On fuzzy number calculus

Witold Kosiński

International Journal of Applied Mathematics and Computer Science (2006)

  • Volume: 16, Issue: 1, page 51-57
  • ISSN: 1641-876X

Abstract

top
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.

How to cite

top

Kosiński, Witold. "On fuzzy number calculus." International Journal of Applied Mathematics and Computer Science 16.1 (2006): 51-57. <http://eudml.org/doc/207777>.

@article{Kosiński2006,
abstract = {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.},
author = {Kosiński, Witold},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {fuzzy numbers; bounded variation},
language = {eng},
number = {1},
pages = {51-57},
title = {On fuzzy number calculus},
url = {http://eudml.org/doc/207777},
volume = {16},
year = {2006},
}

TY - JOUR
AU - Kosiński, Witold
TI - On fuzzy number calculus
JO - International Journal of Applied Mathematics and Computer Science
PY - 2006
VL - 16
IS - 1
SP - 51
EP - 57
AB - 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.
LA - eng
KW - fuzzy numbers; bounded variation
UR - http://eudml.org/doc/207777
ER -

References

top
  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). Zbl0661.94029
  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. Zbl0383.94045
  6. Goetschel R. Jr. and Voxman W. (1986): Elementaryi fuzzy calculus. - Fuzzy Sets Syst., Vol. 18, No. 1, pp. 31-43. Zbl0626.26014
  7. Klir G.J. (1997): Fuzzy arithmetic with requisite constraints. - Fuzzy Sets Syst., Vol. 91, No. 2, pp. 165-175. Zbl0920.04007
  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. Zbl1043.03041
  10. 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. 
  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. Zbl1053.03030
  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. Zbl1102.03310
  13. 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. Zbl1058.68662
  14. Kosiński W. and Prokopowicz P. (2004): Algebra of fuzzy numbers.- Matematyka Stosowana. Matematyka dla Spoleczenstwa, 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, Jorg Siekmann, R. Tadeusiewicz, Lofti A. Zadeh, Eds.), Lecture Notes on Artificial Intelligence. - Berlin: Springer, Vol. 3070, pp. 320-325. Zbl1058.68689
  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). Zbl0659.90063
  19. Piegat A. (1999): Fuzzy Modeling and Control. - Warsaw: PLJ, (in Polish). Zbl0976.93001
  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. Łeski, Eds.). - Gliwice: Silesian University of Technology Press, pp. 291-310. 
  22. Wagenknecht M., Hampel R., Schneider V. (2001): Computational aspectsof fuzzy arithmetic based on Archimedean t-norms. - Fuzzy Sets Syst., Vol. 1231, pp. 49-62. Zbl0997.65071
  23. Zadeh L.A. (1965): Fuzzy sets. - Inf. Contr., Vol. 8, No. 3, pp. 338-353. Zbl0139.24606
  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. Zbl0397.68071
  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. Zbl0553.68049

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.