Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
391078 | Fuzzy Sets and Systems | 2009 | 13 Pages |
Abstract
Additivity of an uncertainty measure on an MV-algebra has a clear meaning. If the divisibility is dropped, we come up to a so-called Girard algebra. There we discuss strong resp. weak additivity based on so-called divisible disjoint unions resp. on additivity for all sub-MV-algebras. We obtain a description of those extensions from additive measures on an MV-algebra to the canonical Girard algebra extension of pairs which are strongly additive and valuation measures. Finally, we prove the non-existence of strongly additive measure extensions, if the underlying MV-algebra is a finite chain with more than two non-trivial elements.
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