Temporal reasoning methods have been successful in temporal knowledge graphs (TKGs) and are widely employed in many downstream application areas. Most existing TKG reasoning models transform time intervals into continuous time snapshots, with each snapshot representing a subgraph of the TKG. Although such processing can produce satisfactory outcomes, it ignores the integrity of a time interval and increases the amount of data. Meanwhile, many previous works focuses on the logic of sequentially occurring facts, disregarding the complex temporal logics of various time intervals. Consequently, we propose a Reinforcement Learning-based Model for Temporal Knowledge Graph Reasoning with Time Intervals (RTTI), which focuses on time-aware multi-hop reasoning arising from complex time intervals. In RTTI, we construct the time learning part to obtain the time embedding of the current path. It simulates the temporal logic with relation historical encoding and compute the time interval between two facts through the temporal logic feature matrix. Furthermore, we propose a new method for representing time intervals that breaks the original time interval embedding method, and express the time interval using median and embedding changes of two timestamps. We evaluate RTTI on four public TKGs for the link prediction task, and experimental results indicate that our approach can still perform well on more complicated tasks. Meanwhile, our method can search for more interpretable paths in the broader space and improve the reasoning ability in sparse spaces.