This research is focused on obtaining the shortest tour between two sites based on the Travelling Salesman Problem (TSP) using the Interval Valued Intuitionistic Fuzzy Set (IVIFS), by applying the new Branch and Bound (B & B) method. For allotting the tour (route) of starting the point and ending with the same point, the B & B method is used to handle this problem. Moreover, the Haar wavelet method-based ranking and the modulus subtraction method to find the penalty to reduce the cost of the addressed problem. Furthermore, numerical examples have been provided for validating the cost of the proposed method’s graphical representation.