Mathematical Model Reveals Novel Approach to Rule Extraction in Financial Data

Extracting rules from financial data is crucial in fraud applications where minority classes are often imbalanced. A new mathematical model has been developed by researchers to address this challenge, known as “weighted scaled dominance.” This approach uses a combination of fuzzy sets and confidence measures to identify relevant patterns.

Approach

The model begins with the extraction of rules from input-output pairs using a type-2 fuzzy system. For each antecedent, upper and lower membership values are calculated, and rules combining matched fuzzy sets are extracted. The firing strength of each rule is then computed using the lower and upper bounds of the firing strength.

To handle imbalanced data, the researchers employed “weighted scaled dominance,” which involves dividing the firing strength of a given rule by the summation of the firing strengths of all rules with the same consequent class. This approach allows minority classes to be given greater weight in the decision-making process.

Mathematical Formulation

The mathematical formulation of the model is as follows:

• Equation (2): The sum of the membership values of all input-output pairs.
• Equation (3): The calculation of the membership value using fuzzy sets.
• Equation (4): The extracted rule in the form of an antecedent and consequent class.
• Equation (5): The firing strength calculation using the lower and upper bounds.
• Equation (6): The computation of the scaled firing strength.
• Equations (7-8): The calculation of the weighted scaled dominance.

Implementation

The model was implemented using a type-2 fuzzy system, which involves the following steps:

Step A: Raw Rule Extraction

Calculate upper and lower membership values for each antecedent

Extract rules combining matched fuzzy sets

Compute firing strength for each extracted rule

Step B: Weighted Scaled Dominance

Group rules with same antecedents and conflicting classes

Compute scaled confidence and support using Equations (9-12)

Calculate scaled dominance using Equation (13)

Compute weighted scaled dominance using Equation (15)

Prediction Phase

Once an input pattern is entered, the upper and lower membership values are calculated. The predicted class is then determined by selecting the rule with the highest average value in the weighted scaled dominance.

Conclusion

The study demonstrates a novel approach to rule extraction in financial data, which can be used to improve fraud detection and prevention strategies. The model’s ability to handle imbalanced data makes it particularly effective for identifying minority classes, such as fraudulent transactions.