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2006 | 16 | 1 | 51-57
Tytuł artykułu

On fuzzy number calculus

Treść / Zawartość
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.
Słowa kluczowe
Rocznik
Tom
16
Numer
1
Strony
51-57
Opis fizyczny
Daty
wydano
2006
otrzymano
2005-10-07
poprawiono
2006-02-04
Twórcy
  • Kazimierz Wielki University of Bydgoszcz Institute of Environmental Mechanics and Applied Computer Science, ul. Chodkiewicza 30, 85-064 Bydgoszcz, Poland
Bibliografia
  • Alexiewicz A. (1969): Functional Analysis. - Warsaw: Polish Scientific Publishers (in Polish).
  • Chen Guanrong and Pham Trung Tat (2001): Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems. - Boca Raton, FL, CRS Press.
  • Czogała E. and Pedrycz W. (1985): Elements and Methods of Fuzzy Set Theory. - Warsaw: Polish Scientific Publishers (in Polish).
  • 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.
  • Dubois D. and Prade H. (1978): Operations on fuzzy numbers.- Int. J. Syst. Sci., Vol. 9, No. 6, pp. 613-626.
  • Goetschel R. Jr. and Voxman W. (1986): Elementaryi fuzzy calculus. - Fuzzy Sets Syst., Vol. 18, No. 1, pp. 31-43.
  • Klir G.J. (1997): Fuzzy arithmetic with requisite constraints. - Fuzzy Sets Syst., Vol. 91, No. 2, pp. 165-175.
  • 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).
  • 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.
  • Kosiński W., Prokopowicz P. and Ślęzak D. (2002b): Drawback of fuzzy arthmetics - New intutions and propositions, In: Proc. Methods of Aritificial Intelligence (T. Burczynski, W. Cholewa, W. Moczulski, Eds.). - Gliwice: PACM, pp. 231-237.
  • 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.
  • 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.
  • Kosiński W. (2004): On defuzzification of ordered fuzzy numbers, In: Proc. ICAISC 2004, 7th Int. Conference, Zakopane, Poland, June 2004 (L. Rutkowski, Jorg Siekmann, R. Tadeusiewicz, Lofti A. Zadeh, Eds.), LNAI. - Berlin: Springer, Vol. 3070, pp. 326-331.
  • Kosiński W. and Prokopowicz P. (2004): Algebra of fuzzy numbers.- Matematyka Stosowana. Matematyka dla Spoleczenstwa, Vol. 5, No. 46, pp. 37-63, (in Polish).
  • 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, Jorg Siekmann, R. Tadeusiewicz, Lofti A. Zadeh, Eds.), Lecture Notes on Artificial Intelligence. - Berlin: Springer, Vol. 3070, pp. 320-325.
  • Łachwa A. (2001): Fuzzy World of Sets, Numbers, Relations, Fazts, Rules and Decisions. - Warsaw: EXIT, (in Polish).
  • Łojasiewicz S. (1973): Introduction to the theory of real functions.- Warsaw: Polish Scientific Publishers, (in Polish).
  • Martos B. (1983): Nonlinear Programming - Theory and Methods.- Warsaw: Polish Scientific Publishers, (in Polish).
  • Piegat A. (1999): Fuzzy Modeling and Control. - Warsaw: PLJ, (in Polish).
  • Prokopowicz P. (2005): Algorithmic operations on fuzzy numbers and their applications. - Ph. D. thesis, Institute of Fundamental Technological Research, Polish Acad. Sci., (in Polish).
  • 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. Łeski, Eds.). - Gliwice: Silesian University of Technology Press, pp. 291-310.
  • Wagenknecht M., Hampel R., Schneider V. (2001): Computational aspectsof fuzzy arithmetic based on Archimedean t-norms. - Fuzzy Sets Syst., Vol. 1231, pp. 49-62.
  • Zadeh L.A. (1965): Fuzzy sets. - Inf. Contr., Vol. 8, No. 3, pp. 338-353.
  • 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.
  • 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
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv16i1p51bwm
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