Gödel logic is the fuzzy logic of the minimum triangular norm and its residuum. Using the functional representation of the Lindenbaum algebra of Gödel logic, we analyze the interaction between the integral operator and the logical connectives. On these grounds, we put forth a notion of finitely additive probability measure for Gödel logic. Our first main result shows that such measures precisely correspond to integrating the truth value functions induced by Gödel formulas with respect to a Borel probability measure on the real unit cube [0, 1]n. Our second main result shows that they also coincide with convex combinations of finitely many [0, 1]-valued assignments.
Defuzzifying formulas in Gödel logic through finitely additive measures / S. Aguzzoli, B. Gerla, V. Marra - In: Fuzzy Systems, 2008. FUZZ-IEEE 2008. (IEEE World Congress on Computational Intelligence). IEEE International Conference on[s.l] : IEEE Computer Society Press, 2008. - ISBN 978-1-4244-1818-3. - pp. 1886-1893 (( convegno WCCI 2008, FUZZ IEEE 2008 tenutosi a Hong Kong nel 2008 [10.1109/FUZZY.2008.4630627].
Defuzzifying formulas in Gödel logic through finitely additive measures
S. AguzzoliPrimo
;V. MarraUltimo
2008
Abstract
Gödel logic is the fuzzy logic of the minimum triangular norm and its residuum. Using the functional representation of the Lindenbaum algebra of Gödel logic, we analyze the interaction between the integral operator and the logical connectives. On these grounds, we put forth a notion of finitely additive probability measure for Gödel logic. Our first main result shows that such measures precisely correspond to integrating the truth value functions induced by Gödel formulas with respect to a Borel probability measure on the real unit cube [0, 1]n. Our second main result shows that they also coincide with convex combinations of finitely many [0, 1]-valued assignments.
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
