Abstract: Tourists' authentic perceptions are crucial for the development of world heritage resources. The paper focuses on exploring the relationships between tourists' authentic perceptions and authenticity-based tourism development of world heritage. Through the empirical study on the Forbidden City in Beijing, we find that the relationships between the above two factors can be simulated by the model of set theory in algebra. As a result, five types of set relationships are proposed: "separation relation", "intersection relation", "inclusion relation Ⅰ", "inclusion relation Ⅱ" and "superposition relation". According to sample distribution rules, the set relationships can be further divided into primary set relationships and secondary set relationships. The study on set relationships based on demographic characteristic of tourists by using two-way analysis of variance method shows that the tourists in different groups of gender, ages, levels of education, visit frequencies and levels of early perspectives have different perceptions for the set relationships. The findings in this paper are helpful for identifying effects of the authenticity-based exploitation of world heritage resources and proposing future strategies for world heritage resources from tourists' authentic perspectives.

Key words: set relationships, tourists&rsquo, authentic perceptions, authenticity-based development, world heritage resources, the Forbidden City