UDC 519.766.2
ON FUZZINESS OF MAMDANI RULE AS A BINARY RELATION OVER FUZZY NUMBERS
K. V. Bukhensky, PhD in physics and mathematics, 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, PhD in pedagogics, 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.
A. B. Dubois, PhD in physics and mathematics, associate professor, RSREU, Ryazan, Russia;
orcid.org/0000-0002-5924-4128, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
K. V. Anisimov, third year student, Faculty of Computer Engineering, RSREU, Ryazan, Russia;
orcid.org/0000-0001-8889-0818, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
The aim is to investigate fuzziness of binary fuzzy relation (FR) expressing Mamdani rule (implication) in dependence on its constituent fuzzy sets (FSs) given as LR-type fuzzy numbers (FNs). This work is the proceeding of the former investigation of fuzziness transformations on linear and nonlinear operations with FNs. As a measure of math fuzziness the Yager index of fuzziness with linear Hamming metric was used. Cases of FNs relations for same and different classes were investigated. Formulas for Mamdani rule FR index of fuzziness in general case of unimodal and polymodal (fuzzy interval) LR-type FNs were obtained.
Key words: fuzzy relation, LR-type fuzzy number, membership function, shape function, index of fuzziness, antecedent, consequent, Mamdani rule.