Факультет комп'ютерних наук, фізики та математики

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Author: search.filters.author.Савченко, О. Г.Subject: search.filters.subject.Monad

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    FUZZY METRIZATION OF THE SPACES OF IDEMPOTENT MEASURES
    (2020) Brydun, V.; Savchenko, A.; Zarichnyi, M.; Савченко, О. Г.
    In idempotent mathematics, the idempotent measures (Maslov measures) are counterparts of the probability measures. We provide a fuzzy metrization of the set of idempotent measures on fuzzy metric spaces. We prove that this fuzzy metrization determines a monad in the category of fuzzy metric spaces and non-expanding maps.
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    Probability measure monad on the category of fuzzy ultrametric spaces
    (2011) Savchenko, А.; Zarichnyi, M.; Савченко, О. Г.
    It is proved that the probability measure functor comprises a monad on the category of fuzzy ultrametric spaces and nonexpanding maps. It is also proved that the G-symmetric power functor admits an extension on the Kleisli category of this monad (i.e. the category of fuzzy ultrametric spaces and nonexpanding measure-valued maps).