Flood classification is an effective way to improve flood forecasting accuracy. According to the opposite unity mathematical theorem in Variable Sets theory, this paper proposes a Variable Sets principle and method for flood classification, which is based on the mathematical theorem of dialectics basic laws. This newly proposed method explores a novel way to analyze and solve engineering problems by utilizing a dialectical thinking. In this paper, the Tuwei River basin, located in the Yellow River tributary, is taken as an example for flood classification. The results obtained in this study reveal the problems in a previous method—Set Pair Analysis classification method. The variable sets method is proven to be theoretically rigorous, computationally simple. The classification results are objective, accurate and consistent with the actual situations. This study demonstrates the significant importance of using a scientifically sound method in solving engineering problems.
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.
