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- Title
SPACES OF NON-ADDITIVE MEASURES GENERATED BY TRIANGULAR NORMS.
- Authors
SUKHORUKOVA, KH.
- Abstract
We consider non-additive measures on the compact Hausdorff spaces, which are generalizations of the idempotent measures and max-min measures. These measures are related to the continuous triangular norms and they are defined as functionals on the spaces of continuous functions from a compact Hausdorff space into the unit segment. The obtained space of measures (called ∗-measures, where ∗ is a triangular norm) are endowed with the weak* topology. This construction determines a functor in the category of compact Hausdorff spaces. It is proved, in particular, that the ∗-measures of finite support are dense in the spaces of ∗-measures. One of the main results of the paper provides an alternative description of ∗-measures on a compact Hausdorff space X, namely as hyperspaces of certain subsets in X × [0, 1]. This is an analog of a theorem for max-min measures proved by Brydun and Zarichnyi.
- Subjects
TRIANGULAR norms; HAUSDORFF spaces; GENERALIZATION; CONTINUOUS functions; FUNCTIONALS
- Publication
Matematychni Studii, 2023, Vol 59, Issue 2, p215
- ISSN
1027-4634
- Publication type
Article
- DOI
10.30970/ms.59.2.215-224