Development of kimberlite exploration Geographic Information System  Fig. 4. Geologic Map of Mainpur-Deobhog area Fuzzy logical operation All the available information that provides evidence for kimberite exploration is combined together by means of fuzzy logical operation. The fuzzy logical operation is used for the development of KEGIS as fuzzy logic allows for more flexible combinations for weighted information and can be readily implemented with a GIS modeling language. All these are based on subjective empirical models linked to weights or fuzzy memberships values assigned subjectively using knowledge of the process involved to estimate the relative importance of the input map. This is carried out in stages, with the ultimate product being a predictive map indicating the relative favourability of kimberlite emplacement. The combination processes involves weighing and fusion of evidence carried out in a number of different ways. Fuzzy membership functions are subjectively assigned weight to each type of evidences, thereby controlling the relative weighting of the data. Alternatively, the evidences could have been weighted statistically, using the observed association of the evidence map with known occurrences of kimberlite pipes. Several operations can be employed using the evidence maps with combination of fuzzy membership value together. For the development of KEGIS, fuzzy algebraic product, fuzzy algebraic sum and, fuzzy gamma operations are deployed. Fuzzy algebraic product With combination of all six evidence maps and the employed fuzzy algebraic product, the combined membership function is defined as  Where µ = Fuzzy membership value for ith map And, i = 1 to 6 (evidence maps are combined) The combined fuzzy membership values tend to be very small with this operator, due to effect of multiplying several numbers less than 1. The output is always smaller than or equal to the smallest contributing membership value and is therefore, "decreasive". Fuzzy algebraic sum This operator is complementary to the algebraic product, defined as.  Where µ = Fuzzy membership value for ith map And, i = 1 to 6 (evidence maps are combined) The result is always larger (or equal to the largest) contributing fuzzy membership value. The effect is therefore, "increasive". Two pieces of that both evidences favouring a hypothesis are reinforced into one another and the combined evidences are more supportive than either piece of evidence taken individually. In case of present investigation fuzzy algebraic sum of (0.95, 0.1) is 1(1-0.95) X (1-0.1) that is equal to 1.0 (FMV). The increasive effect of combining several favourable pieces of evidences is automatically limited by the maximum value 1.0, which can never be exceeded. Note that, whereas the fuzzy algebraic product is an algebraic product, the fuzzy algebraic sum is not an algebraic summation. Gamma operation (Gamma = 0.95) Fuzzy algebraic sum and fuzzy algebraic product were combined together by means of Gamma operation. This is defined in terms of Combination = (Fuzzy algebraic sum) x ? (Fuzzy algebraic product) (1- ?) Where ? is parameter chosen in the range (0,1) When ? is 1, the combination is same as the fuzzy algebraic sum and when ? is 0, the combination is equal to the fuzzy algebraic product. Judicious choice of g produce output values that ensure a flexible compromise between the "increasive" tendencies of the fuzzy algebraic sum and the "decresive" effects of fuzzy algebraic product. The data integration and combination of Fuzzy operation results obtained during KEGIS are used in development of strategy for Kimberlite exploration. |