J. Aust. Math. Soc.
79 (2005), 305-318|
Loomis-Sikorski theorem for monotone
-complete effect algebras
Slovak Academy of Sciences
SK-814 73 Bratislava
| We show that monotone
-complete effect algebras under some conditions
-homomorphic images of effect-tribes (as monotone
-complete effect algebras), which are nonempty
systems of fuzzy sets closed under complements,
sums of fuzzy sets less than 1, and containing
all pointwise limits of nondecreasing fuzzy sets.
Because effect-tribes are generalizations of
-algebras of subsets, we present a generalization
of the Loomis-Sikorski theorem for such effect
algebras. We show that we can choose an
effect-tribe to be a system of affine fuzzy sets.
In addition, we present a new version of the
Loomis-Sikorski theorem for
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