Neural computing in pharmaceutical products and process development - Computer-Aided Applications in Pharmaceutical Technology - page 121

Fuzzifi cation is the process of mapping crisp numerical values to the
membership functions of the fuzzy variables. By clustering the outputs,
overlapping fuzzy data sets are defi ned. Distances between elements of the
same cluster are minimized, whereas distances between clusters are
maximized (Sproule et al., 2002). Depending on the number of fuzzy sets,
a different number of if . . . then. . . rules is defi ned. Then, based on fuzzy
sets and defi ned rules, input variables are expressed as fuzzy sets on the
basis of their association with the output set in each rule. The resulting
patterns of membership values are formed into representative fuzzy sets
for each input variable (Sproule et al., 2002).
The fuzzy rule can be defi ned as follows: If antecedent then consequent .
As previously explained, fuzzy logic is based upon the intuitive way of
human reasoning, hence it is possible to have many different levels of a
certain feature, for example, its degree of membership. Therefore,
operators are applied to membership functions in order to refl ect the
linguistic meaning of a certain membership degree. Some of the operators
that can be used are a little, slightly, very, extremely, somewhat, indeed,
etc. When the fuzzy rule is presented, a conclusion (consequent) is given
a certain confi dence factor that describes the degree of membership to the
extremes of the fuzzy set.
Since it is possible that some of the input variable(s) do not affect
output variable(s) to a greater extent, all rules are checked and those that
do not contribute to knowledge representation are excluded from the
fi nal rule base. Every rule contributes to predicting the output to a certain
degree, based on the degree of membership of the input values to the
input fuzzy sets (Sproule et al., 2002). De-fuzzifi cation is the process of
producing a quantifi able result in fuzzy logic, given fuzzy sets, and
corresponding membership degrees. De-fuzzifi cation is an interpretation
of the membership degrees of the fuzzy sets into specifi c decision or real
value, that is, fuzzy outputs are transformed into crisp numerical values.
One of the most common de-fuzzifi cation techniques is the center-of-
gravity method (Mamdani, 1976). Since fuzzy set membership functions
typically have the form of a triangle, the de-fuzzifi cation process is
performed by chopping off parts of the triangle to form a trapezoid (or
other form). In order to chop off part of the triangle, the degree of
membership needs to be known. Then, once the trapezoids for each
property are constructed, they are superimposed one upon another to
form one geometric shape. Then, the centroid of this shape, called the
fuzzy centroid , is calculated. The x -coordinate of the centroid is the de-
fuzzifi ed value. Different methods of de-fuzzifi cation that are available
are (Van Leekwijck, 1999) adaptive integration, basic de-fuzzifi cation

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