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Background: The renaming of program identifiers is the most common refactoring operation. Because some identifiers are related to each other, developers may need to rename related identifiers together. Aims: To understand how developers rename multiple identifiers simultaneously, it is necessary to consider the relationships between identifiers in the program and the brief matching for non-identical but semantically similar identifiers. Method: We investigate the relationships between co-renamed identifiers and identify the types of their relationships that contribute to improving the recommendation using more than 1M of renaming instances collected from the histories of open-source software projects. We also evaluate and compare the impact of co-renaming and the relationships between identifiers when inflections occur in the words in identifiers are taken into account. Results: We revealed several relationships of identifiers that are frequently found in the co-renamed identifiers, such as the identifiers of methods in the same class or an identifier defining a variable and another used for initializing the variable, depending on the type of the renamed identifiers. Additionally, the consideration of inflections did not affect the tendency of the relationships. Conclusion: These results suggest an approach that prioritizes the identifiers to be recommended depending on their types and the type of the renamed identifier.