<p>As an extended form of fuzzy sets, interval-valued fuzzy sets possess many advantages in dealing with uncertainty and can be used to solve a wide range of complex decision-making problems. Additionally, fuzzy rough sets, as an important mathematical model in granular computing theory, have been successfully applied in many different fields. In order to effectively integrate these two ideas and use them to cope with realistic decision-making problems, this paper proposes a novel interval-valued fuzzy rough set model based on interval overlap functions and interval grouping functions. Firstly, in the interval-valued fuzzy approximation space, a pair of lower and upper interval-valued fuzzy rough approximation operators derived from the interval overlap and grouping functions is defined by use of a construction method. Then, several basic properties of the model are systematically investigated, focusing on revealing the intrinsic mathematical associations between the presented interval-valued fuzzy rough approximation operators and diversified interval-valued fuzzy relations. In terms of application, a new energy vehicle selection method based on the obtained interval-valued fuzzy rough sets is proposed. At last, the feasibility of the proposed decision-making approach is illustrated by a case analysis, a comparative analysis together with a sensitivity analysis.</p>