Článek v odborném periodiku

Fuzzy Sets and Systems

20

2006

157

2771-2782

0165-0114

prof. Ing. Vilém Novák, DrSc. (ÚVAFM Ostravská Univerzita)

Semisimple MV-algebra; Clan; Bauer simplex

Integral representation theorem will be established for finitely additive probability measures (states) on semisimple MV-algebras.
This result generalizes the well-known theorem of Butnariu and Klement in case of sigma- order continuous states on tribes of fuzzy sets.Precisely, it will be demonstrated that every state on a separating clan of continuous fuzzy sets arises as an integral with respect to a unique Borel probability measure. The key technique leading to this result exploits the geometrical?topological properties of the state space: the set of all states on every MV-algebra forms a Bauer simplex