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On fuzzy number calculus

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Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Some generalizations of the concept of ordered fuzzy numbers (OFN) are defined to handle fuzzy inputs in a quantitative way, exactly as real numbers are handled. Additional two structures, an algebraic one and a normed (topological) one, are introduced to allow for counting with a more general type of membership relations.
Rocznik
Strony
51--57
Opis fizyczny
Bibliogr. 25 poz., wykr.
Twórcy
autor
  • Polish-Japanese Institute of Information Technology Research Center, ul. Koszykowa 86, 02-008 Warsaw, Poland, wkos@pjwstk.edu.pl
Bibliografia
  • [1] Alexiewicz A. (1969): Functional Analysis. - Warsaw: Polish Scientific Publishers (in Polish).
  • [2] Chen Guanrong and Pham Trung Tat (2001): Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems. - Boca Raton, FL, CRS Press.
  • [3] Czogała E. and Pedrycz W. (1985): Elements and Methods of Fuzzy Set Theory. - Warsaw: Polish Scientific Publishers (in Polish).
  • [4] Drewniak J. (2001): Fuzzy numbers. In: Fuzzy Sets and their Applications (J. Chojcan, J. Łęski, Eds.).-Gliwice: Silesian University of Technology Press, pp. 103-129.
  • [5] Dubois D. and Prade H. (1978): Operations on fuzzy numbers. -Int. J. Syst. Sci., Vol. 9, No. 6, pp. 613-626.
  • [6] Goetschel R. Jr. and Voxman W. (1986): Elementary fuzzy calculus. -Fuzzy Sets Syst., Vol. 18, No. 1, pp. 31-43.
  • [7] Klir G.J. (1997): Fuzzy arithmetic with requisite constraints. - Fuzzy Sets Syst., Vol. 91, No. 2, pp. 165-175.
  • [8] Kosiński W., Piechór K., Prokopowicz K. and Tyburek K. (2001): On algorithmic approach to opertions on fuzzy numbers, In: Methods of Artificial Intelligence in Mechanics and Mechanical Engineering (T. Burczyński, W. Cholewa, Eds.).-Gliwice: PACM, pp. 95-98 (in Polish).
  • [9] Kosiński W., P. Prokopowicz P. and Ślęzak D. (2002a): Fuzzy numbers with algebraic operations: algorithmic approach, In: Intelligent Information Systems 2002 (M. Klopotek, S.T. Wierzchoń, M. Michalewicz, Eds.). Proc.IIS'2002, Sopot, Poland - Heidelberg: Physica Verlag, pp. 311- 320.
  • [10] Kosiński W., Prokopowicz P. and Ślęzak D. (2002b): Drawback of fuzzy arthmetics - New intutions and propositions, In: Proc. Methods of Aritificial Intelligence (T. Burczyński, W. Cholewa, W. Moczulski, Eds.). - Gliwice: PACM, pp. 231-237.
  • [11] Kosiński W., Prokopowicz P. and Ślęzak D. (2003a): On algebraic operations on fuzzy numbers, In: Intelligent Information Processing and Web Mining, Proc. Int. Symp. IIS: IIPWM'03, Zakopane, Poland, 2003 (M. Klopotek, S.T. Wierzchoń, K. Trojanowski, Eds.). - Heidelberg: Physica Verlag, pp. 353-362.
  • [12] Kosiński W., Prokopowicz P. and Ślęzak D. (2003b): Ordered fuzzy numbers. - Bull. Polish Acad. Sci., Ser. Sci. Math.,Vol. 51, No. 3, pp. 327-338.
  • [13] Kosiński W. (2004): On defuzzification of ordered fuzzy numbers, In: Proc. ICAISC 2004, 7th Int. Conference, Zakopane, Poland, June 2004 (L. Rutkowski, Jörg Siekmann, R. Tadeusiewicz, Lofti A. Zadeh, Eds.), LNAI. - Berlin: Springer, Vol. 3070, pp. 326-331.
  • [14] Kosiński W. and Prokopowicz P. (2004): Algebra of fuzzy numbers. - Matematyka Stosowana. Matematyka dla Społeczeństwa, Vol. 5, No. 46, pp. 37-63, (in Polish).
  • [15] Koleśnik R., Prokopowicz P. and Kosiński W. (2004): Fuzzy Calculator - useful tool for programming with fuzzy algebra, In: Artficial Intelligence and Soft Computing - ICAISC 2004, 7th Int. Conference, Zakopane, Poland (L. Rutkowski, Jörg Siekmann, R. Tadeusiewicz, Lofti A. Zadeh, Eds.), Lecture Notes on Artificial Intelligence. - Berlin: Springer, Vol. 3070, pp. 320-325.
  • [16] Łachwa A. (2001): Fuzzy World of Sets, Numbers, Relations, Fazts, Rules and Decisions. -Warsaw: EXIT, (in Polish)
  • [17] Łojasiewicz S. (1973): Introduction to the theory of real functions.-Warsaw: Polish Scientific Publishers, (in Polish).
  • [18] Martos B. (1983): Nonlinear Programming - Theory and Methods -Warsaw: Polish Scientific Publishers, (in Polish).
  • [19] Piegat A. (1999): Fuzzy Modeling and Control.-Warsaw: PLJ, (in Polish).
  • [20] Prokopowicz P. (2005): Algorithmic operations on fuzzy numbers and their applications. - Ph. D. thesis, Institute of Fundamental Technological Research, Polish Acad. Sci., (in Polish).
  • [21] Wagenknecht M. (2001): On the approximate treatment of fuzzy arithmetics by inclusion, linear regression and informationcontent estimation, In: Fuzzy Sets and Their Applications (J. Chojcan, J. Łęski, Eds.). - Gliwice: Silesian University of Technology Press, pp. 291-310.
  • [22] Wagenknecht M., Hampel R., Schneider V. (2001): Computational aspects of fuzzy arithmetic based on Archimedean t-norms. - Fuzzy Sets Syst., Vol. 123/1, pp. 49-62.
  • [23] Zadeh L.A. (1965): Fuzzy sets. - Inf. Contr., Vol. 8, No. 3, pp. 338-353.
  • [24] Zadeh L.A. (1975): The concept of a linguistic variable and its application to approximate reasoning, Part I. - Inf. Sci.,Vol. 8, No. 3, pp. 199-249.
  • [25] Zadeh L.A. (1983): The role of fuzzy logic in the management of uncertainty in expert systems.-Fuzzy Sets Syst., Vol. 11, No. 3, pp. 199-227.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ1-0028-0004
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