About TController
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,
TakagiSugeno FIS – applicable when numerical data basis is sufficient. Reduces inference time.
Advantage ∞
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,
*TakagiSugeno FIS: requires sufficient data basis.
Traditional: Mamdanitype FIS ∞
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: TController 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 ∞
 Divide output variable space into intervals, each interval corresponds to one rule. Minimum number of rules is 2,
 Divide each input variable space into intervals, each interval corresponds to one linguistic variable. Minimum number of linguistic variables is 2,
 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.
Advantages over traditional FIS ∞
 Logical inference and composition are combined into one specific step,
 high speed geometrical defuzzification method with zero systematic error,
 number of rules is driven by features of output variable only,
 procedure of rule building is intuitive for experts via analysis of possible situations for output variable,
 fast defuzzification,

simple hardware implementation.