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.
Faculty of Computer Science and Information Systems, Technical University of Szczecin, ul.Żołnierska 49, 71-210 Szczecin, Poland
Bibliografia
Bezdek J. (1993): ditorial, fuzzy models - What are they, and why?.- IEEE Trans. Fuzzy Syst., Vol. 1, No. 1, pp. 1-6.
Driankov D., Hellendorn H. and Reinfrank M. (1993): An Introduction to Fuzzy Control. - Berlin:Springer.
Dubois D. and Prade H. (1988): Possibility Theory. - New York: Plenum Press.
Dubois D. and Prade H. (1996): An introduction to fuzzy systems. - Int. J. Appl. Math. Comput. Sci., Vol. 6, No. 3, pp. 485-503.
Dubois D. and Prade H. (1997): The three semantics of fuzzy sets. - Fuzzy Sets Syst., Vol. 90, No. 2, pp.141-150.
Kaufmann A. and Gupta M.M. (1991): Introduction to Fuzzy Arithmetic.- New York: Van Nostrand Reinhold.
Klir G.J. (1997): Fuzzy arithmetic with requisite constraints. - Fuzzy Sets Syst., Vol. 91, pp. 165-175.
Klir G.J. and Folger T.A. (1988): Fuzzy Sets, Uncertainty, and Information.- Englewood Cliffs: Prentice Hall.
Kosiński W., Prokopowicz P. and Ślęzak D. (2003): Ordered fuzzy numbers.- Bull. Polish Acad. Sci. Math., Vol. 51, No. 3, pp. 329-341.
Pearsal J. (Ed.) (1999): The New Oxford Dictionary of English.- Oxford: Oxford University Press.
Piegat A. (2001): Fuzzy Modeling and Control. - Heidelberg, New York: Springer-Verlag.
Piegat A. (2004): Is fuzzy evaluation a measurement? In: Soft Computing, Tools, Techniques and Applications (P. Grzegorzewski, M. Krawczakand S. Zadrożny, Eds.). - Warszawa:Akademicka Oficyna Wydawnicza EXIT, pp. 257-266.
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).
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.
Yager R.R. and Filev D.P. (1994): Essentials of Fuzzy Modeling and Control. - London: Wiley.
Zadeh L.A. (1978): Fuzzy sets as a basis for a theory of possibility. - Fuzzy Sets Syst., Vol. 1, No. 28, pp. 3-28.
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.
Zimmermann H.J. (1996): Fuzzy Set Theory. - Boston: Kluwer.