UDC 519.766.2
FUZZINESS TRANSFORMATIONS ON LINEAR OPERATIONS WITH LR-TYPE FUZZY NUMBERS
K. V. Bukhensky, Ph.D. (Phys. and Math.), associate professor, deputy rector for academic work, 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. (Ped.), associate professor, department of higher mathematics, 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, Ph.D. (Phys. and Math.), associate professor, department of higher mathematics, 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.
A. S. Safoshkin, Lecturer, department of higher mathematics, RSREU, Ryazan, Russia;
orcid.org/0000-0002-1419-979X, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
The aim of the work is to investigate fuzziness transformations on functional mapping fuzzy sets (FS) and on linear operations (FSs addition and multiplication FS by real number). FS are represented by LRtype fuzzy numbers (FN) used as linguistic variable term sets in fuzzy inference systems. The notions of spread vagueness and math fuzziness were differentiated. As a measure of FS’s math fuzziness the Yager’s index of fuzziness with linear metric was chosen. Math fuzziness index was shown to be invariant with respect to linear functional transformations of FSs as well as to addition of LR-type FNs with similar shape functions. The formula for math fuzziness index for the sum of LR-type FNs with different arbitrary shape functions is derived. In order to prove theoretical results numerical experiments were accomplished.
Key words: fuzzy set, LR-type fuzzy number, membership function, shape function, index of math fuzziness, spread vagueness, Zadeh’s extension principle, alpha-cut of a fuzzy set.