Fuzzy logic is essentially an expert system structure tailored to deal with continuous-valued inputs and outputs instead of discrete lexical elements.
Thus, fuzzy logic
can potentially reduce the number of rules required in a system. This is achieved through clever preprocessing of the inputs, where each continuous input value is "fuzzified" or converted from a precise numeric value to a degree-of-membership in a "fuzzy set" as shown in Figure 10. Fuzzy logic is attractive because it allows for conflicting "expert opinion," thereby allowing the use of information normally excluded from scientific models. For design, fuzzy logic can be used to
define a range of feasible design parameters even when historical data are insufficient to use tractional probability-based approaches.
When an input falls into a region where two or more fuzzy sets overlap, it simply produces a degree-of-membership in each of the overlapping sets. An output term of a fuzzy logic system is itself a fuzzy set, which must be "defuzzified" or converted back to a precise (i.e., "crisp") numeric value. This is done by taking the centroid of the part of the output fuzzy set lying below the degree-of-membership output value. This degree-of-membership can result from a straight mapping of input fuzzy set to output fuzzy set, as shown by Rule 1 in Figure 10, or from a logical combination of rules12 as used in an expert system (Rule 2 in Figure 10). When two or more inference rules trigger on a given output, the "crisp" output is calculated as the centroid of the areas of the contributing rules.
- Fuzzy Logic Set Membership
By providing the means for an expert system structure to treat continuous inputs and outputs as lexical elements, it eliminates the stepwise approximation a classical expert system would normally be forced to use in such a situation. This significantly reduces the number of inference rules
required and makes the program structure more clear. Also, because the mapping between inputs, outputs and lexical elements is done via simple curve functions, a fuzzy system is easier to "fine tune". Thus a given fuzzy solution can be taken to other similar domains by rescaling or reshaping the input and output curves while leaving the logical inferences unchanged.
12The AND operator selects the smallest degree-of-membership of its operands, while the OR operator selects the largest degree-of-membership.