Geodesic
What is not clear in fuzzy control systems?
International Journal of Applied Mathematics and Computer Science, Tome 16 (2006) no. 1, pp. 37-49

Voir la notice de l'article provenant de la source Library of Science

The paper presents a number of unclear, unsolved or partly solved problems of fuzzy logic, which hinder precise transformation of expert knowledge about proper control of a plant in a fuzzy controller. These vague problems comprise the realization of logical and arithmetic operations and another basic problem, i.e., the construction of membership functions. The paper also indicates how some of the above problems can be solved.
Keywords: fuzzy control, fuzzy systems, fuzzy arithmetic, fuzzy logic, necessity, possibility
Mots-clés : sterowanie rozmyte, system rozmyty, arytmetyka rozmyta, logika rozmyta, możliwość 
Piegat, A. What is not clear in fuzzy control systems?. International Journal of Applied Mathematics and Computer Science, Tome 16 (2006) no. 1, pp. 37-49. http://geodesic.mathdoc.fr/item/IJAMCS_2006_16_1_a2/
@article{IJAMCS_2006_16_1_a2,
     author = {Piegat, A.},
     title = {What is not clear in fuzzy control systems?},
     journal = {International Journal of Applied Mathematics and Computer Science},
     pages = {37--49},
     year = {2006},
     volume = {16},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IJAMCS_2006_16_1_a2/}
}
TY  - JOUR
AU  - Piegat, A.
TI  - What is not clear in fuzzy control systems?
JO  - International Journal of Applied Mathematics and Computer Science
PY  - 2006
SP  - 37
EP  - 49
VL  - 16
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IJAMCS_2006_16_1_a2/
LA  - en
ID  - IJAMCS_2006_16_1_a2
ER  - 
%0 Journal Article
%A Piegat, A.
%T What is not clear in fuzzy control systems?
%J International Journal of Applied Mathematics and Computer Science
%D 2006
%P 37-49
%V 16
%N 1
%U http://geodesic.mathdoc.fr/item/IJAMCS_2006_16_1_a2/
%G en
%F IJAMCS_2006_16_1_a2

[1] Borgelt Ch. and Kruse R. (2003): Learning possibilistic graphical models from data.-IEEE Trans. Fuzzy Syst., Vol. 11, No. 2, pp. 159-172.

[2] Civanlar M.R. and Trussel H.J. (1986): Constructing membership functions using statistical data. - Fuzzy Sets Syst., Vol. 18, No. 1, pp. 1-13.

[3] Devi B.B. and Sarma V.V.S. (1985): Estimation of fuzzy memberships from histograms. - Inf. Sci., Vol. 35, No. 1, pp. 43-59.

[4] Driankov D., Hellendoorn H. and Reinfrank M. (1993): An introduction to fuzzy control. -- Berlin, Heidelberg, Springer-Verlag.

[5] Dubois D. and Prade H. (1983): Unfair coins and necessity measures: Towards a possibilistic interpretation of histograms. - Fuzzy Sets Syst., Vol. 10, No. 1, pp. 15-20.

[6] Dubois D. and Prade H. (1986): Possibility Theory. - New York, London: Plenum Press.

[7] Dubois D., Foulloy L. and Mauris G. (2004): Probability - Possibility transformations, triangular fuzzy sets, and probabilistic inequalities.-Reliable Computing, Vol. 10, No. 4, pp. 273-297.

[8] Kaufmann A. and Gupta M.M. (1991): Introduction to Fuzzy Arithmetic.-New York: Van Nostrand Reinhold.

[9] Kosiński W., Prokopowicz P. and Ślęzak D. (2003): On algebraic operations on fuzzy reals, In: Neural Networks and Soft Computing (Rutkowski L., Siekmann J., Tadeusiewicz R., Zadeh L.A., Eds.). - Heidelberg: Physica Verlag pp. 54-61.

[10] Piegat A. (2001): Fuzzy Modeling and Control. - Heidelberg: Physica Verlag.

[11] Piegat A. (2005): A new definition of the fuzzy set. - Appl. Math. Comput. Sci., Vol. 15, No. 1, pp. 125-140.

[12] Rakus-Anderson E. (2003): The Newton interpolation method with fuzzy numbers as the entries, In: Neural Networks and Soft Computing (Rutkowski L., Siekmann J., Tadeusiewicz R., Zadeh L.A., Eds.) - Heidelberg: Physica Verlag, pp. 310-315.

[13] Yager R.R. and Filev D. (1994): Essentials of Fuzzy Modeling and Control.- New York: Wiley.

[14] Von Altrock C. (1995): Fuzzy Logic. - Muenchen: R. Oldenburg Verlag.

[15] Zadeh L.A. (1978): Fuzzy sets as a basis for a theory of possibility.- Fuzzy Sets Syst., Vol. 1, No. 1, pp. 3-28.

[16] Zhou C. (2002): Fuzzy-arithmetic-based Lyapunov synthesis to the design of stable fuzzy controllers: Computing with Words approach. - Appl. Math. Comput. Sci., Vol. 12, No. 3, pp. 411-422.

[17] Zimmermann H.J. and Zysno P. (1980): Latent connectives in human decision making.-Fuzzy Sets Syst., Vol. 4, No. 1, pp. 37-51.

[18] Zimmermann H.J. (1991): Fuzzy Set Theory and Its Applications. -Boston: Kluwer.