Fuzzy Knowledge and Recurrent Neural Networks: A Dynamical Systems Perspective

Hybrid neuro-fuzzy systems – the combination of artificial neural networks with fuzzy logic – are becoming increasingly popular. However, neuro-fuzzy systems need to be extended for applications which require context (e.g., speech, handwriting, control). Some of these applications can be modeled in the form of finite-state automata. This chapter presents a synthesis method for mapping fuzzy finite-state automata (FFAs) into recurrent neural networks. The synthesis method requires FFAs to undergo a transformation prior to being mapped into recurrent networks. Their neurons have a slightly enriched functionality in order to accommodate a fuzzy representation of FFA states. This allows fuzzy parameters of FFAs to be directly represented as parameters of the neural network. We present a proof the stability of fuzzy finite-state dynamics of constructed neural networks and through simulations give empirical validation of the proofs.

[1]  Edward T. Lee,et al.  Fuzzy Neural Networks , 1975 .

[2]  Li-Xin Wang,et al.  Adaptive fuzzy systems and control - design and stability analysis , 1994 .

[3]  Raymond L. Watrous,et al.  Induction of Finite-State Languages Using Second-Order Recurrent Networks , 1992, Neural Computation.

[4]  J. Grantner,et al.  Synthesis and analysis of fuzzy logic finite state machine models , 1994, Proceedings of 1994 IEEE 3rd International Fuzzy Systems Conference.

[5]  James L. McClelland,et al.  Finite State Automata and Simple Recurrent Networks , 1989, Neural Computation.

[6]  Karvel K. Thornber,et al.  Fuzzy finite-state automata can be deterministically encoded into recurrent neural networks , 1998, IEEE Trans. Fuzzy Syst..

[7]  Hamid R. Berenji,et al.  Learning and tuning fuzzy logic controllers through reinforcements , 1992, IEEE Trans. Neural Networks.

[8]  Marc Acheroy,et al.  Fuzzy reasoning and neural networks for decision making problems in uncertain environment , 1994, Proceedings of 1994 IEEE 3rd International Fuzzy Systems Conference.

[9]  L. Wang,et al.  Fuzzy systems are universal approximators , 1992, [1992 Proceedings] IEEE International Conference on Fuzzy Systems.

[10]  Karvel K. Thornber,et al.  Equivalence in knowledge representation: automata, recurrent neural networks, and dynamical fuzzy systems , 1999, Proc. IEEE.

[11]  C. Lee Giles,et al.  Rule Revision With Recurrent Neural Networks , 1996, IEEE Trans. Knowl. Data Eng..

[12]  Manolis A. Christodoulou,et al.  Structural properties of gradient recurrent high-order neural networks , 1995 .

[13]  C. P. Pappis,et al.  A Fuzzy Logic Controller for a Trafc Junction , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[14]  E. Mamdani,et al.  FUZZY LOGIC CONTROLLER FOR A TRAFFIC JUNCTION , 1977 .

[15]  Mike Casey,et al.  The Dynamics of Discrete-Time Computation, with Application to Recurrent Neural Networks and Finite State Machine Extraction , 1996, Neural Computation.

[16]  Lotfi A. Zadeh,et al.  Information Title : Fuzzy languages and their relation to human and machine intelligence , 2022 .

[17]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[18]  Amita Pathak,et al.  Fuzzy Grammars in Syntactic Recognition of Skeletal Maturity from X-Rays , 1986, IEEE Transactions on Systems, Man, and Cybernetics.

[19]  H. R. van Nauta Lemke,et al.  Application of a fuzzy controller in a warm water plant , 1976, Autom..

[20]  Hikmet Senay,et al.  Fuzzy command grammars for intelligent interface design , 1992, IEEE Trans. Syst. Man Cybern..

[21]  Karvel K. Thornber,et al.  The fidelity of fuzzy-logic inference , 1993, IEEE Trans. Fuzzy Syst..

[22]  Marios M. Polycarpou,et al.  High-order neural network structures for identification of dynamical systems , 1995, IEEE Trans. Neural Networks.

[23]  Jeffrey L. Elman,et al.  Finding Structure in Time , 1990, Cogn. Sci..

[24]  F. A. Unal,et al.  A fuzzy finite state machine implementation based on a neural fuzzy system , 1994, Proceedings of 1994 IEEE 3rd International Fuzzy Systems Conference.

[25]  C. Lee Giles,et al.  Constructing deterministic finite-state automata in recurrent neural networks , 1996, JACM.

[26]  Piero P. Bonissone,et al.  Industrial applications of fuzzy logic at General Electric , 1995, Proc. IEEE.

[27]  Hava T. Siegelmann,et al.  On the Computational Power of Neural Nets , 1995, J. Comput. Syst. Sci..

[28]  T. I. Liu,et al.  Design for machining using expert system and fuzzy logic approach , 1995, Journal of Materials Engineering and Performance.

[29]  Hans Martin Lipp,et al.  Fuzzy specification of finite state machines , 1990, Proceedings of the European Design Automation Conference, 1990., EDAC..

[30]  B. Gaines,et al.  THE LOGIC OF AUTOMATA , 1975 .

[31]  Mo-Yuen Chow,et al.  A hybrid fuzzy/neural system used to extract heuristic knowledge from a fault detection problem , 1994, Proceedings of 1994 IEEE 3rd International Fuzzy Systems Conference.

[32]  Karvel K. Thornber,et al.  A key to fuzzy-logic inference , 1993, Int. J. Approx. Reason..

[33]  Antonio Torralba,et al.  FASY: a fuzzy-logic based tool for analog synthesis , 1996, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[34]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[35]  Padhraic Smyth,et al.  Learning Finite State Machines With Self-Clustering Recurrent Networks , 1993, Neural Computation.

[36]  Terry L. Hardy.  Multi-objective decision-making under uncertainty: Fuzzy logic methods , 1994 .

[37]  S. Chiu,et al.  Fuzzy logic for control of roll and moment for a flexible wing aircraft , 1991, IEEE Control Systems.

[38]  C. Lee Giles,et al.  Learning and Extracting Finite State Automata with Second-Order Recurrent Neural Networks , 1992, Neural Computation.

[39]  Hugues Bersini,et al.  Recurrent fuzzy systems , 1994, Proceedings of 1994 IEEE 3rd International Fuzzy Systems Conference.

[40]  W. Ames.  Mathematics in Science and Engineering , 1999 .

[41]  Chuen-Chien Lee.  FUZZY LOGIC CONTROL SYSTEMS: FUZZY LOGIC CONTROLLER - PART I , 1990 .