Fuzzy set approaches

Data classification models are a very popular form of data analysis. Common classification methods include tree...

induction, Bayesian classification and belief networks, and neural networks. This tip, from Han and Kamber's book Data Mining Concepts and Techniques (Morgan Kaufman), discusses a less popular method, but one that is growing in appeal: fuzzy logic.

Rule-based systems for classification have the disadvantage that they involve sharp cutoffs for continuous attributes. For example, consider the following rule for customer credit application approval. The rule essentially says that applications for customers who have a job for two or more years and who have a high income (i.e., of at least \$50K) are approved:

IF (years_employed >= 2) ^ (income >= 50K) THEN credit = "approved"

With this rule, a customer who has had a job for at least two years will receive credit if her income is, say \$50K, but not if it is \$49K. Such harsh thresholding may seem unfair. Instead, fuzzy logic can be introduced into the system to allow "fuzzy" thresholds or boundaries to be defined. Rather than having a precise cutoff between categories or sets, fuzzy logic uses truth values between 0.0 and 1.0 to represent the degree of membership that a certain value has in a given category. Hence, with fuzzy logic, we can capture the notion that an income or \$49K is, to some degree, high, although not as high as an income of \$50K.

Fuzzy logic is useful for data mining systems performing classification. It provides the advantage of working at a high level of abstraction. In general, the use of fuzzy logic in rule-based systems involves the following:

• Attribute values are converted to fuzzy values. Values for the continuous attribute income are mapped into the discrete categories {low, medium, high}, and the fuzzy membership or truth values are calculated. Fuzzy logic systems typically provide graphical tools to assist users in this step.
• For a given new sample, more than one fuzzy rule may apply. Each applicable rule contributes a vote for membership in the categories. Typically, the truth values for each predicted category are summed.
• The sums obtained above are combined into a value that is returned by the system. This process may be done by weighing each category by its truth sum and multiplying by the mean truth value of each category. The calculations involved may be more complex, depending on the complexity of the fuzzy membership graphs.

Fuzzy logic systems have been used in numerous areas for classification, including health care and finance.

This was first published in May 2001

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