Fuzzy logic, implemented in Fuzzy Inference Systems (FIS), makes use of human common sense or expert knowledge to build control systems or model data.

### Purpose ∞

Extension of traditional methods of data modeling and control.

### Common types of FIS ∞

Mamdani FIS – applicable when numerical data basis is incomplete and can be extended by human expert knowledge,
Takagi-Sugeno FIS – applicable when numerical data basis is sufficient. Reduces inference time.

Good solution can be created at low cost using expert knowledge.

### Problems ∞

• Good interpretability vs. good accuracy,
• small number of input variables,
• time consuming tuning,
• Mamdani FIS: Dependency on defuzzification method – same rule gives different results depending on defuzzification function (Centre of Gravity, Minimum, First Maximum). Reasoning for defuzzyfication function choice based only on experiments,

*Takagi-Sugeno FIS: requires sufficient data basis.

#### Features ∞

• Defuzzyfication method is chosen based on experiments and expert knowledge,
• there are no standards for rule building,
• rule form:,where is the rule number , is the input number (linguistic variable), and are linguistic terms, keyword marks a clause, keyword marks a conjunction.

### New: T-Controller FIS v ∞

#### Features ∞

• Peculiar defuzzification method,
• rule building is driven by expected output, rules are disjunct: each output value correspond only to one rule,
• rule form:, where is the rule number , is the input number (linguistic variable), , , are linguistic terms, keyword marks a clause, keyword marks a conjunction, keyword marks a disjunction.

#### Rule building ∞

1. Divide output variable space into intervals, each interval corresponds to one rule. Minimum number of rules is 2,
2. Divide each input variable space into intervals, each interval corresponds to one linguistic variable. Minimum number of linguistic variables is 2,
3. Define rules: Each valid combination of input variables forms a conjunction () of clauses (). Valid conjunctions, corresponding to one rule are connected to a disjunction ().

#### Defuzzification ∞

Defuzzyfication is performed on Geometrical Transformation Machine trained on (ideal) fuzzyfied output values.