View source for Issue:A method to obtain trapezoidal approximations of intuitionistic fuzzy numbers from trapezoidal approximations of fuzzy sets

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{{issue/title
 | title           = A method to obtain trapezoidal approximations of intuitionistic fuzzy numbers from trapezoidal approximations of fuzzy sets
 | shortcut        = nifs/15/1/13-25
}}
{{issue/author
 | author          = Adrian Ban
 | institution     = Department of Mathematics and Informatics, University of Oradea
 | address         = Universitâţii 1, 410087 Oradea, Romania
 | email-before-at = aiban
 | email-after-at  = uoradea.ro
}}
{{issue/author
 | author          = Lucian Coroianu
 | institution     = Department of Mathematics and Informatics, University of Oradea
 | address         = Universitâţii 1, 410087 Oradea, Romania
 | email-before-at = lcoroianu
 | email-after-at  = uoradea.ro
}}
{{issue/data
 | conference      = 13<sup>th</sup> [[ICIFS]], Sofia, 9-10 May 2009
 | issue           = Conference proceedings, [[Notes on Intuitionistic Fuzzy Sets/15/1|"Notes on Intuitionistic Fuzzy Sets", Volume 15 (2009) Number 1]], pages 1—12
 | file            = NIFS-15-1-13-25.pdf
 | format          = PDF
 | size            = 162
 | abstract        = 
The well-known Karush-Kuhn-Tucker theorem can be used, as in the fuzzy case, to find the trapezoidal approximation of a given intuitionistic fuzzy number. The method is quite technical such that obtaining the trapezoidal approximation of an intuitionistic fuzzy numbers from the trapezoidal approximation of a fuzzy number is proposed in the present paper. Among the advantages of this method is the immediate extension of important properties in fuzzy case to intuitionistic fuzzy case.

 | keywords        = Fuzzy number, [[Intuitionistic fuzzy number]], Trapezoidal fuzzy number
 | references      = 
# [[Krassimir Atanassov|K. T. Atanassov]], [[Issue:Intuitionistic fuzzy sets|Intuitionistic fuzzy sets]], [[Fuzzy Sets and Systems]] 20 (1986) 87-96.
# K. T. Atanassov, [[Intuitionistic Fuzzy Sets: Theory and Applications]], Springer-Verlag, Heidelberg, New York, 1999.
# A. I. Ban, Nearest interval approximation of an intuitionistic fuzzy number, in: B. Reusch (Ed.), Computational Intelligence, Theory and Applications, Springer, 2006, pp. 229-240.
# A. I. Ban, Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the expected interval, Fuzzy Sets and Systems 159 (2008) 1327-1344.
# A. I. Ban, Approximation of intuitionistic fuzzy numbers by trapezoidal fuzzy numbers preserving the expected interval, ''submitted''.
# A. I. Ban, On the nearest parametric approximation of a fuzzy number - Revisited, Fuzzy Sets and Systems (2009), doi: 10.1016/j.fss.2009.05.001.
# P. Grzegorzewski, Metrics and orders in space of fuzzy numbers, Fuzzy Sets and Systems 97 (1998) 83-94.
# P. Grzegorzewski, Intuitionistic fuzzy numbers-principles, metrics and ranking, in: K. T. Atanassov, O. Hryniewicz, J. Kacprzyk (Eds.), [[Soft Computing Foundations and Theoretical Aspects]], Academic House Exit, Warszawa, 2004, pp. 235-249.
# P. Grzegorzewski, E. Mrówka, Trapezoidal approximations of fuzzy numbers revisited, Fuzzy Sets and Systems 158 (2007) 757-768.
# C.-T. Yeh, On improving trapezoidal and triangular approximations of fuzzy numbers, International Journal of Approximate Reasoning 48 (2008) 297-313.

 | citations       = 
 | see-also        = 
}}