The Heronian mean (HM) operator has the valuable characteristic of determining correlations among aggregated values. The HM operator is a massive feasible and more flexible technique to manage hurdle and awkward data in the circumstances of the fuzzy set (FS) theory. The major aims of this investigation are to analyze the novel theory of complex neutrosophic uncertain linguistic (CNUL) setting and their beneficial theories. The CNUL information includes uncertain linguistic sets, truth grade, abstinence grade, and falsity grade in the shape of complex numbers. In the occurrence of the novel concept of CNUL data, we try to invent the well-known theory of CNUL arithmetic HM (CNULAHM), CNUL weighted arithmetic HM (CNULWAHM), CNUL geometric HM (CNULGHM), CNUL weighted geometric HM (CNULWGHM) operators, which can help to aggregate the group of alternatives into a singleton element. Several attractive properties and their related results are also demonstrated. Additionally, to demonstrate the feasibility and rationality of the invented operators, multi-attribute group decision-making (MAGDM) performance is evaluated based on the invented works. Finally, we illustrated several examples to diagnose the sensitive analysis and graphically shown of the invented operators to express the consistency and feasibility of the evaluated works.