Construction And Optimization Of Fuzzy Polynomial Min-max Neural Network

Fuzzy min-max polynomial neural network(FMPNN)is a kind of fuzzy min-max neural network(FMM)which combines ensemble learning method and the structure of polynomial neural network.FMM is a kind of classical fuzzy neural network,which can handle classification problems effectively.But it still has some limitations:(1)The training process of FMM is very sensitive to the input order of samples.(2)There are some parameters in the training process of FMM,which has a great influence on the training results.In this paper,FMPNN is proposed to overcome these disadvantages.The main innovations are as follows.1.A ensemble fuzzy min-max neural network(EFMNN)is proposed.The EFMNN is a five-layer neural network based on bagging technique which is a classical ensemble learning method.There are two new types of neurons in the structure of EFMNN,named fuzzy min-max neuron(FMN)and voting neuron(VN).FMNs and VNs constitute the third and fourth layers of the EFMNN respectively.FMN can be regarded as a typical FMM,and VN is constructed based on voting mechanism.Compared with the traditional FMM,the EFMNN has better classification performance.FMM is very sensitive to the input order of data,and EFMNN can overcome this limitation.2.A fuzzy min-max polynomial neural network is proposed.It is a neural network based on multi-layer structure.The multi-layer structure refers to the topology of polynomial neural network.There are two types of FMPNN named bootstrap sampling based FMPNN(BS-FMPNN)and bagging technology based FMPNN(BT-FMPNN)are developed.There are three kinds of fuzzy min-max neurons and two kinds of classification neurons are proposed in these two structures.The three types of fuzzy min-max neuron include bootstrap fuzzy min-max neuron(BFMN),hyperbox fuzzy min-max neuron(HFMN),and ensemble fuzzy min-max neuron(EFMN).The two types of classification neurons are hyperbox classification neuron(HCN)and ensemble classification neuron(ECN).The proposed FMPNN combines the polynomial neural network structure and the FMM,and demonstrates the advantages of the two models.3.A fuzzy min-max polynomial neural network optimized by particle swarm optimization(PSO-FMPNN)is proposed.There are two parameters in the construction of FMPNN can directly affect the result of training.Therefore,particle swarm optimization(PSO)algorithm is used to optimize the FMPNN in this paper.PSO is carried out by exchanging information with each other to determine more appropriate parameters and find the optimal model.