In recent years, network security has become a major concern. Using the Internet to store and analyze data has become an integral aspect of the production and operation of many new and traditional enterprises. However, many enterprises lack the necessary resources to secure information security, and selecting the best network security service provider has become a real issue for many enterprises. This research introduces a novel decision-making method utilizing the 2-tuple linguistic complex q-rung orthopair fuzzy numbers to tackle this issue. (...) We propose the 2TLCq-ROF concept by combining the complex q-rung orthopair fuzzy set with 2-tuple linguistic terms, including the fundamental definition, operational rules, scoring, and accuracy functions. Aggregation operators are the fundamental mathematical approach used to combine various inputs into a single output. Taking into account the interaction between the attributes, we develop the 2TLCq-ROF Hamacher operators by using the innovative operational rules. These operators include the 2TLCq-ROFH weighted average, 2TLCq-ROFH ordered weighted average, 2TLCq-ROFH hybrid average, 2TLCq-ROFH weighted geometric, 2TLCq-ROFH ordered weighted geometric, and 2TLCq-ROFH hybrid geometric operators. In addition, we talk about the properties of 2TLCq-ROFH operators such as idempotency, commutativity, monotonicity, and boundedness and also examine their spatial cases. To tackle the problems of the 2TLCq-ROF multiattribute group decision-making environment, we develop a novel approach according to the COPRAS model. Finally, to validate the feasibility of the given strategy, we employ a quantitative example related to select the best network security service provider. In comparison with existing approaches, the developed decision-making algorithm is most extensively used and reduces the loss of information. (shrink)