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A New Definition of the Fuzzy Set

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The present fuzzy arithmetic based on Zadeh's possibilistic extension principle and on the classic definition of a fuzzy set has many essential drawbacks. Therefore its application to the solution of practical tasks is limited. In the paper a new definition of the fuzzy set is presented. The definition allows for a considerable fuzziness decrease in the number of arithmetic operations in comparison with the results produced by the present fuzzy arithmetic.
Rocznik
Strony
125--140
Opis fizyczny
Bibliogr. 19 poz., rys., wykr.
Twórcy
autor
  • Faculty of Computer Science and Information Systems Technical University of Szczecin ul. Zolnierska 49, 71-210 Szczecin, Poland, Andrzej.Piegat@wi.ps.pl
Bibliografia
  • [1] Bezdek J. (1993): Editorial, fuzzy models — What are they, and why?. — IEEE Trans. Fuzzy Syst., Vol. 1, No. 1, pp. 1–6.
  • [2] Driankov D., Hellendorn H. and Reinfrank M. (1993): An Introduction to Fuzzy Control. — Berlin: Springer.
  • [3] Dubois D. and Prade H. (1988): Possibility Theory. — New York: Plenum Press.
  • [4] Dubois D. and Prade H. (1996): An introduction to fuzzy systems. —Int. J. Appl. Math. Comput. Sci., Vol. 6, No. 3, pp. 485–503.
  • [5] Dubois D. and Prade H. (1997): The three semantics of fuzzy sets.—Fuzzy Sets Syst., Vol. 90, No. 2, pp.141–150.
  • [6] Kaufmann A. and Gupta M.M. (1991): Introduction to Fuzzy Arithmetic.—New York: Van Nostrand Reinhold.
  • [7] Klir G.J. (1997): Fuzzy arithmetic with requisite constraints. — Fuzzy Sets Syst., Vol. 91, pp. 165–175.
  • [8] Klir G.J. and Folger T.A. (1988): Fuzzy Sets, Uncertainty, and Information.—Englewood Cliffs: Prentice Hall.
  • [9] Kosiński W., Prokopowicz P. and Ślęzak D. (2003): Ordered fuzzy numbers. — Bull. Polish Acad. Sci. Math., Vol. 51, No. 3, pp. 329–341.
  • [10] Pearsal J. (Ed.) (1999): The New Oxford Dictionary of English. —Oxford: Oxford University Press.
  • [11] Piegat A. (2001): Fuzzy Modeling and Control. — Heidelberg, New York: Springer-Verlag.
  • [12] Piegat A. (2004): Is fuzzy evaluation a measurement? In: Soft Computing, Tools, Techniques and Applications (P. Grzegorzewski, M. Krawczak and S. Zadrożny, Eds.). — Warszawa: Akademicka Oficyna Wydawnicza EXIT, pp. 257–266.
  • [13] Piegat A. (2005a): On practical problems with explanation of the difference between possibility and probability. — Contr. Cybern., (accepted for publication in No. 2 in 2005).
  • [14] Piegat A. (2005b): Informative value of the possibilistic extension principle, In: Enhanced Methods in Computer Security, Biometric and Artificial Intelligence Systems (J. Pejas and A. Piegat, Eds.).—New York: Springer Science Business Media, Inc., pp. 301–310.
  • [15] Yager R.R. and Filev D.P. (1994): Essentials of Fuzzy Modeling and Control. — London: Wiley.
  • [16] Zadeh L.A. (1965): Fuzzy Sets. — Inf. Contr., Vol. 8, No. 3, pp. 338–353.
  • [17] Zadeh L.A. (1978): Fuzzy sets as a basis for a theory of possibility.—Fuzzy Sets Syst., Vol. 1, No. 28, pp. 3–28.
  • [18] Zadeh L.A. (2002): From computing with numbers to computing with words – From manipulation of measurements to manipulation of perceptions. — Int. J. Appl. Math. Comput. Sci., Vol. 12, No. 3, pp. 307–324.
  • [19] Zimmermann H.J. (1996): Fuzzy Set Theory.—Boston: Kluwer.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ1-0008-0021
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