• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.4
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• pp.327-332
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• 2005

We investigatea new fuzzy-neural networks-Hybrid Fuzzy set based polynomial Neural Networks (HFSPNN). These networks consist of genetically optimized multi-layer with two kinds of heterogeneous neurons thatare fuzzy set based polynomial neurons (FSPNs) and polynomial neurons (PNs). We have developed a comprehensive design methodology to determine the optimal structure of networks dynamically. The augmented genetically optimized HFSPNN (namely gHFSPNN) 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 gHFSPNN leads to the selection leads to the selection of preferred nodes (FSPNs or PNs) available within the HFSPNN. In the sequel, 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 gHFSPNN is 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
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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.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.67 no.8
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• pp.1071-1079
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• 2018

In this study, the design methodology as well as network architecture of Support Vector Machine based Polynomial Neural Network, which is a kind of the dynamically generated neural networks, is introduced. The Support Vector Machine based polynomial neural networks is given as a novel network architecture redesigned with the aid of polynomial neural networks and Support Vector Machine. The generic polynomial neural networks, whose nodes are made of polynomials, are dynamically generated in each layer-wise. The individual nodes of the support vector machine based polynomial neural networks is constructed as a support vector machine, and the nodes as well as layers of the support vector machine based polynomial neural networks are dynamically generated as like the generation process of the generic polynomial neural networks. Support vector machine is well known as a sort of robust pattern classifiers. In addition, in order to enhance the structural flexibility as well as the classification performance of the proposed classifier, multi-objective particle swarm optimization is used. In other words, the optimization algorithm leads to sequentially successive generation of each layer of support vector based polynomial neural networks. The bench mark data sets are used to demonstrate the pattern classification performance of the proposed classifiers through the comparison of the generalization ability of the proposed classifier with some already studied classifiers.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.1
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• pp.135-142
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• 2012

In this paper, we proposed a new architecture called radial basis function-based polynomial neural networks classifier that consists of heterogeneous neural networks such as radial basis function neural networks and polynomial neural networks. The underlying architecture of the proposed model equals to polynomial neural networks(PNNs) while polynomial neurons in PNNs are composed of Fuzzy-c means-based radial basis function neural networks(FCM-based RBFNNs) instead of the conventional polynomial function. We consider PNNs to find the optimal local models and use RBFNNs to cover the high dimensionality problems. Also, in the hidden layer of RBFNNs, FCM algorithm is used to produce some clusters based on the similarity of given dataset. The proposed model depends on some parameters such as the number of input variables in PNNs, the number of clusters and fuzzification coefficient in FCM and polynomial type in RBFNNs. A multiobjective particle swarm optimization using crowding distance (MoPSO-CD) is exploited in order to carry out both structural and parametric optimization of the proposed networks. MoPSO is introduced for not only the performance of model but also complexity and interpretability. The usefulness of the proposed model as a classifier is evaluated with the aid of some benchmark datasets such as iris and liver.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.11a
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• pp.483-487
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• 2005

We introduce a new architecture of hetero-hybridized feed-forward neural networks composed of fuzzy set-based polynomial neural networks (FSPNN) and polynomial neural networks (PM) that are based on a genetically optimized multi-layer perceptron and develop their comprehensive design methodology involving mechanisms of genetic optimization and Information Granulation. The construction of Information Granulation based HFSPNN (IG-HFSPNN) exploits fundamental technologies of Computational Intelligence(Cl), namely fuzzy sets, neural networks, and genetic algorithms(GAs) and Information Granulation. The architecture of the resulting genetically optimized Information Granulation based HFSPNN (namely IG-gHFSPNN) results from a synergistic usage of the hybrid system generated by combining new fuzzy set based polynomial neurons (FPNs)-based Fuzzy Neural Networks(PM) with polynomial neurons (PNs)-based Polynomial Neural Networks(PM). The design of the conventional genetically optimized HFPNN exploits the extended Group Method of Data Handling(GMDH) with some essential parameters of the network being tuned by using Genetie Algorithms throughout the overall development process. However, the new proposed IG-HFSPNN adopts a new method called as Information Granulation to deal with Information Granules which are included in the real system, and a new type of fuzzy polynomial neuron called as fuzzy set based polynomial neuron. The performance of the IG-gHFPNN is quantified through experimentation.

• Proceedings of the KIEE Conference
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• 2005.05a
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• pp.3-5
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• 2005

In this paper. we introduce a new structure of fuzzy-neural networks Fuzzy Set-based Polynomial Neural Networks (FSPNN). The two underlying design mechanisms of such networks involve genetic optimization and information granulation. The resulting constructs are Fuzzy Polynomial Neural Networks (FPNN) with fuzzy set-based polynomial neurons (FSPNs) regarded as their generic processing elements. First, we introduce a comprehensive design methodology (viz. a genetic optimization using Genetic Algorithms) to determine the optimal structure of the FSPNNs. This methodology hinges on the extended Group Method of Data Handling (GMDH) and fuzzy set-based rules. It concerns FSPNN-related parameters such as the number of input variables, the order of the polynomial, the number of membership functions, and a collection of a specific subset of input variables realized through the mechanism of genetic optimization. Second, the fuzzy rules used in the networks exploit the notion of information granules defined over systems variables and formed through the process of information granulation. This granulation is realized with the aid of the hard C-Means clustering (HCM). The performance of the network is quantified through experimentation in which we use a number of modeling benchmarks already experimented with in the realm of fuzzy or neurofuzzy modeling.

• Journal of Electrical Engineering and Technology
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• v.3 no.1
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• pp.108-114
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• 2008

Polynomial networks have been known to have excellent properties as classifiers and universal approximators to the optimal Bayes classifier. In this paper, the use of polynomial neural networks is proposed for efficient implementation of the polynomial-based classifiers. The polynomial neural network is a trainable device consisting of some rules and three processes. The three processes are assumption, effect, and fuzzy inference. The assumption process is driven by fuzzy c-means and the effect processes deals with a polynomial function. A learning algorithm for the polynomial neural network is developed and its performance is compared with that of previous studies.

• Proceedings of the KIEE Conference
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• 2001.07d
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• pp.2762-2764
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• 2001

In this study, we introduce and investigate a class of dynamic perceptron architectures, discuss a comprehensive design methodology and carry out a series of numeric experiments. The proposed dynamic perceptron architectures are called as Polynomial Neural Networks(PNN). PNN is a flexible neural architecture whose topology is developed through learning. In particular, the number of layers of the PNN is not fixed in advance but is generated on the fly. In this sense, PNN is a self-organizing network. PNN has two kinds of networks, Polynomial Neuron(FPN)-based and Fuzzy Polynomial Neuron(FPN)-based networks, according to a polynomial structure. The essence of the design procedure of PN-based Self-organizing Polynomial Neural Networks(SOPNN) dwells on the Group Method of Data Handling (GMDH) [1]. Each node of the SOPNN exhibits a high level of flexibility and realizes a polynomial type of mapping (linear, quadratic, and cubic) between input and output variables. FPN-based SOPNN dwells on the ideas of fuzzy rule-based computing and neural networks. Simulations involve a series of synthetic as well as experimental data used across various neurofuzzy systems. A detailed comparative analysis is included as well.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.372-372
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• 2000

In this paper, we propose Neuro Fuzzy Polynomial Networks(NFPN) based on Polynomial Neural Network(PNN) and Neuro-Fuzzy(NF) for model identification of complex and nonlinear systems. The proposed NFPN is generated from the mutually combined structure of both NF and PNN. The one and the other are considered as the premise part and consequence part of NFPN structure respectively. As the premise part of NFPN, NF 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. As the consequence part of NFPN, 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. NFPN is available effectively for multi-input variables and high-order polynomial according to the combination of NF with PNN. Accordingly it is possible to consider the nonlinearity characteristics of process and to get better output performance with superb predictive ability. In order to evaluate the performance of proposed models, we use the nonlinear function. The results show that the proposed FPNN can produce the model with higher accuracy and more robustness than any other method presented previously.

• 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.