• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.7
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• pp.1315-1320
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• 2007

In this paper, we introduce a new fuzzy model called fuzzy combined polynomial neural networks, which are based on the representative fuzzy model named polynomial fuzzy model. In the design procedure of the proposed fuzzy model, the coefficients on consequent parts are estimated by using not general least square estimation algorithm that is a sort of global learning algorithm but weighted least square estimation algorithm, a sort of local learning algorithm. We are able to adopt various type of structures as the consequent part of fuzzy model when using a local learning algorithm. Among various structures, we select Polynomial Neural Networks which have nonlinear characteristic and the final result of which is a complex mathematical polynomial. The approximation ability of the proposed model can be improved using Polynomial Neural Networks as the consequent part.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.05a
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• pp.130-133
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• 2000

In this paper, a new design methodology named FNNN(Fuzzy Polynomial Neural Network) algorithm is proposed to identify the structure and parameters of fuzzy model using PNN(Polynomial Neural Network) structure 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 modified quadratic besides the biquadratic polynomial used in the GMDH. 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. Each node of the FPNN is defined as fuzzy rules and its structure is a kind of neuro-fuzzy architecture Several numerical example are used to evaluate the performance of out proposed model. Also we used the training data and testing data set to obtain a balance between the approximation and generalization of proposed model.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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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.

• Proceedings of the KIEE Conference
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• 2005.10b
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• pp.322-324
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• 2005

In this paper, we introduce the advanced Self-Organizing Fuzzy Polynomial Neural Network based on optimized FPN by evolutionary algorithm and discuss its comprehensive design methodology involving mechanisms of genetic optimization, especially genetic algorithms (GAs). The proposed model gives rise to a structurally and parametrically optimized network through an optimal parameters design available within Fuzzy Polynomial Neuron(FPN) by means of GA. Through the consecutive process of such structural and parametric optimization, an optimized and flexible the proposed model is generated in a dynamic fashion. The performance of the proposed model is quantified through experimentation that exploits standard data already used in fuzzy modeling. These results reveal superiority of the proposed networks over the existing fuzzy and neural models.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.63 no.4
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• pp.534-540
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• 2014

In this paper, we propose a fuzzy combined Polynomial Neural Network(PNN) for pattern classification. The fuzzy combined PNN comes from the generic TSK fuzzy model with several linear polynomial as the consequent part and is the expanded version of the fuzzy model. The proposed pattern classifier has the polynomial neural networks as the consequent part, instead of the general linear polynomial. PNNs are implemented by stacking the simple polynomials dynamically. To implement one layer of PNNs, the various types of simple polynomials are used so that PNNs have flexibility and versatility. Although the structural complexity of the implemented PNNs is high, the PNNs become a high order-multi input polynomial finally. To estimate the coefficients of a polynomial neuron, The weighted linear discriminant analysis. The output of fuzzy rule system with PNNs as the consequent part is the linear combination of the output of several PNNs. To evaluate the classification ability of the proposed pattern classifier, we make some experiments with several machine learning data sets.

• 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.

• 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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• 2005.07d
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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.

• Proceedings of the KIEE Conference
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• 2006.04a
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• pp.270-272
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• 2006

In this paper, we discuss optimal design of Fuzzy Polynomial Neural Networks by means of Genetic Algorithms(GAs) using symbolic coding for non-linear data. One of the major subject of genetic algorithms is representation of chromosomes. The proposed model optimized by the means genetic algorithms which used symbolic code to represent chromosomes. The proposed gFPNN used 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. The performance of the proposed model is quantified through experimentation that exploits standard data already used in fuzzy modeling. These results reveal superiority of the proposed networks over the existing fuzzy and neural models.