Abstract:The fuzzy set theory introduced by L. A. 2adeh (1965) expresses the notion of gradational membership by introduction of membership function of fuzzy subset. Assume we have a set U, a fuzzy subset of U, A is a subset of Uin which the characteristic function A(u)takes values in the real interval (0.1), that is, the membership function, instead of only being l or 0 (belonging to or not), allows a degree of membership. There are many fuzzy objects and concepts in geology and mineral resources assessment, such as "favorability for ore-deposition”, "recognition criteria", “ore-controlling factors, etc”. Therefore, the fuzzy set theory provides geologists with a useful tool in mathematically analysing complex geological problems. In this paper the direct fuzzy recognition method is used to test 12 granitic intrusions in south China with-known uranium deposits of different scale or without any economic uranium mineralization, and then to predict the uranium potential of other 14 granitic intrusions in the same region that have not yet been examined or explored in detail. The fuzzy cluster analysis is also used as another method to determine the uranium potential of these intrusions. The two approaches give approximately similar results. The direct fuzzy recognition is made by constructing a membership function of "favorability for ore-deposition". On the basis of the experience and knowledge acquired by the Chinese uranium geologists and geochemists concerning the uranium deposits in granites in south China, the following geological and geochemical conditions are selected as favorable factors for uranium ore-deposition: the average uranium abundance of the intrusion, the uneven distribution of uranium within the intrusion represented by standard deviation and diversity coefficient of uranium content in granite, the exposed area of the intrusion, the development of fracture structure and the presence of uraniferous wall rocks of the intrusion. The membership function of each factor is established as follows: where a, b, c1, c2 are parameters determined from the 12 known intrusions. Using the operational rules of fuzzy set, we obtain the composite membership function of all factors. Taking λ1=0.8, λ2=0.4 as the threshold of the possible occurrence of big-medium-sized deposits, and that of smaller deposits separately, the degree of fitting for the 12 known intrusions is ll/12, and only one intrusion is wrongly judged regarding the scale of deposit. On the basis of the calculated composite degree of membership of the 14 unknown intrusions, it is predicted that in the intrusions No.15 and No.16 the big-medium sized uranium deposits might occur, while in the intrusions No.14, No.18 and No.22 the smaller ones might be discovered. The fuzzy cluster analysis of these 26 granitic intrusions provides similar conclusion regarding their uranium potential. The first step of this analysis is to construct the matrix of similarity coefficient which is subsequently reconstructed in order to fit the transitivity. Then, with thresholdλ=0.84, these 26 intrusions are divided into six classes, and a cluster tree derivation diagram is obtained. An analysis of this diagram reveals that the intrusions No.15 and No.16, along with almost all known uranium-productive intrusions, fall into the same class-class No.l, suggesting that uranium deposits are most likely to occur within these two intrusions.
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孙文鹏, 陈庆兰, 次小林.1983.应用模糊集合论方法评价华南若干花岗岩体铀成矿远景[J].矿床地质,2(2):68~76.1983.The application of fuzzy set method to the evaluation of uranium potential of some granitic intrusions in south China[J].Mineral Deposits2(2):68~76
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