On the Characteristic Functions of Fuzzy Systems

Authors

  • Horia-Nicolai L. Teodorescu Technical Univ. Gh Asachi Iasi, Romania and Institute of Computer Science, Romanian Academy

Keywords:

Sugeno system, characteristic function, continuity

Abstract

We provide several properties of the input-output (characteristic) function of the SISO / MISO Sugeno fuzzy systems with c.o.g. defuzzification. The properties analyzed are related to continuity under various conditions for the input membership functions, including the case when the input space is a topological space.

References

Buckley, J.J., Hayashi, Y., Fuzzy input-output controllers are universal approximators, Fuzzy Sets and Systems, Vol. 58, Issue 3, 24 Sep. 1993, pp. 273-278 http://dx.doi.org/10.1016/0165-0114(93)90503-A

Buckley, J.J., Hayashi, Y., Numerical relationships between neural networks, continuous functions, and fuzzy systems. Fuzzy Sets and Systems, Vol. 60, Issue 1, 25 Nov. 1993, pp. 1-8 http://dx.doi.org/10.1016/0165-0114(93)90283-N

Buckley, J.J., Hayashi, Y., Can fuzzy neural nets approximate continuous fuzzy functions? Fuzzy Sets and Systems, Vol. 61, Issue 1, 10 Jan. 1994, pp. 43-51 http://dx.doi.org/10.1016/0165-0114(94)90283-6

Dongrui W., Mendel, J.M., On the Continuity of Type-1 and Interval Type-2 Fuzzy Logic Systems. Fuzzy Systems, IEEE Transactions on, Feb. 2011, Vol. 19, Issue 1, pp. 179 - 192

Mendel, J.M., John, R.I., and Liu, F., Interval Type-2 Fuzzy Logic Systems Made Simple. IEEE Transactions on Fuzzy Systems, Vol. 14, No. 6, December 2006, pp. 808-821 http://dx.doi.org/10.1109/TFUZZ.2006.879986

Teodorescu, H.N., Relations between fuzzy and crisp systems. In: Teodorescu H.N. (Editor), Fuzzy signals and systems. AMSE Press, 1990

Teodorescu, H.N., Taylor and Bi-local Piecewise Approximations with Neuro-Fuzzy Systems, Studies in Informatics and Control, vol. 21 (4), pp. 367-376, 2012. (http://sic.ici.ro/sic2012_4/art02.php)

Tong, R.M., A control engineering review of fuzzy systems, Automatica, Vol. 13, No. 6, November 1977, pp. 559-569 http://dx.doi.org/10.1016/0005-1098(77)90077-2

Yu-Ru S., Sugianto, L.F., Lee, E.S., A Note on Continuity and Semicontinuity of Fuzzy Mappings. Fuzzy Information Processing Society, 2007. NAFIPS '07. Annual Meeting of the North American ~, 24-27 June 2007, pp. 106 - 111

Published

2013-06-02

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