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Knowledge-Driven Modeling of Mineral Prospectivity 217

have evidential scores equal to zero, suggesting their complete non-favourability for
epithermal Au deposit occurrence. Likewise, the three lowest classes of ANOMALY are
completely non-indicative of presence of epithermal Au deposit occurrences. It is
uncommon practise in mineral prospectivity mapping to use minimum and maximum
fuzzy scores of 0 and 1, respectively, because by using them suggests that one has
complete knowledge about the spatial association of any set of spatial evidence with the
mineral deposits of interest (cf. Bárdossy and Fodor, 2005). Here, the minimum and
maximum fuzzy scores of 0 and 1, respectively, are used only for the purpose of
demonstrating their effects on the output compared to the output of multi-class index
overlay modeling described earlier and to the outputs of the other modeling techniques
that follow further below.
The preceding examples of fuzzy membership functions are applicable to spatial data
of continuous fields to be used as evidence in support of the proposition of mineral
prospectivity. For spatial data of discrete geo-objects to be used as evidence in support
of the proposition of mineral prospectivity (e.g., a lithologic map to be used as evidence
of ‘favourable host rocks’), discontinuous fuzzy membership functions are defined based
on sound judgment of their pairwise relative importance or relevance to the proposition
under examination. In this regard, the application of the AHP (Saaty, 1977) may be
useful as has been demonstrated in, for example, operations research (i.e., an inter-
disciplinary branch of applied mathematics for decision-making) (Triantaphyllou, 1990;
Pendharkar, 2003), although the application of the AHP to assign fuzzy scores to classes
of evidence (rather than to assign weights to evidential maps) for mineral prospectivity
mapping has not yet been demonstrated. Proving this proposition is, however, beyond
the scope of this volume. The criteria for judgment of favourability of various lithologic
units as host rocks may include, for example, a-priori knowledge of host rock lithologies
of mineral deposits of the type sought, chemical reactivity, age with respect to that of
mineralisation of interest, etc. Knowledge of quantitative spatial associations between
various mapped lithologic units and mineral deposits of interest in well-explored areas
may also be considered as a criterion for judging which lithologic units are favourable
host rocks for the same type of mineral deposits in frontier areas. Prudence must be
exercised, nonetheless, in doing so because the degree of spatial association between
known host lithologies and mineral deposits varies from one area to another depending
on the present level of erosion and, therefore, on the areas of mapped lithologies and
number of mineral deposit occurrences. This caveat also applies to the knowledge
representation of host rock evidence via the preceding techniques as well as to
interpretations of results of applications of data-driven techniques for mineral
prospectivity mapping (Carranza et al., 2008a).
Although assignment of fuzzy membership grades or definition of fuzzy membership
functions is a highly subjective exercise, the choice of fuzzy membership scores or the
definition of fuzzy membership functions must reflect realistic spatial associations
between mineral deposits of interest and spatial evidence as illustrated, for example, in
Figs. 7-11 and 7-12. Because the fuzzy membership scores propagate through a model
and ultimately determine the output, fuzzification is the most critical stage in fuzzy logic