Mamdani Model based Adaptive Neural Fuzzy Inference System and its Application

Hybrid algorithm is the hot issue in Computational Intelligence (CI) study. From in-depth discussion on Simulation Mechanism Based (SMB) classification method and composite patterns, this paper presents the Mamdani model based Adaptive Neural Fuzzy Inference System (M-ANFIS) and weight updating formula in consideration with qualitative representation of inference consequent parts in fuzzy neural networks. M-ANFIS model adopts Mamdani fuzzy inference system which has advantages in consequent part. Experiment results of applying M-ANFIS to evaluate traffic Level of service show that M-ANFIS, as a new hybrid algorithm in computational intelligence, has great advantages in non-linear modeling, membership functions in consequent parts, scale of training data and amount of adjusted parameters.

Authors:

• Yuanyuan Chai
• Limin Jia
• Zundong Zhang

Keywords:

• Fuzzy neural networks
• Mamdani fuzzy inference
• M-ANFIS

References:

[1] R. C. Eberhart, Overview of computational intelligence, Proceedings
of the 20th Annual International Conference of the IEEE Engineering
in Medicine and Biology Society, 20(3),1998.
[2] L. A. Zadeh, Soft Computing and Fuzzy Logic, IEEE Software,
11(6):48-56, 1994.
[3] J. S. R. Jang, ANFIS:Adaptive-Network-Based Fuzzy Inference
System, IEEE Transactions On Systems, Man, And Cybernetics
,23(3):665-685, 1993.
[4] M. M. Gupta, Fuzzy Logic and Fuzzy Systems: Recent Developments
and Future Diwctions, Intelligent Systems Research Laboratory, 1996.
[5] M.A. Dena, F. Palis and A. Zeghbib, Modeling and control of nonlinear
systems using soft computing techniques, Applied Soft Computing,
7:728-738,2007.
[6] T. Furuhashi, Fusion of fuzzy/ neuro/ evolutionary computing for
knowledge acquisition, Proceedings of the IEEE, 89(9),2001.
[7] H. Takagi and I. Hayashi, Artificial neural network-driven fuzzy
reasoning, Proc. Int. Workshop Fuzzy System Applications (IIZUKA88),
Iizuka, Japan, 217C218,1988.
[8] C. T. Lin and C. S. G. Lee, Neural-network-based fuzzy logic control
and decision system, IEEE Transactions on computers, 40(12):1320-
1336,1991.
[9] C. T. Lin and C. S. G. Lee, Reinforcement Structure/Parameter Learning
for an Integrated Fuzzy Neural Network, IEEE Transactions on
Fuzzy Systems, 2(1):46-63, 1994.
[10] L.X.Wang and J.M. Mendel, Back-propagation fuzzy systems as nonlinear
dynamic system identifiers, Proceedings of the IEEE International
Conference on Fuzzy Systems, San Diego, March 1992.
[11] L.X. Wang and J. M. Mendel, Fuzzy Basis Functions, Universal
Approximation, and Orthogonal Least-Squares Learning, IEEE TRANSACTIONS
ON NEURAL NETWORKS, 3(5):807-814,September 1992.
[12] J.-S. R. Jang and C.-T. Sun, Functional equivalence between radial
basis function networks and fuzzy inference systems, IEEE Transaction
on Neural Networks 4(1)(1993)156-159.
[13] J.-S. R. Jang, C.-T. Sun and E. Mizutani, Neuro-Fuzzy and Soft
Computing: A Computational Approach to Learning and Machine
Intelligence, First Edition, Prentice Hall, 1997.
[14] E.H.Mamdani and S.Assilian, An experiment in linguistic synthesis
with a fuzzy logic controller, International Journal of Man-Machine
Studies, 7(1):1-13,1975.
[15] F. Esragh and E.H. Mamdani, A general approach to linguistic approximation,
Fuzzy Reasoning and Its Applications, Academic Press,1981.
[16] E. H. Mamdani, Application of Fuzzy Logic to Approximate Reasoning
Using Linguistic Synthesis, IEEE Trans. Computers, 26(12):1182-
1191, 1977.
[17] T. Takagi and M. Sugeno, Derivation of fuzzy control rules from human
operators control actions, Proc. IFAC Symp. on Fuzzy lnformation,
Knowledge Representation and Decision Analysis, 55-60, July 1983.
[18] T. Takagi and M. Sugeno, Fuzzy identification of systems and its
applications to modeling and control, IEEE Trans. Syst., Man, Cybern,
15:116-132, 1985.
[19] R.R.Yager and D.P.Filev, SLIDE:A simple adaptive defuzzification
method, IEEE transaction on Fuzzy Systems, 1(1):69-78,February
1992.
[20] D. E. Rumelhart, G. E. Hinton and R. J. Williams, Learning internal
representations by error propagation, Parallel distributed processing:
explorations in the microstructure of cognition. 1: 318-
362,foundations, 1986.
[21] D.E. Rumelhart, The Basic Ideas in Neural Networks, Communications
of the ACM, 37(3):87-92,1994.
[22] M.Minsky and S.Papert, Perceptrons, MIT Press, Cambridge, MA.,
1969.
[23] J. Moody and C. Darken, Learning with Localized Receptive Fields,
Proceedings of the 1988 Connectionist Models Summer School, 133-
143, Morgan Kaufmann, 1988.
[24] J.Moody and C.Darken, Fast learning in networks of locally-turned
processing units, Neural Computation, 1:281-294,1989.