Mirko Navara presents Fuzzy logical operations and their generators

On 2019-04-25 12:00:00 at G205, Karlovo náměstí 13, Praha 2
As noticed already by Abel, an operation which is monotonic, commutative, and
associative is essentially the addition. This principle applies also to fuzzy
logical operations with values in the real unit interval; many of them can be
considered equal up to an isomorphism (i.e., increasing bijection of the set of
values). Although there are constructive proofs of these results, their
computation often becomes unfeasible. We proved that, in many cases, partial
derivatives allow to prove these results in a closed form, admitting also the
use of computer algebra.

References:

Navara, M., Petrík, M., Sarkoci, P.: Explicit formulas for generators of
triangular norms. Publ. Math. Debrecen 77 (2010), 171-191.
http://cmp.felk.cvut.cz/~navara/papers/PMD10.pdf

Navara, M.: Formulas for generators of R-implications. Fuzzy Sets Syst. 359
(2019), 80–89. DOI:10.1016/j.fss.2018.09.011
http://cmp.felk.cvut.cz/~navara/papers/gen_impl_FSS19.pdf

Navara, M., Petrík, M.: Generators of fuzzy logical operations. Submitted.
Za obsah zodpovídá: Petr Pošík