• 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.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.39 no.3
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• pp.18-31
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• 2002

In this study, we introduce a concept of advanced neurofuzzy polynomial networks(ANFPN), a hybrid modeling architecture combining neurofuzzy networks(NFN) and polynomial neural networks(PNN). These networks are highly nonlinear rule-based models. The development of the ANFPN dwells on the technologies of Computational Intelligence(Cl), namely fuzzy sets, neural networks and genetic algorithms. NFN contributes to the formation of the premise part of the rule-based structure of the ANFPN. The consequence part of the ANFPN is designed using PNN. At the premise part of the ANFPN, NFN uses both the simplified fuzzy inference and error back-propagation learning rule. The parameters of the membership functions, learning rates and momentum coefficients are adjusted with the use of genetic optimization. As the consequence structure of ANFPN, PNN is a flexible network architecture whose structure(topology) is developed through learning. In particular, the number of layers and nodes of the PNN are not fixed in advance but is generated in a dynamic way. In this study, we introduce two kinds of ANFPN architectures, namely the basic and the modified one. Here the basic and the modified architecture depend on the number of input variables and the order of polynomial in each layer of PNN structure. Owing to the specific features of two combined architectures, it is possible to consider the nonlinear characteristics of process system and to obtain the better output performance with superb predictive ability. The availability and feasibility of the ANFPN are discussed and illustrated with the aid of two representative numerical examples. The results show that the proposed ANFPN can produce the model with higher accuracy and predictive ability than any other method presented previously.

• 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 Korea Water Resources Association Conference
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• 2010.05a
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• pp.1596-1599
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• 2010

Group method of data handling neural networks model (GMDH-NNM) is used to estimate daily pan evaporation (PE) using limited climatic variables such as max temperature ($T_{max}$), min temperature ($T_{min}$), mean wind speed ($W_{mean}$), mean relative humidity ($RH_{mean}$) and sunshine duration (SD). And, for the performances of GMDH-NNM, it is composed of training and test performances, respectively. The training and test performances are carried out using daily time series data, respectively. From this research, we evaluate the impact of GMDH-NNM for the modeling of the nonlinear time series data. We should, thus, construct the credible data of the daily PE data using GMDH-NNM, and can suggest the methodology for the irrigation and drainage networks system. Furthermore, this research represents that the strong nonlinear relationship such as pan evaporation modeling can be generalized using GMDH-NNM.

• KIEE International Transaction on Systems and Control
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• v.12D no.1
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• pp.12-17
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• 2002

We propose a new category of neurofuzzy networks- Self-organizing Neural Networks(SONN) with fuzzy polynomial neurons(FPNs) and discuss a comprehensive design methodology supporting their development. Two kinds of SONN architectures, namely a basic SONN and a modified SONN architecture are dicussed. Each of them comes with two types such as the generic and the advanced type. SONN dwells on the ideas of fuzzy rule-based computing and neural networks. Simulation involves a series of synthetic as well as experimental data used across various neurofuzzy systems. A comparative analysis is included as well.

• Proceedings of the KIEE Conference
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• 2005.05a
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• pp.12-14
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• 2005

In this paper, we propose a new architecture of Self-Organizing Fuzzy Polynomial Neural Networks(SOFPNN) 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 SOFPNNs hinges on an extended Group Method of Data Handling(GMDH) and exploits a fixed fuzzy inference type in each FPN of the SOFPNN as well as considers a fixed number of input nodes located in each layer. The design procedure applied in the construction of each layer of a SOFPNN deals with its structural optimization involving the selection of preferred nodes (or FPNs) with specific local characteristics (such as the number of input variables, the order of the polynomial of the consequent part of fuzzy rules, a collection of the specific subset of input variables, and the number of membership function) and addresses specific aspects of parametric optimization. Therefore, the proposed SOFPNN gives rise to a structurally optimized structure and comes with a substantial level of flexibility in comparison to the one we encounter in conventional SOFPNNs. To evaluate the performance of the genetically optimized SOFPNN, the model is experimented with using two time series data(gas furnace and chaotic time series).

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.04a
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• pp.301-304
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• 2005

In this paper, we propose a new fuzzy set-based polynomial neuron (FSPN) involving the information granule, and new fuzzy-neural networks - Fuzzy Set based Polynomial Neural Networks (FSPNN). We have developed a design methodology (genetic optimization using Genetic Algorithms) to find the optimal structure for fuzzy-neural networks that expanded from Group Method of Data Handling (GMDH). It is the number of input variables, the order of the polynomial, the number of membership functions, and a collection of the specific subset of input variables that are the parameters of FSPNN fixed by aid of genetic optimization that has search capability to find the optimal solution on the solution space. We have been interested in the architecture of fuzzy rules that mimic the real world, namely sub-model (node) composing the fuzzy-neural networks. We adopt fuzzy set-based fuzzy rules as substitute for fuzzy relation-based fuzzy rules and apply the concept of Information Granulation to the proposed fuzzy set-based rules.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.2
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• pp.127-136
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• 2005

In this paper, a new architecture and comprehensive design methodology of genetically optimized Rule-based Fuzzy Polynomial Neural Networks(gRFPNN) are introduced and a series of numeric experiments are carried out. The architecture of the resulting gRFPNN results from asynergistic usage of the hybrid system generated by combining rule-based Fuzzy Neural Networks(FNN) with polynomial neural networks (PNN). FNN contributes to the formation of the premise part of the overall rule-based structure of the gRFPNN. The consequence part of the gRFPNN is designed using PNNs. At the premise part of the gRFPNN, FNN exploits fuzzy set based approach designed by using space partitioning in terms of individual variables and comes in two fuzzy inference forms: simplified and linear. As the consequence part of the gRFPNN, the development of the genetically optimized PNN dwells on two general optimization mechanism: the structural optimization is realized via GAs whereas in case of the parametric optimization we proceed with a standard least square method-based learning. To evaluate the performance of the gRFPNN, the models are experimented with the use of several representative numerical examples. A comparative analysis shows that the proposed gRFPNN are models with higher accuracy as well as more superb predictive capability than other intelligent models presented previously.

• Proceedings of the KIEE Conference
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• 2005.10b
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• pp.155-157
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• 2005

We propose a new category of hybrid multi-layer neural networks with hetero nodes such as Fuzzy Set based Polynomial Neurons (FSPNs) and Polynomial Neurons (PNs). These networks are based on a genetically optimized multi-layer perceptron. We develop a comprehensive design methodology involving mechanisms of genetic optimization and genetic algorithms, in particular. The augmented genetically optimized HFPNN (namely gHFPNN) results in a structurally optimized structure and comes with a higher level of flexibility in comparison to the one we encounter in the conventional HFPNN. The GA-based design procedure being applied at each layer of HFPNN leads to the selection of preferred nodes (FPNs or PNs) available within the HFPNN. In the sequel, two general optimization mechanisms are explored. First, the structural optimization is realized via GAs whereas the ensuing detailed parametric optimization is carried out in the setting of a standard least square method-based learning. The performance of the gHFPNNs quantified through experimentation where we use a number of modeling benchmarks-synthetic and experimental data already experimented with in fuzzy or neurofuzzy modeling.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.55 no.2
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• pp.45-51
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• 2006

In this paper, we propose a new architecture of Information Granulation based genetically optimized Self-Organizing Fuzzy Polynomial Neural Networks (IG_gSOFPNN) that is based on a genetically optimized multilayer perceptron with fuzzy polynomial neurons (FPNs) and discuss its comprehensive design methodology involving mechanisms of genetic optimization, especially information granulation and genetic algorithms. The proposed IG_gSOFPNN gives rise to a structurally optimized structure and comes with a substantial level of flexibility in comparison to the one we encounter in conventional SOFPNNs. The design procedure applied in the construction of each layer of a SOFPNN deals with its structural optimization involving the selection of preferred nodes (or FPNs) with specific local characteristics (such as the number of input variables, the order of the polynomial of the consequent part of fuzzy rules, and a collection of the specific subset of input variables) and addresses specific aspects of parametric optimization. In addition, the fuzzy rules used in the networks exploit the notion of information granules defined over system's variables and formed through the process of information granulation. That is, we determine the initial location (apexes) of membership functions and initial values of polynomial function being used in the premised and consequence part of the fuzzy rules respectively. This granulation is realized with the aid of the hard c-menas clustering method (HCM). To evaluate the performance of the IG_gSOFPNN, the model is experimented with using two time series data(gas furnace process and NOx process data).