A complete characterization of all weakly additive measures and of all valuations on the canonical extension of any finite MV-chain
A Girard algebra is a commutative lattice-ordered semigroup satisfying some properties; every MV-algebra is a Girard algebra. Let \(m\) is a mapping from a Girard algebra \(L\) to the unit interval, \(m\) be isotone, \(m(a')= 1- m(a)\), \(m(0)= 0\), \(m(1)= 1\). The mapping \(m\) is called weakly additive if it fulfills the additivity condition on all MV-subalgebras of \(L\). The author proves the existence of weakly additive extensions from MV chains in \(L\). This is interesting because of the non-existence of strongly additive measure extensions [\textit{S. Weber}, Fuzzy Sets Syst. 160, No. 3, 371--383 (2009; Zbl 1180.28012)].
scientific article; zbMATH DE number 5705405
scientific article