Historical Seismograms - Evidence from the AD 2000 Izu Islands ...

Applications of Fuzzy Mathematics 313Table 1. Rough Comparison between Intensity Degrees from VI to XIand Building Damage StandardType XI X IX VIII VII VIa b a b a b a b a b a bI 1 O+ 0.991 0.052 0.944 0.065 0.762 0.293 0.400 0.081 0.154 0.040I1 1 O+ 0.877 0.192 0.738 0.258 0.560 0.223 0.260 0.119 0.055 0.025I11 0.953 0.122 0.557 0.182 0.296 0.550 0.136 0.083 0.050 0.034 0 0“Type” refers to building type. Damage conditions are Udestroy” and “severe destroy”Table 2. Quantitative Comparison between Intensities andthe Earth Fissure Standard Represented by Its WidthType of fissures XII XIa (cm) b (cm) a ( 4 b (cm)Rock fissure 163 100 50 27Ground fissure 720 2 GO 140 100Finally, considering a suitable weight distribution function W for different cases,we may apply the fuzzy multifactorial evaluation on the basis of the matrix Q. Thecorresponding formula isP = W 0 Q = (Pi, Pz,. ..,Pm), (4)where the symbol ‘0’’ denotes the compositional operation which is defined byPj = max(min(Wk,qk,j)),k j = 1,2,.. ., m. (5)By using the principle of choosing the closest approach, we may obtain an estimatedearthquake intensity, i.e., the degree in the seismic intensity scale for a givenevent. This intensity must correspond to the maximal component of the vector Pin equation (4).2.2 Exa rnple 3(1) Intensity of the 1937 Hozhei (M = 7.0) Earthquake. According to the historicalrecords (Gu, 1983), about 30% of buildings in the Hozhei region and 20% ofbuildings in the Donming and Dintau regions were destroyed by this earthquake.Let us suppose that the buildings destroyed in the given regions in 1937 are basicallytype I1 buildings, and the conditions of building damage may be consideredas “destroyn and ‘severe destroy”. By using Table 1, we may obtain the degreematrices of approaching corresponding to intensities (XI X IX VIII VIIVI) asfor the Hozhei region, andR1 = (0.5 0.5 0.528 0.628 0.947 0.5)R2 = (0.5 0.5 0.506 0.537 0.888 0.5)