<p>Transportation problems are inevitably affected by numerous imprecise factors like weather, fuel expenses, topography, etc. Hence, the use of crisp parameters to model transportation problems appears to be both insufficient and inaccurate. Consequently, transportation problems using fuzzy/ intuitionistic fuzzy (IF) numbers seem more effective. Interval-valued intuitionistic fuzzy (IVIF) numbers are further generalization of IF numbers where membership and non-membership degrees are closed sub-intervals of [0,&#xa0;1]. This concept of allocating interval values helps in dealing with the hesitancy of decision-maker while assigning fixed values to membership and non-membership degrees. In this article, balanced transportation problems having multiple objectives under the IVIF environment are examined. To overcome inconsistencies in the existing approaches, novel linear as well as non-linear interval-valued membership and non-membership functions have been proposed. Subsequently, an improved IVIF programming approach is developed using these newly defined functions along with theoretical validation. In addition, when goals are associated with objective functions, the proposed approach has been further improvised as IVIF prioritized goal programming. Eventually, a trip planning problem in the tourism industry is exhibited to illustrate the proposed IVIF technique and later, it is amalgamated with prioritized goals to demonstrate the proposed IVIF goal programming approach.</p>