<p>Intuitionistic fuzzy linguistic sets are outlined by a linguistic membership and non-membership degree. In this framework, the decision-makers are capable of considering a linguistic hesitancy degree where they do not simply convey their perception using just one linguistic term. This paper defines unbalanced 2-tuple intuitionistic fuzzy linguistic sets in which, the intuitionistic fuzzy linguistic numbers are composed of linguistic 2-tuples called unbalanced 2-tuple intuitionistic fuzzy linguistic numbers (2-TIFLNs). These 2-tuples belong to a multiplicative unbalanced set that comprises of such terms that are distributed asymmetrically. Further, the linguistic term set in this paper is partitioned into two parts, namely membership terms and non-membership terms. The logic behind partitioning is that it enables decision-makers independently and individually define the membership and non-membership degree for a linguistic term belonging to either set, bringing clarity in the assessment of preferences for linguistic terms. The paper establishes some operational laws of unbalanced 2-TIFLNs and employs them to determine several aggregation operators. Notably, these defined operators exhibit the closure property. The prominent features of these aggregation operators are studied theoretically and graphically. Overall, this research contributes to the process of “computing with words” offering a nuanced approach to handling linguistic information in decision-making contexts.</p>