Page 217 - Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

Knowledge-Driven Modeling of Mineral Prospectivity 219

Fig. 7-13. Examples of output of the fuzzy AND, fuzzy OR, fuzzy algebraic product (FAP) and
fuzzy algebraic sum (FAS) based on input fuzzy scores (A) inclusive of 1 and 0, (B) inclusive of 1
but exclusive of 0 and (C) exclusive of 0 and 1.

score at a location is 1 even though in at least one of the other evidence maps the fuzzy
score is 0, the output fuzzy score for that location is still 1 (Fig. 7-13A). Clearly, the FO
operator is appropriate in combining supplementary sets of evidence, meaning that at
least one of any of the pieces of evidence to be combined via this operator is deemed
necessary to support the proposition of mineral prospectivity at every location.
The fuzzy algebraic product (hereafter denoted as FAP) is defined as

n
μ FAP = ∏μ i (7.11)
= i 1

where μ FAP is the output fuzzy score and μ i represents the fuzzy evidential scores at a
location in i (=1, 2,…, n) evidence maps. The output of the FAP is less than or equal to
the lowest fuzzy score at every location (Fig. 7-13). So, for example, if in one evidence
map the fuzzy score at a location is 0 even though in at least one of the other evidence
maps the fuzzy score is 1, the output fuzzy score for that location is still zero (Fig. 7-