Fuzzy Caratheodory's Theorem and Outer *-Fuzzy Measure

0559705 - ÚTIA 2023 RIV CH eng J - Článek v odborném periodiku
Mesiar, Radko - Li, Ch. - Ghaffari, A. - Saadati, R.
Fuzzy Caratheodory's Theorem and Outer *-Fuzzy Measure.
AXIOMS. Roč. 11, č. 5 (2022), č. článku 240. E-ISSN 2075-1680
Institucionální podpora: RVO:67985556
Klíčová slova: ∗-outer fuzzy measure * t-norm * ∗-fuzzy premeasure * Caratheodory’s theorem
Obor OECD: Pure mathematics
Impakt faktor: 2, rok: 2022
Způsob publikování: Open access
http://library.utia.cas.cz/separaty/2022/E/mesiar-0559705.pdf https://www.mdpi.com/2075-1680/11/5/240

The goal of this paper is to introduce two new concepts ∗-fuzzy premeasure and outer ∗-fuzzy measure, and to further prove some properties, such as Caratheodory’s Theorem, as well as the unique extension of ∗-fuzzy premeasure. This theorem is remarkable for it allows one to construct a ∗-fuzzy measure by first defining it on a small algebra of sets, where its ∗-additivity could be easy to verify, and then this theorem guarantees its extension to a sigma-algebra.
Trvalý link: https://hdl.handle.net/11104/0333420