FNN) based on fuzzy set divide into two structures that is simplified inference structure and linear inference structure. The proposed FPNN is resulted from integration and extension of simplified and linear inference structure of FNN. The consequence structure of the FPNN consist of polynomials represented by networks using connection weights for rules. The networks comprehend simplified(Type 0), linear (Type 1), and quadratic(Type 3) inferences. The proposed FPNN can select polynomial type of consequence part for each rule. Therefore, proposed scheme can offer flexible structure design capability for a system characteristics. Moreover, GAs is applied to networks structure and parameters tuning of proposed FPNN, and its efficient application method is discussed, these subjects are result in GoFPNN that is optimal FPNN. To evaluate proposed model performance, a numerical experiment is carried out.

• Proceedings of the KIEE Conference
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• 2005.05a
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• pp.6-8
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• 2005

In this paper, we discuss model identification of nonlinear data using GAs-based Fuzzy Polynomial Neural Networks(GAs-FPNN). Fuzzy Polynomial Neural Networks(FPNN) is proposed model based Group Method Data Handling(GMDH) and Neural Networks(NNs). Each node of FPNN is expressed Fuzzy Polynomial Neuron(FPN). Network structure of nonlinear data is created using Genetic Algorithms(GAs) of optimal search method. Accordingly, GAs-FPNN have more inflexible than the existing models (in)from structure selecting. The proposed model select and identify its for optimal search of Genetic Algorithms that are no. of input variables, input variable numbers and consequence structures. The GAs-FPNN model is select tuning to input variable number, number of input variable and the last part structure through optimal search of Genetic Algorithms. It is shown that nonlinear data model design using Genetic Algorithms based FPNN is more usefulness and effectiveness than the existing models.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.8
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• pp.664-674
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• 2001

In this paper, as a new category of fuzzy-neural networks architecture, we propose Fuzzy Polynomial Neural Networks (FPNN) and discuss a comprehensive design methodology related to its architecture. FPNN dwells on the ideas of fuzzy rule-based computing and neural networks. The FPNN architecture consists of layers with activation nodes based on fuzzy inference rules. Here each activation node is presented as Fuzzy Polynomial Neuron(FPN). The conclusion part of the rules, especially the regression polynomial, uses several types of high-order polynomials such as linear, quadratic and modified quadratic. As the premise part of the rules, both triangular and Gaussian-like membership functions are studied. It is worth stressing that the number of the layers and the nods in each layer of the FPNN are not predetermined, unlike in the case of the popular multilayer perceptron structure, but these are generated in a dynamic manner. With the aid of two representative time series process data, a detailed design procedure is discussed, and the stability is introduced as a measure of stability of the model for the comparative analysis of various architectures.

• Proceedings of the KIEE Conference
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• 2000.07d
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• pp.2946-2948
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• 2000

In this paper, we proposed the Fuzzy Polynomial Neural Networks(FPNN) model with fuzzy activation node. The proposed FPNN structure is generated from the mutual combination of PNN(Polynomial Neural Networks) structure and fuzzy inference system. The premise of fuzzy inference rules defines by triangular and gaussian type membership function. The fuzzy inference method uses 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. The structure of FPNN is not fixed like in conventional Neural Networks and can be generated. The design procedure to obtain an optimal model structure utilizing FPNN algorithm is shown in each stage. Gas furnace time series data used to evaluate the performance of our proposed model.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.1
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• pp.33-38
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• 2006

In this paper, we propose a new architecture of Fuzzy Polynomial Neural Networks(FPNN) by means of genetically optimized Fuzzy Polynomial Neuron(FPN) and discuss its comprehensive design methodology involving mechanisms of genetic optimization, especially Genetic Algorithms(GAs). The conventional FPNN developed so far are based on mechanisms of self-organization and evolutionary optimization. The design of the network exploits the extended Group Method of Data Handling(GMDH) with some essential parameters of the network being provided by the designer and kept fixed throughout the overall development process. This restriction may hamper a possibility of producing an optimal architecture of the model. The proposed FPNN gives rise to a structurally optimized network and comes with a substantial level of flexibility in comparison to the one we encounter in conventional FPNNs. It is shown that the proposed advanced genetic algorithms based Fuzzy Polynomial Neural Networks is more useful and effective than the existing models for nonlinear process. We experimented with Medical Imaging System(MIS) dataset to evaluate the performance of the proposed model.

• Proceedings of the KIEE Conference
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• 2004.11c
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• pp.346-348
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• 2004

In this rarer, 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 structurenamed 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. In considering the structures of FPNN-like networks such as FPNN and FSPNN, they are almost similar. Therefore they have the same shortcomings as well as the same virtues on structural side. 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 (IG) 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 gas furnace process dataset.

• Proceedings of the KIEE Conference
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• 1999.07g
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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.

• Proceedings of the KIEE Conference
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• 2005.10b
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• pp.152-154
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• 2005

In this paper, we propose a new architecture of Fuzzy Polynomial Neural Networks(FPNN) by means of genetically optimized Fuzzy Polynomial Neuron(FPN) and discuss its comprehensive design methodology involving mechanisms of genetic optimization, especially Genetic Algorithms(GAs). The design of the network exploits the extended Group Method of Data Handling(GMDH) with some essential parameters of the network being provided by the designer and kept fixed throughout the overall development process. This restriction may hamper a possibility of producing an optimal architecture of the model. The proposed FPNN gives rise to a structurally optimized network and comes with a substantial level of flexibility in comparison to the one we encounter in conventional FPNNs. It is shown that the proposed genetic algorithms-based Fuzzy Polynomial Neural Networks is more useful and effective than the existing models for nonlinear process. We experimented with Medical Imaging System(MIS) dataset to evaluate the performance of the proposed model.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.10a
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• pp.429-432
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• 2004

본 논문은 기존의 퍼지 다항식 뉴럴 네트워크 (Fuzzy Polynomial Neural Networks ; FPNN) 모델을 이용하여 비선형성 데이터에 대한 추론을 제안한다. 복잡한 비선형 시스템의 모델동정을 위하여 생성된 GMDH 방법에 기초한 FPNN의 각 노드는 퍼지 규칙을 기반으로 구축되었으며, 층이 진행되는 동안 모델 스스로 노드의 선택과 제거를 통해 최적의 네트워크 구조를 생성할 수 있는 유연성을 가지고 있다. FPNN 각각의 활성노드를 퍼지다항식 뉴론(Fuzzy Polynomial Neuron ; FPN)이라고 표현한다. FPNN의 후반부 구조는 입출력 변수 사이 의 간략과 회귀다항식 (1차, 2차, 변형된 2차식) 함수에 의해 구현된다. 규칙의 전반부 멤버쉽 함수는 삼각형과 가우시안형의 멤버쉽 함수가 사용된다. 또한 유전자 알고리즘을 사용하여 각노드의 부분표현식을 구성하는 입력변수의 수, 입력변수와 차수의 선택 동조를 통하여 최적의 Genetic Algorithms(GAs)을 이용한 FPNN모델을 설계하는 것이 유용하고 효과적임을 보인다.