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Knowledge-Driven Modeling of Mineral Prospectivity                   215






















           Fig. 7-12. Two examples of fuzzy membership functions for knowledge-based representation of
           multi-element stream sediment anomaly scores as spatial evidence of mineral prospectivity in the
           case study area. (A) A linear fuzzy membership function defined by parameters α and γ, which are
           two geochemical anomaly scores describing the spatial association between mineral deposits and
           geochemical  anomalies (see text for further  explanation). (B) A fuzzy membership function
           consisting of a linear function and a nonlinear functions defined, respectively, by the last condition
           and the first three conditions of the equation above the graph. The parameters α and γ used in (A)
           are also used in (B). The linear function represents decreasing fuzzy scores from 1.0 for y = γ to,
                                         +
           say, 0.9 for maximum y. The nonlinear S  function represents decreasing fuzzy scores from 1.0 for
                                  +
           y = γ to 0.0 for y ≤ α. The S  function requires another parameter, β, at which the function is
           forced through the cross-over point [i.e., μ g (y) = 0.5] (see text for further explanation). The slope
           of the nonlinear function changes with different values of β.

           for the present case β could be 0.24, which would mean that one considers locations with
           ANOMALY scores below 0.24 to be considerably less prospective than locations with
           anomaly scores above 0.24. The fuzzy membership function in equation (7.8) or Fig. 7-
           12B is, thus, apparently consistent with the conceptual knowledge-based representation
           of spatial evidence illustrated in Fig. 7-8.
              A  fuzzy  membership function defined for  spatial data of a continuous field (e.g.,
           distance to certain structures, geochemical  anomalies, etc.) to be used as evidence in
           support  of the proposition of mineral prospectivity may be  applied  directly to such
           spatial data in map form. Here, for comparison with the results of the multi-class index
           overlay modeling, the model of fuzzy membership function depicted in equation (7.6)
           and illustrated in Fig. 7-11B is applied to derive fuzzy membership scores for the same
           classes of proximity to faults/fractures used in the multi-class index overlay modeling
           (see Table 7-V). The averages of distances in the classes of proximity to individual sets
           of structures are used in the calculation of fuzzy membership scores by application of the
           fuzzy membership function. Likewise, the model of fuzzy membership function depicted
           in equation (7.8) and illustrated in Fig. 7-12B is applied to derive fuzzy  membership
           scores for the same classes of  ANOMALY  used in the multi-class index overlay
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