This paper presents the fuzzy analytic hierarchy process (FAHP) for risk assessment of debris-flow
occurrence using three different fuzzy numbers. Three layers are involved in the structure of the FAHP: the
goal layer, the criteria layer, and the sub-criteria layer. In the criteria and sub-criteria layers, nine major
influence factors are grouped into three categories: (1) topological and geological conditions, which
includes the influence factors of slope angle, type of deposit, grain size distribution, and surface plants; (2)
watershed conditions, which includes effective watershed area and quantity of outflow of sediment; and (3)
rainfall conditions, which includes rainfall intensity, duration, and accumulated rainfall. Judgment
regarding the relative influence of these factors is based on a nine-level scale used to form the fuzzy
reciprocal judgment matrices for evaluating the weighting vectors for each layer. Two cases of debris-flow
disasters that occurred in eastern Taiwan were tested using the FAHP; one was a debris flow, and the other
a mudslide. The results showed that the proposed FAHP models using the three kinds of fuzzy numbers as
well as the associated influence factors and criteria can successfully predict the risk of debris-flow hazard
occurrence. Furthermore, the predicted overall risk indices obtained from the FAHP using the three kinds
of fuzzy numbers were smaller than those obtained from AHP, but more practical due to consideration of
the uncertainty and vagueness involved in natural hazards.
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