A fuzzy modeling system or a fuzzy controller can be implemented by understanding sampled valued variables, translated from the real-life world into a fuzzy domain. The model or the controller will estimate an output, either for a decision-making action or to impose a set-point in a closed-loop control system. Those processes are defined as “fuzzification,” i.e., going through the membership functions of the input data into fuzzy sets and their corresponding pertinence degrees to those sets, through a “fuzzy processing” or also called inference engine; and “defuzzification,” i.e., it is a transformation from such a fuzzy evaluation into crispy variables, ready for control, or modeling analysis (Yen, 1999). Such a methodology could be compared to have a phasor domain analysis, or a Laplace domain analysis. Fuzzy data processing requires to be done in the fuzzy domain with proper direct and inverse transformations.

Chapter Contents:

• 4.1 Fuzzification, defuzzification, and fuzzy inference engine
• 4.1.1 Fuzzification
• 4.1.2 Defuzzification
• 4.1.3 Fuzzy inference engine (implication)
• 4.2 Fuzzy operations in different universes of discourse
• 4.3 Mamdani's rule-based Type 1 fuzzy inference
• 4.4 Takagi–Sugeno–Kang (TSK), Type 2 fuzzy inference, parametric fuzzy, and relational-based
• 4.5 Fuzzy model identification and supervision control

Inspec keywords: fuzzy set theory; power engineering computing; power system control; fuzzy control; closed loop systems; fuzzy reasoning

Other keywords: Laplace domain analysis; relational approach; inverse transformations; fuzzy sets; fuzzy inference; fuzzy data processing; sampled valued variables; direct transformations; defuzzification; phasor domain analysis; fuzzy modeling system; fuzzy controller; fuzzification; membership functions; rule based approach; closed-loop control system; pertinence degrees

Subjects: Reasoning and inference techniques; Fuzzy control; Combinatorial mathematics; Power engineering computing; Combinatorial mathematics; Control of electric power systems; Power system control