Abbreviations table.

The interval-valued q-rung orthopair fuzzy sets being an extension of interval-valued intuitionistic and interval-valued Pythagorean fuzzy sets is more flexible model to address vague information that has only two attributes yes or no. The combination of the concept of graph structures with interval-valued q-rung orthopair fuzzy sets termed interval-valued q-rung orthopair fuzzy graphs has been introduced in the literature. Due to its nature, interval-valued q-rung orthopair fuzzy graph provides a vast space for membership and non-membership values. In this study, we initiate the notions of covering and matching in the paradigm of interval-valued q-rung orthopair fuzzy graphs (IVq-ROFGs) and provide the analysis of fuzzy air conditioning system (FACS) based on these concepts. Some results and theorems related to these concepts, previously established for different fuzzy graphs, are also extended. In the beginning, we introduce the idea of covering in IVq-ROFGs and investigate several characteristics of some special types of IVq-ROFGs like cyclic IVq-ROFGs, complete IVq-ROFGs and complete bipartite IVq-ROFGs. Afterwards, we introduce the concept of matching in IVq-ROFGs and discuss various types of matchings within this frame. To demonstrate the effectiveness of our study, we apply the concepts of SAs and SIS in IVq-ROFGs supported by algorithm and pseudocode, to establish an appropriate framework for the FACS. This framework assesses the relationship between room temperature and target temperature. Finally, comparative study is conducted to verify that the presented model is the extension of the existing models in the literature.