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The application of horizontal membership functions to fuzzy arithmetic operations

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The fuzzy numbers arise in decision making, control theory, fuzzy systems and approximate reasoning problems. The operations on them are becoming more and more popular. The aim of this paper is to present the fuzzy arithmetic operations on fuzzy numbers in a new way, using the horizontal membership functions (HMFs). The horizontal membership functions enable to introduce uncertain, interval or fuzzy variable-values together with crisp values in arithmetic operations without using Zadeh's extension principle. Thus, a relatively easy aggregation of crisp and uncertain knowledge has become possible. The numerical example of this developed method is also provided.
Rocznik
Strony
3--10
Opis fizyczny
Bibliogr. 13 poz., rys., tab.
Twórcy
  • Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin, Poland
Bibliografia
  • [1] Dubois D., Prade H., Operations on fuzzy numbers, International Journal of System Science, No. 9, pp. 613-626.
  • [2] Dymova L., Soft computing in economics and finance, Springer-Verlag, Berlin-Heidelberg, 2011
  • [3] Hanss M., Applied fuzzy arithmetic, Springer-Verlag, Berlin, 2005
  • [4] Kaufmann A., Gupta M., Introduction to Fuzzy Arithmetic Theory and Application, Van Nostrand Reinhold, New York, 1991.
  • [5] Klir G.J., Folger T.A., Fuzzy Sets, Uncertainty, and Information, Prentice Hall, Englewood Cliffs, NJ, 1988.
  • [6] Moore, R.E. Interval analysis, Prentice Hall Englewood Cliffs, 1966.
  • [7] Piegat A., Fuzzy modeling and control, Physica Verlag, Heidelberg-New York, 2001.
  • [8] Piegat A., Landowski M., Is the conventional interval-arithmetic correct?, Journal of Theoretical and Applied Computer Science, vol. 6, no. 2, pp. 27-44, 2012.
  • [9] Piegat A., Pluciński M., Fuzzy number addition with the application of horizontal membership functions, Journal of Intelligent and Fuzzy Systems (under review)
  • [10] Piegat A., Tomaszewska K., Decision-Making under uncertainty using Info-Gap Theory and new multidimensional RDM interval arithmetic, Electrotechnical Review, vol. 89, no. 8, pp. 71-76, 2013.
  • [11] Ross T.J., Fuzzy Logic with Engineering Applications, McGraw-Hill, Hightstown, NJ, 1995.
  • [12] Zadeh L.A., Fuzzy sets, Information and Control, 1965.
  • [13] Zimmermann H. J., Fuzzy Set Theory and Its Applications, 3rd ed., Kluwer Academic Publishers, Boston, MA, 1996.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-445789ba-6eef-4608-bcde-a3e5e0cc3c9e
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