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

shortcut

http://ifigenia.org/wiki/issue:nifs/15/1/13-25

Title of paper: A method to obtain trapezoidal approximations of intuitionistic fuzzy numbers from trapezoidal approximations of fuzzy sets Author(s): Adrian Ban Department of Mathematics and Informatics, University of Oradea, Universitâţii 1, 410087 Oradea, Romania aiban@uoradea.ro Lucian Coroianu Department of Mathematics and Informatics, University of Oradea, Universitâţii 1, 410087 Oradea, Romania lcoroianu@uoradea.ro Presented at: 13th ICIFS, Sofia, 9-10 May 2009 Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 15 (2009) Number 1, pages 1—12 Download:  PDF (162  Kb, File info) 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: K. T. Atanassov, 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: The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.