Abstract
The theory of q-rung orthopair fuzzy sets (q-ROFSs) is emerging for the provision of more comprehensive and useful information in comparison to their counterparts like intuitionistic and Pythagorean fuzzy sets, especially when responding to the models of vague data with membership and non-membership grades of elements. In this study, a significant generalized model q-ROFS is used to introduce the concept of q-rung orthopair fuzzy vector spaces (q-ROFVSs) and illustrated by an example. We further elaborate the q-rung orthopair fuzzy linearly independent vectors. The study also involves the results regarding q-rung orthopair fuzzy basis and dimensions of q-ROFVSs. The main focus of this study is to define the concepts of q-rung orthopair fuzzy matroids (q-ROFMs) and apply them to explore the characteristics of their basis, dimensions, and rank function. Ultimately, to show the significance of our proposed work, we combine these ideas and offer an application. We provide an algorithm to solve the numerical problems related to human flow between particular regions to ensure the increased government response action against frequently used path (heavy path) for the countries involved via directed q-rung orthopair fuzzy graph (q-ROFG). At last, a comparative study of the proposed work with the existing theory of Pythagorean fuzzy matroids is also presented.