The notation of extended intuitionistic fuzzy number is introduced and the representation of the weighted extended trapezoidal intuitionistic approximation of an intuitionistic fuzzy number is given in this paper. The problem related to aggregation is addressed about approximating the given intuitionistic fuzzy numbers or aggregating the given intuitionistic fuzzy numbers and then approximating the output of aggregation in two cases. Some examples are enumerated to show the benefits of the conclusions proposed in this paper and the conclusions are applied to multiple attribute decision making based on intuitionistic fuzzy information.
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