Zero-shot slot filling is a domain adaptation approach to handle unseen slots in new domains without training instances. Previous studies implemented zero-shot slot filling by predicting both slot entities and slot types. Because of the lack of knowledge about new domains, the existing methods often fail to predict slot entities for new domains as well as cannot effectively predict unseen slot types even when slot entities are correctly identified. Moreover, for some seen slot types, those methods may suffer from the domain shift problem, because the unseen context in new domains may change the explanations of the slots. In this study, we propose intrinsic representations to alleviate the domain shift problems above. Specifically, we propose a multi-relation-based representation to capture both the general and specific characteristics of slot entities, and an ontology-based representation to provide complementary knowledge on the relationships between slots and values across domains, for handling both unseen slot types and unseen contexts. We constructed a two-step pipeline model using the proposed representations to solve the domain shift problem. Experimental results in terms of the F1 score on three large datasets-Snips, SGD, and MultiWOZ 2.3-showed that our model outperformed state-of-the-art baselines by 29.62, 10.38, and 3.89, respectively. The detailed analysis with the average slot F1 score showed that our model improved the prediction by 25.82 for unseen slot types and by 10.51 for seen slot types. The results demonstrated that the proposed intrinsic representations can effectively alleviate the domain shift problem for both unseen slot types and seen slot types with unseen contexts.