Fuzzy networks with feedback rule bases for complex systems modelling

This paper proposes a novel approach for modelling complex interconnected systems by means of fuzzy networks with feedback rule bases. The nodes in these networks are rule bases connected in a feedback manner whereby outputs from some rule bases are fed as inputs to the same or preceding rule bases. The approach allows any fuzzy network of this type to be presented as an equivalent fuzzy system by linguistic composition of its nodes. The composition process makes use of formal models for fuzzy networks, basic operations in such networks, their properties and advanced operations. These models, operations and properties are used for defining several types of networks with single or multiple local and global feedback. The proposed approach facilitates the understanding of complex interconnected systems by improving the transparency of their models.

[1]  Antonio Fiordaliso,et al.  A constrained Takagi-Sugeno fuzzy system that allows for better interpretation and analysis , 2001, Fuzzy Sets Syst..

[2]  Thomas Sudkamp,et al.  A Method of Converting a Fuzzy System to a Two-Layered Hierarchical Fuzzy System and Its Run-Time Efficiency , 2009, IEEE Transactions on Fuzzy Systems.

[3]  Luigi Fortuna,et al.  Complex dynamics through fuzzy chains , 2004, IEEE Transactions on Fuzzy Systems.

[4]  Alexander E. Gegov,et al.  Complexity Management in Fuzzy Systems - A Rule Base Compression Approach , 2007, Studies in Fuzziness and Soft Computing.

[5]  David A. Sanders,et al.  Mamdani fuzzy networks with feedforward rule bases for complex systems modelling , 2016, J. Intell. Fuzzy Syst..

[6]  Korris Fu-Lai Chung,et al.  Cascaded fuzzy neural network model based on syllogistic fuzzy reasoning , 2001, IEEE Trans. Fuzzy Syst..

[7]  Antonio Fernández-Caballero.  Contribution of fuzziness and uncertainty to modern artificial intelligence , 2009, Fuzzy Sets Syst..

[8]  David A. Sanders,et al.  Rule base compression in fuzzy systems by filtration of non-monotonic rules , 2014, J. Intell. Fuzzy Syst..

[9]  T. Ross.  Fuzzy Logic with Engineering Applications , 1994 .

[10]  Jaime Gil-Aluja,et al.  Fuzzy Sets in the Management of Uncertainty , 2004 .

[11]  Carlos Alberola-López,et al.  Matrix Modeling of Hierarchical Fuzzy Systems , 2008, IEEE Transactions on Fuzzy Systems.

[12]  John Q. Gan,et al.  Low-level interpretability and high-level interpretability: a unified view of data-driven interpretable fuzzy system modelling , 2008, Fuzzy Sets Syst..

[13]  Jonathan M. Garibaldi,et al.  Uncertain Fuzzy Reasoning: A Case Study in Modelling Expert Decision Making , 2007, IEEE Transactions on Fuzzy Systems.

[14]  David A. Sanders,et al.  Filtration of Non-Monotonic Rules for Fuzzy Rule Base Compression , 2014, Int. J. Comput. Intell. Syst..

[15]  Yong-Ming Li,et al.  Approximation theory of fuzzy systems based upon genuine many-valued implications - MIMO cases , 2002, Fuzzy Sets Syst..

[16]  Yung C. Shin,et al.  Interaction analysis for MIMO nonlinear systems based on a fuzzy basis function network model , 2007, Fuzzy Sets Syst..

[17]  M. Jamshidi.  Large-Scale Systems: Modeling, Control and Fuzzy Logic , 1996 .

[18]  Jin S. Lee,et al.  A class of hierarchical fuzzy systems with constraints on the fuzzy rules , 2005, IEEE Transactions on Fuzzy Systems.

[19]  Wei-Wei Lin,et al.  Decentralized PDC for large-scale T-S fuzzy systems , 2005, IEEE Transactions on Fuzzy Systems.

[20]  Bart De Schutter,et al.  Stability of Cascaded Fuzzy Systems and Observers , 2009, IEEE Transactions on Fuzzy Systems.

[21]  Q GanJohn,et al.  Low-level interpretability and high-level interpretability , 2008 .

[22]  Nedyalko Petrov,et al.  Advanced modelling of complex processes by fuzzy networks , 2011 .

[23]  Serge Guillaume,et al.  Designing fuzzy inference systems from data: An interpretability-oriented review , 2001, IEEE Trans. Fuzzy Syst..

[24]  Ming-Ling Lee,et al.  Modeling of hierarchical fuzzy systems , 2003, Fuzzy Sets Syst..

[25]  Lothar Litz,et al.  Reduction of fuzzy control rules by means of premise learning - method and case study , 2002, Fuzzy Sets Syst..

[26]  David A. Sanders,et al.  Complexity management methodology for fuzzy systems with feedforward rule bases , 2015, Int. J. Knowl. Based Intell. Eng. Syst..

[27]  Zong-Mu Yeh,et al.  A systematic approach for designing multistage fuzzy control systems , 2004, Fuzzy Sets Syst..

[28]  Norbert Stoll,et al.  A robust design criterion for interpretable fuzzy models with uncertain data , 2006, IEEE Transactions on Fuzzy Systems.

[29]  Bing Chen,et al.  Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping and application to chemical processes , 2005, IEEE Transactions on Fuzzy Systems.

[30]  Shaocheng Tong,et al.  Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping approach , 2007, Fuzzy Sets Syst..

[31]  Jeich Mar,et al.  A car-following collision prevention control device based on the cascaded fuzzy inference system , 2005, Fuzzy Sets Syst..

[32]  Tian-Ping Zhang.  Stable adaptive fuzzy sliding mode control of interconnected systems , 2001, Fuzzy Sets Syst..

[33]  James J. Buckley,et al.  Simulating Fuzzy Systems , 2005, Studies in Fuzziness and Soft Computing.

[34]  Nikhil R. Pal,et al.  Fuzzy logic approaches to structure preserving dimensionality reduction , 2002, IEEE Trans. Fuzzy Syst..

[35]  Karl-Heinz Temme,et al.  The chaining syllogism in fuzzy logic , 2004, IEEE Transactions on Fuzzy Systems.

[36]  Alexander E. Gegov,et al.  Linguistic composition based modelling by fuzzy networks with modular rule bases , 2015, Fuzzy Sets Syst..

[37]  Richard Lai,et al.  Designing a hierarchical fuzzy logic controller using the differential evolution approach , 2007, Appl. Soft Comput..

[38]  Feng Wan,et al.  How to determine the minimum number of fuzzy rules to achieve given accuracy: a computational geometric approach to SISO case , 2005, Fuzzy Sets Syst..

[39]  Bo Yang,et al.  Automatic Design of Hierarchical Takagi–Sugeno Type Fuzzy Systems Using Evolutionary Algorithms , 2007, IEEE Transactions on Fuzzy Systems.

[40]  Lawrence O. Hall,et al.  Rule chaining in fuzzy expert systems , 2001, IEEE Trans. Fuzzy Syst..

[41]  Wen-June Wang,et al.  Stability and stabilization of fuzzy large-scale systems , 2004, IEEE Transactions on Fuzzy Systems.

[42]  Alexander E. Gegov.  Fuzzy Networks for Complex Systems - A Modular Rule Base Approach , 2010, Studies in Fuzziness and Soft Computing.

[43]  Sung-Bae Cho,et al.  Personalized mining of web documents using link structures and fuzzy concept networks , 2007, Appl. Soft Comput..

[44]  Iluminada Baturone,et al.  Automatic tuning of complex fuzzy systems with Xfuzzy , 2007, Fuzzy Sets Syst..

[45]  Manuel Landajo,et al.  A note on smooth approximation capabilities of fuzzy systems , 2001, IEEE Trans. Fuzzy Syst..

[46]  Hongbin Zhang,et al.  Decentralized $H_{\infty }$ Filter Design for Discrete-Time Interconnected Fuzzy Systems , 2009, IEEE Transactions on Fuzzy Systems.

[47]  Yong-Ming Li,et al.  Approximation theory of fuzzy systems based upon genuine many-valued implications - MIMO cases , 2002, Fuzzy Sets Syst..