Data Quality Enhancement Technology to Improve Decision Support - Efficient Decision Support Systems: Practice and Challenges from Current to Future - page 71

2.2 Type-1 fuzzy logic system
Fuzzy logic was developed by Lotfi Zadeh a professor at the University of California,
Berkley. Fuzzy system is useful for real world problems where there are different kinds of
uncertainty [18]. The idea of fuzzy logic was to show that there is a world behind
conventional logic. This kind of logic is the proper way to model human thinking. Fuzzy
logic is recently getting the attention of artificial intelligence researchers. It is being used to
build expert systems for handling ambiguities and vagueness associated with real world
problems. Figure 2 shows the architecture of Type-1 Fuzzy system with gradient descent
algorithm.

x  X

y  ) f ( x  Y

Fig. 2. Structure of Type-1 Fuzzy Logic system with Gradient Descent Algorithm
Gradient descent Algorithm: Gradient descent technique is a training algorithm which was
used to tune the membership function parameters in fuzzy system. Using this algorithm the
membership function parameters can be optimized and the error rate is reduced to get more
accurate results. The details of the algorithm were explained in [19].
Fuzzification Process: According to [20] fuzzifying has two meanings. The first is the
process fining the fuzzy value of a crisp one. The second is finding the grade of membership
of a linguistic value of a linguistic variable corresponding to a fuzzy or scalar input. The
most used meaning is the second. Fuzzification is done by membership functions.
Inference Process: The next step is the inference process which involves deriving conclusions
from existing data [20]. The inference process defines a mapping from input fuzzy sets into
output fuzzy sets. It determines the degree to which the antecedent is satisfied for each rule.
These results in one fuzzy set assigned to each output variable for each rule. MIN is an
inference method. According to [21] MIN assigns the minimum of antecedent terms to the
matching degree of the rule. Then fuzzy sets that represent the output of each rule are
combined to form a single fuzzy set. The composition is done by applying MAX which
corresponds to applying fuzzy logic OR, or SUM composition methods [20].
Defuzzification Process: Defuzzification is the process of converting fuzzy output sets to
crisp values [20]. According to [22] there are three defuzzification methods used : Centroid ,
Average Maximum and Weighted Average . Centroid method of Defuzzification is the most
commonly used method. Using this method the defuzzified value is defined by: