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Bibliography

Journal Article

Fuzzy Caratheodory's Theorem and Outer *-Fuzzy Measure

Mesiar Radko, Li Ch., Ghaffari A., Saadati R.

: AXIOMS vol.11, 240

: ∗-outer fuzzy measure, t-norm, ∗-fuzzy premeasure, Caratheodory’s theorem

: 10.3390/axioms11050240

: http://library.utia.cas.cz/separaty/2022/E/mesiar-0559705.pdf

: https://www.mdpi.com/2075-1680/11/5/240

(eng): 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.

: BA

: 10101

2019-01-07 08:39