Incorporating Expert Knowledge Continued from page 9 Fuzzy Tallness 1 0.9 True Possibly Tall Fuzzy Tallness 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 20 Uncertain Possibly Short False 30 40 50 60 70 80 90 100 Height (inches) Figure 1: Graphic example of the membership function Tallness. The semantic statement might be, “a height of 82 inches is always considered tall,” whereas “a height below 38 inches is never considered tall.” A height of about 70 inches is ambiguous for tallness and given a membership value of 0.5.5. A Spatial Example In a fuzzy logic model in ArcGIS, evidence rasters are assigned membership values with the Fuzzy Membership tool. Table 2 (on page 12) defines the fuzzy membership functions available. Memberships are combined using the Fuzzy Overlay tool to select a fuzzy combination operator based on how the evidence interacts. Table 3 defines five fuzzy operators. In a given model, different operators may be used. These operators provide greater flexibility than a weighted-sum or weighted-overlay model and let the expert incorporate greater sensitivity based on knowledge of how the evidence interacts. In practice, operators for combining evidence are relatively easy to select, but fuzzy membership may require some tuning of the membership parameters to represent expert knowledge. A Simple Expert Semantic Summary Figure 3 is a simple example of a fuzzy logic spatial model. This geologic model for Carlin-type gold deposits uses datasets that are available with the Spatial Data Modeller tools (www.ige.unicamp.br/sdm/ default_e.htm). [Carlin-type gold deposits, with ore grades commonly between 1 and 5 grams per ton, are primarily mined from open pits in Nevada. They are named for the most prolific goldfield in the Northern Hemisphere, the Carlin Trend Field.] From a semantic description of the criteria for finding Carlin-type gold deposits, a simplified expert semantic model might consist of the following statements: „ High values of antimony (Sb) or arsenic (As) are favorable for Carlin-type gold. Use stream-sediment geochemistry to define a mineralization geochemical factor. „ Host rocks of Carlin-type deposits are primarily Paleozoic and Mesozoic dirty carbonate rocks. Use a geologic map to define a lithologic factor. „ Dirty carbonate rocks are chemically low in potassium (K). Use stream-sediment geochemistry to make a lithologic adjustment to the mineralization geochemical factor. Elevated K differentiates Carlin-type gold deposits from volcanic-rock-hosted gold deposits, although both types are high in Sb or As. From these semantic statements, a simple outline of the fuzzy logic model can be defined. A Simple Fuzzy Logic Model Frequently such models have submodels or factors that describe complex aspects of the spatial model. These submodels often represent factors defined by a single discipline; thus, “the Expert” for the entire model is—in practice—often a team of experts who bring knowledge from diverse fields when defining the decision process. A final model is derived by combining the factors. The following semantic statements describe the process for determining the geochemical, lithologic-adjusted geochemical, and lithologic factors in the model shown in Figure 3. Table 3: Summary of fuzzy combination operators implemented in the Fuzzy Overlay tool in ArcGIS 10. WHERE is the membership value for crisp measurement x, and I indicates each of the n evidence layers. 10 ArcUser Spring 2010 www.esri.com