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research-article

Aggregation of inconsistent rules for fuzzy rule base simplification

Published: 01 January 2017 Publication History

Abstract

This paper proposes a rule base simplification method for fuzzy systems. The method is based on aggregation of rules with different linguistic values of the output for identical permutations of linguistic values of the inputs which are known as inconsistent rules. The simplification removes the redundancy in the fuzzy rule base by replacing each group of inconsistent rules with a single equivalent rule. The simulation results show that the aggregated fuzzy system with the consistent rule base approximates quite well the original fuzzy system with the inconsistent rule base. The main advantage of the proposed method over other methods is that it does not require any refinement of the rule base using additional data sets or expert knowledge. In this context, the method is quite suitable for applications where rule base refinement is unacceptable due to time constraints or impossible due to lack of additional data or knowledge.

References

[1]
M. Guven and K. Passino, Avoiding exponential parameter growth in fuzzy systems, IEEE Transactions on Fuzzy Systems 9(1) (2001), 194–199.
[2]
Y. Kim, S. Ahn and W. Kwon, Computational complexity of general fuzzy logic control and its simplification for a loop controller, Fuzzy Sets and Systems 111 (2000), 215–224.
[3]
B. Lazzerini and F. Marcelloni, Reducing computation overhead in MISO fuzzy systems, Fuzzy Sets and Systems 113 (2000), 485–496.
[4]
N. Pal, V. Eluri and G. Mandal, Fuzzy logic approaches to structure preserving dimensionality reduction, IEEE Transactions on Fuzzy Systems 10(3) (2002), 277–286.
[5]
A. Gegov, Distributed Fuzzy Control of Multivariable Systems, Kluwer, Dordrecht, 1996.
[6]
M. Gupta, J. Kiszka and G. Trojan, Multivariable structure of fuzzy control systems, IEEE Transactions on Systems, Man and Cybernetics 16(5) (1986), 638–655.
[7]
F. Wan, H. Shang, L. Wang and Y. Sun, How to determine the minimum number of fuzzy rules to achieve given accuracy: a computational geometric approach to SISO case, Fuzzy Sets and Systems 150 (2005), 199–209.
[8]
N. Xiong and L. Litz, Reduction of fuzzy control rules by means of premise learning – method and case study, Fuzzy Sets and Systems 132 (2002), 217–231.
[9]
H. Roubos and M. Setnes, Compact and transparent fuzzy models and classifiers through iterative complexity reduction, IEEE Transactions on Fuzzy Systems 9(4) (2001), 516–524.
[10]
M. Setnes, R. Babuska and H. Verbruggen, Rule-based modelling: precision and transparency, IEEE Transactions on Systems, Man and Cybernetics 28(1) (1998), 165–169.
[11]
V. Lacrose, Complexity Reduction of Fuzzy Controllers: Application to Multivariable Control, PhD Thesis, Toulouse Laboratory for Systems Analysis and Architecture, 1997.
[12]
M. Jamshidi, Large Scale Systems: Modelling, Control and Fuzzy Logic, Prentice Hall, Upper Saddle River, 1997.
[13]
Y. Yam, P. Baranyi and C. Yang, Reduction of fuzzy rule base via singular value decomposition, IEEE Transactions on Fuzzy Systems 7(2) (1999), 120–132.
[14]
C. Tao, Comments on reduction of fuzzy rule base via singular value decomposition, IEEE Transactions on Fuzzy Systems 9(4) (2001), 675–676.
[15]
W. Combs and J. Andrews, Combinatorial rule explosion eliminated by a fuzzy rule configuration, IEEE Transactions on Fuzzy Systems 6(1) (1998), 1–11.
[16]
J. Mendel and Q. Liang, Comments on combinatorial rule explosion eliminated by a fuzzy rule configuration, IEEE Transactions on Fuzzy Systems 7(3) (1999), 369–371.
[17]
S. Chen, F. Yu and H. Chung, Decoupled fuzzy controller design with single-input fuzzy logic, Fuzzy Sets and Systems 129 (2002), 335–342.
[18]
A. Gegov and M. Frank, Hierarchical fuzzy control of multivariable systems, Fuzzy Sets and Systems 72 (1995), 299–310.
[19]
S. Mollov, Fuzzy Control of Multiple-Input Multiple-Output Processes, PhD Thesis, Delft University of Technology, 2002.
[20]
A. Gegov and M. Frank, Decomposition of multivariable systems for distributed fuzzy control, Fuzzy Sets and Systems 73 (1995), 329–340.
[21]
C. Xu, Linguistic decoupling control of fuzzy multivariable processes, Fuzzy Sets and Systems 44 (1991), 209–217.
[22]
C. Xu and Y. Lu, Decoupling in fuzzy systems: A cascade compensation approach, Fuzzy Sets and Systems 29 (1989), 177–185.
[23]
O. Huwendiek and W. Brockmann, Function approximation with decomposed fuzzy systems, Fuzzy Sets and Systems 101 (1999), 273–286.
[24]
M. Joo and J. Lee, Universal approximation by hierarchical fuzzy system with constraints on the fuzzy rule, Fuzzy Sets and Systems 130 (2002), 175–188.
[25]
M. Joo and J. Lee, A class of hierarchical fuzzy systems with constraints on the fuzzy rules, IEEE Transactions on Fuzzy Systems 13(2) (2005), 194–203.
[26]
M. Lee, H. Chung and F. Yu, Modelling of hierarchical fuzzy systems, Fuzzy Sets and Systems 138 (2003), 343–361.
[27]
G. Raju, J. Zhou and R. Kisner, Hierarchical fuzzy control, International Journal of Control 54(5) (1991), 1201–1216.
[28]
L. Wang, Analysis and design of hierarchical fuzzy systems, IEEE Transactions on Fuzzy Systems 7(5) (1999), 617–624.
[29]
J. Jang, C. Sun and F. Mizutani, Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence, Prentice Hall, Upper Saddle River, 1997.
[30]
J. Yan, M. Ryan and J. Power, Using Fuzzy Logic, Prentice Hall, New York, 1994.
[31]
A. Gegov, Complexity Management in Fuzzy Systems, Springer, Berlin, 2007.
[32]
M. Negnevitsky, Artificial Intelligence: A Guide to Intelligent Systems, Pearson Education, Harlow, 2002.
[33]
T. Ross, Fuzzy Logic with Engineering Applications, Wiley, Chichester, 2004.

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        Published In

        cover image International Journal of Knowledge-based and Intelligent Engineering Systems
        International Journal of Knowledge-based and Intelligent Engineering Systems  Volume 21, Issue 3
        2017
        63 pages

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        IOS Press

        Netherlands

        Publication History

        Published: 01 January 2017

        Author Tags

        1. Fuzzy systems
        2. complexity theory
        3. simulation
        4. data simplification
        5. control systems

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