A method of approximating intuitionistic fuzzy numbers by trapezoidal intuitionistic fuzzy numbers with respect to a well-known metric is studied in this paper. Firstly, the representations of extended trapezoidal intuitionistic approximations of intuitionistic fuzzy numbers are discussed. Then the representations of trapezoidal intuitionistic and triangular intuitionistic approximations of intuitionistic fuzzy numbers are provided. Finally, the algorithms and examples of trapezoidal intuitionistic and triangular intuitionistic approximations are given, and the results of approximations are applied on ranking of intuitionistic fuzzy numbers.
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