Analysis of membership function convergence in fuzzy time series
Okładka tom 7
PDF (Język Polski)

Keywords

fuzzy sets
time-series
system dynamics model ling
membership function

How to Cite

UrbanW. (2005). Analysis of membership function convergence in fuzzy time series. The Malopolska School of Economics in Tarnow Research Papers Collection, (7), 157-167. https://doi.org/10.25944/znmwse.2005.07.157167

Abstract

The paper presents the results of research on the convergence towards a limit form of membership functions in fuzzy time series, generated with difference equations, that is due to deterministic chaos occurrence. A particularly important tool seems to be an analysis of a scalar series of fields beneath a graph representing a variable membership function of the above mathematical models. This is done by defuzzyfying the above-mentioned time series. It appears possible to approximate the series variability with an exponential function. However, it should be done by means of simulation experiments in order to formulate theoretical conclusions, as an alternative to difficult, complicated analytical research.

https://doi.org/10.25944/znmwse.2005.07.157167
PDF (Język Polski)

References

Anile A. M., Deodato S., and Privitera G., Implementing fuzzy arithmetic, Dipartimento Di Matematica, Università Degli Studi Di Catania, Italy 1994.
View in Google Scholar

Chang W. K., Chów L. R., Chang S. K., Arithmetic operations on level sets of convex fuzzy numbers, Fuzzy Sets and Systems, 1984.
View in Google Scholar

Forrester J. W., Principles of systems, Industrial Dynamics (MIT Press, Cambridge Mass.), 1968.
View in Google Scholar

Hanczar P., Symulowane wyżarzanie - optymalizacja procesów logistycznych [w:] Ekonometria czasu transformacji, praca zbiorowa pod redakcją A.S. Barczaka, WU AE, Katowice 1998.
View in Google Scholar

Homer J. B., Why we iterate: scientific modeling in theory and practice, „System Dynamics Review" 1996, Spring, vol. 12, p. 1-19.
View in Google Scholar

Kaufmann A., Gupta M. M., Introduction to Fuzzy Arithmetic: Theory and Applications, New York: Van Nostrand, 1985.
View in Google Scholar

Klir G. J., Pan Y.: Constrained fuzzy arithmetic: Basic questions and some answers, Soft Computing 2 (1998), no. 2, p. 100-108. 7
View in Google Scholar

Munakata Y., Fuzzy systems: An Overview Communications of the ACM, 1994, March, vol. 37, no. 3 p. 69-76.
View in Google Scholar

Navara M, Zabokrtsk'y Z.: Computational problems of constrained fuzzy arithmetic. In: The State of the Art in Computational Intelligence, P. Sinc'ak, J. Vasc'ak, V. Kvasnicka and R. Mesiar (eds.), Physica-Verlag, Heidelberg; New York 2000, p. 95-98.
View in Google Scholar

Resnick R., Halliday D., Fizyka, PWN, Warszawa 1973.
View in Google Scholar

Schuster H. G.: Chaos deterministyczny. Wprowadzenie, Wydawnictwo Naukowe PWN, Warszawa 1995.
View in Google Scholar

Song Q., Leland R. P. and Chissom B. S., A new fuzzy time-series model of fuzzy number observations, „Fuzzy Sets and Systems", 1995, August, vol. 73, p. 341-348.
View in Google Scholar

Turksen L. B., Stochastic Fuzzy Sets, A Survey Lecture Notes in Economics and Mathematical Systems series, Vol. 310, Springer 1988, p. 168-183.
View in Google Scholar

Urban W., Wykorzystanie teorii grawitacji w analizie funkcjonowania systemów społeczno-ekonomicznych, ZN AE, Kraków 2002.
View in Google Scholar

Urban W., Wprowadzenie do skalarnej analizy chaosu deterministycznego w przestrzeni rozmytych liczb rzeczywistych, ZN AE, Kraków 2001.
View in Google Scholar

Urban W., Podstawy rozmytej dynamiki systemowej, AE, Kraków 1999.
View in Google Scholar

Wołoszyn J., Urban W., Symulacyjna aproksymacja uwarunkowań numerycznych wykorzystania ogólnej teorii grawitacji do opisu relacji społeczno-ekonomicznych, ZN AE, Kraków 2002.
View in Google Scholar

Wołoszyn J., Urban W., Koncepcja filtru aproksymująco-przeskalowującego w działaniach arytmetyki rozmytej, AE Kraków 2001.
View in Google Scholar

Wołoszyn J., Elementy teorii chaosu deterministycznego w badaniach systemów ekonomicznych, ZN AE nr 551, Kraków 2000.
View in Google Scholar

Wołoszyn J., Grafy rozmyte i możliwości ich wykorzystania w ekonomii, Zeszyty Naukowe AE, Seria Specjalna; Monografie, nr 90, Kraków 1990.
View in Google Scholar

Zadeh L. A., Fuzzy Logic, Computing with Words, IEEE Transactions on Fuzzy Systems, 1996, May, vol. 4, p. 103-111.
View in Google Scholar

Zadeh L. A., Fuzzy sets and their application to pattern classification and clustering analysis in [VanRysin1977].
View in Google Scholar

Zadeh L. A., Fuzzy sets, „Information and Control" 1965, no. 8.
View in Google Scholar

Zieliński J. S., Inteligentne systemy w zarządzaniu. Teoria i praktyka: praca zbiorowa, Wydawnictwo Naukowe PWN, Warszawa 2000.
View in Google Scholar

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