Variable sets method for urban flood vulnerability assessment

On the basis of dialectics basic laws and mathematical theorems of variable sets, this paper proposes a variable sets method for urban flood vulnerability assessment. In this method, the comprehensive relative membership degree of multi-indices is represented by an index relative difference degree, which follows the characteristics of dialectical philosophy and mathematics. According to the quality-quantity exchange theorem, the relative difference degree of two adjacent levels (h and h+1), whose index standard interval values cross the boundaries, equals 0 in the urban flood vulnerability assessment. On the basis of the opposite unity theorem, the sum of relative membership degrees should be equal to 1 when indices lie in the adjacent degrees h and h+1. The variable sets method is proved to be theoretically rigorous and computationally simple. This paper takes 29 cities of Hunan province as an example to assess the urban flood vulnerability, and then compares the results from this newly developed method with the assessment results obtained from the fuzzy comprehensive evaluation and fuzzy set pair analysis methods.