Construction and Supervised Learning of Long-Term Grey Cognitive Networks

Modeling a real-world system by means of a neural model involves numerous challenges that range from formulating transparent knowledge representations to obtaining reliable simulation errors. However, that knowledge is often difficult to formalize in a precise way using crisp numbers. In this paper, we present the long-term grey cognitive networks which expands the recently proposed long-term cognitive networks (LTCNs) with grey numbers. One advantage of our neural system is that it allows embedding knowledge into the network using weights and constricted neurons. In addition, we propose two procedures to construct the network in situations where only historical data are available, and a regularization method that is coupled with a nonsynaptic backpropagation algorithm. The results have shown that our proposal outperforms the LTCN model and other state-of-the-art methods in terms of accuracy.

[1]  M. Nagai,et al.  Reviewing crisp, fuzzy, grey and rough mathematical models , 2007, 2007 IEEE International Conference on Grey Systems and Intelligent Services.

[2]  Alan J. Mayne,et al.  Generalized Inverse of Matrices and its Applications , 1972 .

[3]  Koen Vanhoof,et al.  A review on methods and software for fuzzy cognitive maps , 2019, Artificial Intelligence Review.

[4]  Koen Vanhoof,et al.  Fuzzy-Rough Cognitive Networks , 2018, Neural Networks.

[5]  I. Barany,et al.  Central limit theorems for Gaussian polytopes , 2006 .

[6]  M. Friedman The Use of Ranks to Avoid the Assumption of Normality Implicit in the Analysis of Variance , 1937 .

[7]  Jose L. Salmeron,et al.  Fuzzy grey cognitive maps and nonlinear Hebbian learning in process control , 2013, Applied Intelligence.

[8]  Jesús Alcalá-Fdez,et al.  KEEL Data-Mining Software Tool: Data Set Repository, Integration of Algorithms and Experimental Analysis Framework , 2011, J. Multiple Valued Log. Soft Comput..

[9]  Bart Kosko,et al.  Fuzzy Cognitive Maps , 1986, Int. J. Man Mach. Stud..

[10]  Jose L. Salmeron,et al.  Uncertainty Propagation in Fuzzy Grey Cognitive Maps With Hebbian-Like Learning Algorithms , 2019, IEEE Transactions on Cybernetics.

[11]  Koen Vanhoof,et al.  Nonsynaptic Error Backpropagation in Long-Term Cognitive Networks , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[12]  Jose L. Salmeron,et al.  Modelling grey uncertainty with Fuzzy Grey Cognitive Maps , 2010, Expert Syst. Appl..

[13]  F. Wilcoxon Individual Comparisons by Ranking Methods , 1945 .

[14]  D. Serre Matrices: Theory and Applications , 2002 .

[15]  Jose L. Salmeron,et al.  A Fuzzy Grey Cognitive Maps-based Decision Support System for radiotherapy treatment planning , 2012, Knowl. Based Syst..

[16]  J. Fox Applied Regression Analysis, Linear Models, and Related Methods , 1997 .

[17]  Jing Liu,et al.  Learning Large-Scale Fuzzy Cognitive Maps Based on Compressed Sensing and Application in Reconstructing Gene Regulatory Networks , 2017, IEEE Transactions on Fuzzy Systems.

[18]  Koen Vanhoof,et al.  Short-term Cognitive Networks, Flexible Reasoning and Nonsynaptic Learning , 2019, Neural Networks.

[19]  Bernard Widrow,et al.  30 years of adaptive neural networks: perceptron, Madaline, and backpropagation , 1990, Proc. IEEE.

[20]  Bart Kosko,et al.  Hidden patterns in combined and adaptive knowledge networks , 1988, Int. J. Approx. Reason..

[21]  Robert Ivor John,et al.  Grey sets and greyness , 2012, Inf. Sci..

[22]  Jose L. Salmeron,et al.  Fuzzy Grey Cognitive Maps in reliability engineering , 2012, Appl. Soft Comput..

[23]  Jose L. Salmeron,et al.  Forecasting Risk Impact on ERP Maintenance with Augmented Fuzzy Cognitive Maps , 2012, IEEE Transactions on Software Engineering.

[24]  J. Deng,et al.  Introduction to Grey system theory , 1989 .

[25]  Jing Liu,et al.  Time-Series Forecasting Based on High-Order Fuzzy Cognitive Maps and Wavelet Transform , 2018, IEEE Transactions on Fuzzy Systems.

[26]  Robert Hecht-Nielsen,et al.  Theory of the backpropagation neural network , 1989, International 1989 Joint Conference on Neural Networks.

[27]  Léon Bottou,et al.  Stochastic Gradient Descent Tricks , 2012, Neural Networks: Tricks of the Trade.

[28]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.