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Regular version of the site

Article

Canonical sequences of monotone measures

Fuzzy Sets and Systems. 2020. Vol. 379. P. 1-19.
Bronevich A., Rozenberg I. N.

It is an important feature of a monotone measure that it is not additive in general. In the paper, we propose the mathematical tool, based on canonical sequences of monotone measures, for analyzing additivity of monotone measures on subalgebras and give a way of generating such monotone measures. It turns out that the generating rule can be considered as an effect of a linear operator defined on the set of monotone measures. We also investigate in what cases the sequence of such operators behaves commutatively and preserve continuity properties from the generating monotone measure.