UDC 519.766.2
ANALYTICAL IMPLEMENTATION OF CENTROID DEFUZZIFICATION METHOD AFTER AGGREGATION OF MAMDANI IMPLICATION CONSEQUENTS
K. V. Bukhensky, Ph.D. (Phys. and Math.), associate professor, Head of the Department of Higher Mathematics, RSREU, Ryazan, Russia; orcid.org/0000-0003-2602-2112, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
A. N. Konyukhov, Ph.D. (in pedagogical sciences), associate professor, RSREU, Ryazan, Russia;
orcid.org/0000-0002-1523-7110, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
The aim is to obtain analytical COG defuzzification formulas for aggregated consequents of Mamdani inference using LR-representation of linguistic variable (LV) terms. There are two requirements: 1) possibility to express analytically inverse functions to shape functions of LR-type fuzzy number (FN); 2) possibility to integrate analytically a shape function F(t) and (1-t)F(t) being a shape function as well. The technique was demonstrated for arbitrary number of output LV terms described by FNs with different shape functions of five types. Three thousand uniformly distributed random vectors of rule firing strengths were generated to verify formulas. Defuzzification time is shown to be reduced by more than two orders of magnitude. The results obtained could be used for fuzzy controller performance and fuzzy design software enhancement. Analytical representation makes further optimization of COG defuzzification method and its modifications possible.
Key words: : fuzzy set, LR-type fuzzy number, membership function, shape function, antecedent, consequent, Mamdani inference, linguistic variable term, defuzzification, center of gravity (COG) method.