UDC 519.766.26
A RAPID ALGORITHM OF FUZZINESS INDICES CALCULATION FOR UNIMODAL LR-TYPE FUZZY NUMBERS
K. V. Bukhensky, Ph.D. (Phys. and Math.), associate professor, deputy rector, 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. Sci.), 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, Ph.D. (Phys. and Math.), 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.
A. S. Safoshkin, Lecturer, 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 design rapid algorithm of fuzziness indices calculation for unimodal LR-type fuzzy numbers (FN). The sphere of application: fuzzy inference systems for devices using fuzzy control. The formulas of four known indices for fuzzy sets (FS) with discrete support were extended to continuous case. The table of fuzziness indices values for most commonly used sample FS described by their membership functions was calculated. It was shown that indices values appeared to be specific for each sample set and independent of FS’s support length. Revealed properties of indices made possible to design a simple algorithm of fuzziness indices calculation for unimodal LR-type fuzzy numbers. It uses the table of indices and evaluates contribution of shape functions weighted by support length to overall fuzziness. The approach is also applicable for the solution of inverse problem of forming fuzzy number with predefined index of fuzziness value.
Key words: Key words: fuzzy set, membership function, LR-type fuzzy number, measure of fuzziness, fuzziness index, fuzzy inference system.