Expected-value techniques for Monte Carlo modeling of well logging problems

Fuzzification of continuous-value spatial evidence for mineral prospectivity mapping

“…This is because the former approach uses a function based on weighted average, expected value, which mathematically treats uncertainty and probability together (e.g., Mosher et al, 2010;Runge et al, 2011;Gupta et al, 2013) but the latter does not. Therefore, as shown in Fig.…”

“…6a). Mathematically, the expected value treats uncertainty and probability (e.g., Mosher et al, 2010;Runge et al, 2011;Gupta et al, 2013) because each event value (here, evidential value like FD) is multiplied by its probability of occurrence (here, fuzzy score) and then divided by sum of the probabilities (here, fuzzy scores) as a weighted average multicriteria decision-making function (c.f. Bonham-Carter, 1994;Carranza, 2008;Feizizadeh et al, 2014).…”

“…Bonham-Carter, 1994;Carranza, 2008;Feizizadeh et al, 2014). Using a weighted average is an approach that has been widely applied to combine information from several criteria into a single evaluation model to modulate uncertainty Feizizadeh et al, 2014), such as index overlay for MPM (e.g., Bonham-Carter, 1994;Carranza, 2008) or geo-hazard susceptibility mapping (e.g., Feizizadeh et al, 2014), and other application fields as expected value approach for example in welllogging (Mosher et al, 2010), financial supports (e.g., Gupta et al, 2013), and biological sciences (e.g., Runge et al, 2011). Furthermore, weighted average integrating approaches like expected value have been used to synthesize continuous fuzzy values (e.g., Xue et al, 2008;Chen et al, 2014) in fuzzy systems (e.g., Heilpern, 1992).…”

“…In addition, this paper proposes to adapt the concept of expected value to further improve fuzzy logic MPM because the problem of modeling evidential attributes that are incompletely known or completely unknown (Xu, 2007a,b) and the relative importance and integration of fuzzy evidential values can be and has been addressed by using expected values (e.g., Heilpern, 1992Heilpern, , 1997Rubinstein, 1981;Wang and Chin, 2011;Ye, 2011;Liu, 2013;Gupta et al, 2013). The expected value approach is based on the idea that event level interaction and probabilities, here evidential attributes and their corresponding evidential scores representing the probability of mineral deposit occurrence, can be averaged to produce unbiased estimates that properly account for potential future events in modeling (e.g., Mosher et al, 2010). The expected value method in conjunction with fuzzy models has been applied in ranking and decision-making problems (e.g., Heilpern, 1992;Guo and Tanaka, 2001;Wang and Zhang, 2009 a,b;Wang and Chin, 2011;Ye, 2011;Gupta et al, 2013).…”

Geometric average of spatial evidence data layers: A GIS-based multi-criteria decision-making approach to mineral prospectivity mapping

“…In this paper, uncertainties of geological processes portrayed as features in mineral exploration maps (i.e., different geo-exploration data sets) and uncertainties with interpretations of exploration data and lack of proven historical weights of evidential features (incomplete information), which affect MPM as mentioned above, were considered by applying modified expected value and geometric average functions that mathematically treat uncertainty (e.g., Mosher et al, 2010;Runge et al, 2011;Gupta et al, 2013;Yousefi and Carranza, 2015a). To achieve this, continuous maps of fuzzy evidence layers were integrated using the adapted functions to generate two prospectivity models, one using the expected value method for MPM and one using the adapted geometric average function.…”