Fuzzy logic in classiification

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Fuzzy logic is most known for its application in control. However, it could be used also in classification, i.e. when one needs to assign an object to one of a few classes (in many practical applications merely two) according to some observable features.

Credit scoring is commonly known example of classification problems. Let us assume we have to assign scoring to a company based on its financials: good or bad. Let’s say we know from investigation of historical data the likelihood of bankruptcy depends heavily on two factors:
a. current assets, i.e. how much cash or easy-to-cash stuff the company has,
b. cash flow, i.e. how much cash it can generate.

Obviously, to have the model size independent we need to normalize both factors, e.g. by current liabilities (how much it has to pay soon).

Look at the following model:

Engine: Credit
InputVariable: current_assets
  enabled: true
  range: 0.000 3.000
  term: good SShape 0.500 2.000
InputVariable: cash_flow
  enabled: true
  range: -3.000 3.000
  term: good SShape -0.100 1.500
  term: excellent SShape 0.250 2.000
OutputVariable: scoring
  enabled: true
  range: -2.000 2.000
  accumulation: none
  defuzzifier: WeightedAverage
  default: 0.000
  lock-valid: false
  lock-range: false
  term: good Constant -2.000
  term: bad Constant 2.000
RuleBlock: 
  enabled: true
  conjunction: Minimum
  disjunction: Maximum
  activation: AlgebraicProduct
  rule: if current_assets is good and cash_flow is good then scoring is good
  rule: if current_assets is not good and cash_flow is not good then scoring is bad
  rule: if cash_flow is excellent then scoring is good

Load it and play! Disclaimer: this is an out-of-blue example without any applicability in real life.

The output value has its interpretation too: the probability of default = 10^scoring. So, if the output is 2, it means the default is practically certain. If you play with the model you can see the output equals 1 when cash flow is bad and current assets are good. In this case the model says “I don’t know” and assumes the probability of 1 percent, which basically is the average of bankruptcies annually (at least in my country).

A (debatable) by-conclusion of the example is that the Sugeno approach seems to be better (simpler) for classification.

I hope you like the example.

Witold

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