Comparison of classical methods of processing fuzzy information with methods using idea of ordered fuzzy numbers based on general linguistic Mamdani model

• Autorzy: Prokopowicz P.
• Języki publikacji: EN

Abstrakty

EN

Model of ordered fuzzy numbers (OFN) was defined and described in [4][5]. For this model simple and effective methods of arithmetical operations were suggested [4] [5] [6] [7]. OFNs representation is quite easy in the implementation as well as operations on them. Thanks to OFNs using we can free ourselves of the situation, in which results of operations on convex fuzzy numbers (classical model) we get "wider- more and more imprecise. In this paper author wants to pay attention on an important ownership of ordered fuzzy numbers - possibility of practical using as convex fuzzy numbers. Results of the simulation of using OFN to steering simplified fuzzy model of moving vehicle were introduced in [9]. Analysis and comparing results of the processing of imprecise information are a main aim of this publication. Were compared here chosen classical methods (aggregation of premises being based on MAX-MIN t-norm and reasoning methods based on Mamdani, Larsen, Łukasiewicz operators) with methods based on OFN. To get possibiy general results analysis were based on the very general linguistic model of Mamdani type fuzzy controller where we are operating on values of the linguistic variable amount so as little", average", "much". Carried analysis this way permits to get scores independent of units. With merit of introducing linguistic value in the form of fuzzy numbers, there is a possibility of straight and free graduating presented notions to the sizes dependent on the context in the any concrete situation.

Słowa kluczowe

EN

ordered fuzzy number; fuzzy number; fuzzy control; reasoning methods

PL

numer rozmyty; sterowanie rozmyte; metoda rozumowania

• Wydawca: Instytut Telekomunikacji i Informatyki Uniwersytetu Technologiczno-Przyrodniczego w Bydgoszczy
• Czasopismo: Image Processing & Communications
• Rocznik: 2006
• Tom: Vol. 11, no 1
• Strony: 83--90
• Opis fizyczny: Bibliogr. 10 poz., wykr.

Twórcy

autor

Prokopowicz P.

• Institute of Environmental Mechanics and Applied Computer Science, Kazimierz Wielki University, Chodkiewicza 30, 85-072 Bydgoszcz, Poland,

Bibliografia

• [1] Chen G., Pham T.T., (2001), Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems, CRC press LLC, United States 2001
• [2] Czogała E., Pedrycz W., (1985), Elements and methods of fuzzy set theory (in Polish), PWN, Warszawa 1985
• [3] Kosiński W., P. Prokopowicz P., Ślęzak D., Ordered fuzzy numbers, Bulletin of the Polish Academy of Sciences, Ser. Sci. Math., 51 (3), 2003, Springer Verlag, pp. 327-339.
• [4] Kosiński W., Prokopowicz P., Ślęzak D.,: Counting with fuzzy numbers, XLII Sympo-zjum PTMTS Modelling In Mechanics, Gliwice 2003, Zeszyty Naukowe Katedry Mechaniki 20/2003, str. 221-225
• [5] Kosiński W., Prokopowicz P., Ślęzak D., On algebraic operations on fuzzy numbers, Intelligent Information Processing and Web Mining, Proc. of the International US: II-PWM,03 Conference held in Zakopane, Poland, June 5-5,2003, M. Kłopotek, S.T. Wierzchoń, K.Trojanowski (eds.), Physica-Verlag, Heidelberg 2003, pp. 353-362
• [6] Kosiński W., Prokopowicz P., Ślęzak D.,: 0n algebraic operations on fuzzy reals, in: Advances in Soft Computing, Proc. of the Sixth Int. Conference on Neutral Networks and Soft Computing, Zakopane, Poland June 11-15, 2002, L.Rutkowski , J.Kasprzyk (eds.), Physica-Verlag, Heidelberg, 2003, pp.54-61
• [7] Kosiński W., Prokopowicz P., Algebra liczb rozmytych, Matematyka stosowana, 5(46), 2004, Pismo Polskiego Towarzystwa Matematycznego, Warszawa, 2004, pp.37-63
• [8] Kosiński W., On Defuzzyfication of Orderd Fuzzy Numbers, in: Artifical Intelligence and soft Computing ICAISC 2004, Proc. of the 7th International Conference Zakopane, Poland, June 2004, Rutkowski L., Siekmann J,, Tadeusiewicz R., Zadeh L A., (eds), Springer, Berlin, 2004. pp.326-333
• [9] Prokopowicz P. (2005). Methods based on the ordered fuzzy numbers used in fuzzy control, Proc. Of the Fifth International Workshop on Robot Motion and Control, Dyma-czewo, Poland, June 2005, pp. 349-354
• [10] Zadeh L.A. (1965), Fuzzy sets, Information and Control 8 (1965). str. 338-353