Page 210 - Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

212 Chapter 7

For a particular object or value of spatial evidence, the more completely it belongs to
the fuzzy set of favourable evidence, the closer its membership grade is to 1. Thus,
individual objects or values of spatial evidence portrayed in maps can be evaluated in
terms of their membership in a fuzzy set of favourable evidence based on expert
judgment. Grades of membership are usually represented by a mathematical function
that may be linear or continuous; indeed, many fuzzy sets have extremely nonlinear
membership grade functions (Zimmerman, 1991). The evaluation of fuzzy membership
grades always relates to a certain proposition. In mineral prospectivity mapping, the
grade of membership of a class or value of evidence (i.e., geological attributes) in a
fuzzy set of favourable evidence is evaluated according to the proposition “this location
is prospective for mineral deposits of the type sought”.
Fuzzification is thus carried out by application of a membership function μ A(x) to a
set or map of values of classes of values of spatial evidence. Robinson (2003) has
reviewed several types of fuzzy membership functions that are applicable to
geographical analysis with the aid of a GIS. In knowledge-driven mineral prospectivity
mapping, the choice or definition of a fuzzy membership function in order to fuzzify a
spatial evidence of mineral prospectivity must be based on sound perception or judgment
of spatial association between geological features represented by the evidence and
occurrence of mineral deposits of the type sought. For example, based on the results of
analysis of spatial association between FI and epithermal Au deposit occurrences in the
case study area (see Table 6-IX), the following membership function may be defined for
the fuzzy set ‘favourable distance to FI’:

­ 1 for x <1
μ ( = ) x ° x 4 ( − )1 for ≤ 1 x ≤4 (7.5)
® − )4(
d
° 0 for x >4
¯

where x is distance (km) to FI. The graph and generic form of this function are illustrated
in Fig. 7-11A. The parameters of the function (i.e., 1 and 4, which are α and γ,
respectively, in Fig. 7-11A) are based on (a) range to distances to FI with optimum
positive spatial association with the epithermal Au deposit occurrences, which is 1 km
(see Table 6-IX) and (b) the minimum of the range of distances to FI (e.g., 4 km; see Fig.
6-10B) considered to be completely unfavourable for the occurrence of mineral deposits
of the type sought. The function parameters are chosen arbitrarily based on subjective
judgment or knowledge of spatial association between mineral deposits of interest and
the types of geological features under consideration. The fuzzy membership function in
equation (7.5) or Fig. 7-11A is linear and, thus, inconsistent with the conceptual
knowledge-based representation of spatial evidence illustrated in Fig. 7-8. Alternatively,
the following membership function may be defined for the set ‘favourable distance to
FI’: