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Research Centre
Data - Algorithms - Decision Making
Data - Algorithms - Decision Making
Established in 2005 under support of MŠMT ČR (project 1M0572)
Publications
Every state on semisimple MV-algebra is integral
Typ:
Jornal article
Authors:
Name of journal:
Fuzzy Sets and Systems
Batch:
20
Year:
2006
Number:
157
Pages:
2771-2782
ISSN:
0165-0114
Keywords:
Semisimple MV-algebra; Clan; Bauer simplex
Anotation:
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
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