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.

区间值q-阶正交对模糊集（interval-valued q-rung orthopair fuzzy sets）是区间值直觉模糊集与区间值毕达哥拉斯模糊集的推广形式，相较于仅支持“是/否”两类属性的模糊信息建模方法，其具备更强的灵活性。将图结构概念与区间值q-阶正交对模糊集相结合所得到的区间值q-阶正交对模糊图（interval-valued q-rung orthopair fuzzy graphs，简称IVq-ROFGs），已在相关学术文献中被提出。依托其固有特性，IVq-ROFGs为隶属度与非隶属度的取值提供了更为广阔的空间。本研究首次提出区间值q-阶正交对模糊图框架下的覆盖与匹配概念，并基于这些概念开展了模糊空调系统（fuzzy air conditioning system, FACS）的相关分析工作。此外，此前针对各类模糊图所确立的与这些概念相关的结论与定理，也被推广至本研究场景中。

首先，本文引入IVq-ROFGs中的覆盖概念，并探究了几类特殊IVq-ROFGs的若干性质，包括循环IVq-ROFGs、完全IVq-ROFGs以及完全二部IVq-ROFGs。随后，本文提出IVq-ROFGs中的匹配概念，并讨论了该框架下各类匹配的相关性质。为验证本研究的有效性，本文依托算法与伪代码实现，将SAs与SIS概念应用于IVq-ROFGs中，以此为FACS构建了一套适配的分析框架，该框架可用于评估室温与目标温度之间的关联关系。最后，本文通过对比研究验证了所提模型是对现有文献中已有模型的有效推广。