| Fuzzy mathematics, a sub-division of mathematics applied in the quantitive study on the natural fuzzy phenomina, has been widely used in the geological investigation. In this paper, taking the"Three components"mineral prediction, the comprehensive study of the geological anomaly, the diversity of mineralization and the spectrum of mineral deposits as the guiding theory, we use the fuzzy mathematics in the metallogenic prognosis of the Eastern Part of Gejiu Tin deposite by virtue of the analysis on the geological anomaly. This paper includes three sections as follows.Firstly, study on the threshold of the the abnormal element Sn in the eastern of Gejiu deposite. In the research on the geological anomaly, it is vital to determine the threshold. In this section, by using the geochemical data of the element Sn on some certain spot in the eastern of Gejiu mine and the fuzzy distribution theory, we first establish five subordinate functions of fuzzy sets such as Sn element anomaly, Lower value anomaly, mean value anomaly, high value anomaly and super-high-value anomaly etc. Then, based on the average value of the subordinate function, we work out that the abnormal thresholds of the Sn element, the lower value, the mean value, the high value and the super-high value are respectively 20.82 ppm, 1.12 ppm, 6.89 ppm, 162.44 ppm and 222.83 ppm and at the same time, we find that the fuzzy degrees of the above five fuzzy sets are 0.10, 0.30, 0.18, 0.29 and 0.26, five comparatively small figures, showing the rationality of the thresholds obtained in this section.Secondly, establish the fuzzy relational equation between Sn contained and the location in the eastern part of Laochang mine is. First, based on the geochemical information on the Sn at the earth's surface in the eastern part of Laochang district, we divide the region to be investigated into 10 units, and take 4 of them as the known units and the rest 6 as the units to be doped out, then by virtue of the fuzzy inclusion degree equation, we establish the fuzzy relational equation of the Sn in the known units and the in the units to be predicted and finally, according to the solution of the fuzzy relation equation, we find that the Sn contained in the 6 investigated units are 7.50 ppm, 1.75 ppm, 4.75 ppm, 2.50 ppm, 3.50 ppm and 2.50 ppm respectively and that the observed Sn in the 6 units are respectively 7.16 ppm, 1.96 ppm, 4.05 ppm, 2.10 ppm, 3.85 ppm and 2.46 ppm. The relative errors of the predicted amount of Sn and the observed data in the 6 units are respectively 5%, 12%, 15%, 16%, 10% and 2%.Finally, fuzzy linear regression model for the deposit of the Sn resource is obtained. According to the conclusion that has been reported in the second period for the Sn deposit in the 12 tin ore-bodies and taking the fuzzy clustering analysis into account, we fist classify the tin ore bodies as three types, then we establish the fuzzy linear regression model for the deposit of the Sn resource and the ore -body characteristic indices of the three divided types respectively and finally, based the established models, we predict the tin resource deposit in the 5 units set for the ore-bodies to be doped out and obtain that the predicted tin deposits in the 5 units are respectively 2937.6 tons, 292.8 tons,77 tons, 419.1 tons and 464.6 tons, while the real tin deposits in the 5 units are 3116 tons, 315 tons, 100 tons, 396 tons and 467 tons respectively. The relative errors between the predicted tin deposit and the real tin deposit in the 5 units are respectively 6%, 7%, 23%, 6% and 1%.
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