Page 225 - Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

Knowledge-Driven Modeling of Mineral Prospectivity 227

to locations in a study area with missing data. In many case examples in the literature,
locations in a study area without data are assigned either very low fuzzy scores or fuzzy
scores equal to zero. It has been demonstrated above that assignment of fuzzy scores
equal to zero can produce undesirable and unrealistic results. In this volume, locations in
the case study area without stream sediment geochemical data are assigned fuzzy scores
of zero (meaning they are not considered in the analysis), although this has the same net
effect of using fuzzy scores of zero as exemplified in Fig. 7-16A.
The following section explains a different technique of representing and integrating
multi-class evidential maps in order to model mineral prospectivity. This technique –
evidential belief modeling – provides for explicit representation of evidential
uncertainty.

Evidential belief modeling
Dempster’s (1967, 1968) work on the generalisation of Bayesian lower and upper
probabilities provided the basis for the theory of evidential belief. Shafer (1976) then
defined two evidential belief functions (EBFs), belief and plausibility, to represent the
lower and upper probabilities, respectively, that a given body of evidence supports a
particular proposition. In the last three decades or so, the Dempster-Shafer theory of
evidential belief has attracted considerable attention as a promising method of dealing
with some of the basic problems arising in the fusion of data or combination of evidence.
Zadeh (1986) provided a simplification of the Dempster-Shafer theory of evidential
belief and demonstrated the capability of Dempster’s (1968) rule of combination to
integrate distinct probability distributions. Walley (1987) suggested, however, that
Dempster’s (1968) rule of combination is generally neither suitable for combining
evidence from independent observations nor appropriate for combining prior beliefs with
observational evidence. However, applications of the Dempster-Shafer theory of
evidential belief proved its usefulness in combining pieces of evidence from disparate
sources (e.g., Cohen, 1985; Lee et al., 1987; Kim and Swain, 1989). Chung and Fabbri
(1993) described the representation of geoscience information for data integration based
on interpretation of the Dempster-Shafer theory of evidential belief. An et al. (1994b)
demonstrated the management or representation of uncertainty in the integration of
exploration data using EBFs.
The mathematical formalism of the EBFs is complex (Dempster, 1967; Shafer,
1976). The following explanations for the application of EBFs to mineral prospectivity
mapping are simplified and informal. For a piece of spatial evidence that is used in
evaluating a proposition (i.e., mineral prospectivity), four values, each in the range of
[0,1], are assigned based on evaluation of how much it supports the proposition. These
values are belief (hereafter denoted as Bel), disbelief (hereafter denoted as Dis),
uncertainty (hereafter denoted as Unc) and plausibility (hereafter denoted as Pls). The
Bel and Pls represent, respectively, lower and upper degrees of support provided by a
given piece of spatial evidence to the proposition. This means, for example, that with a
given spatial evidence mineral deposit occurrence is either less (Bel) or more (Pls)
likely. Thus, Pls and Bel together represent the vague or uncertain ‘more-or-less’