Under the background of the “double high” power system, the electricity heat hydrogen system (EHHS) plays a significant role in the process of energy decarbonization. In order to meet the different optimization objectives of the system under different new energy consumption states, a new energy consumption potential assessment and optimized operation method based on intuitionistic fuzzy rough set theory is proposed. By using the intuitionistic fuzzy rough set theory, the continuous attribute data is divided into different levels and the results of its membership and non-membership are gotten at different levels. The membership results of real-time consumption data are matched with the rule sets, and then the system consumption state judgment result is obtained. In this article, the system consumption situation is divided into five states, and compared with the traditional division method, so the system state can be described more comprehensively. At the same time, the fuzzy set is used to deal with the ambiguity of the boundary between each state. The intuition theory is used to solve the problem of the uncertainty of the consumption state, and then the accurate judgment can be realized. In response to different consumption states, an optimal scheduling model is established in which a hydrogen heat energy system (HHES) is involved to meet different requirements, and a hybrid particle swarm optimization algorithm is used to solve the model. Adopting the IEEE-30 bus system as the network structure of EHHS in the simulation, the analysis shows that the dynamic state division method based on intuitionistic fuzzy rough set theory can better be used to judge the system state according to real-time variable factors. The system optimization based on the consumption state division has the advantages of improving the operating economy and increasing the consumption of new energy.