In this paper, an integrated model combining interval deep belief network (IDBN) and neural network with nonlinear weights, called IDBN-NN, is proposed for interval-valued data modeling. Firstly, the IDBN with variable learning rate is designed to initialize parameters of each sub-model. Based on amodified contrastive divergence algorithm the least square method is adopted to identify the coefficients of nonlinear weights in the output layer. Then, to improve the modeling accuracy, the Fuzzy C-Means (FCM) method and the Particle Swarm Optimization (PSO) algorithm are applied to tune the weights of sub-models. Though each sub-model can capture the nonlinear feature of the original system, by intersecting cut sets the synthesizing modeling scheme can further improve the performance of the proposed model. Some numerical examples show that the IDBN-NN with nonlinear output structure can achieve higher accuracy than some interval-valued data modeling methods.

中文翻译：

---

具有区间值数据非线性输出结构的集成神经网络

本文提出了一种将区间深度置信网络（IDBN）和神经网络与非线性权重相结合的集成模型，称为IDBN-NN，用于区间值数据建模。首先，设计具有可变学习率的IDBN来初始化每个子模型的参数。基于改进的对比发散算法，采用最小二乘方法识别输出层中非线性权重的系数。然后，为了提高建模精度，应用了模糊C均值（FCM）方法和粒子群优化（PSO）算法来调整子模型的权重。尽管每个子模型都可以捕获原始系统的非线性特征，但是通过相交割集，综合建模方案可以进一步提高所提出模型的性能。