\(P\)-measures on soft fuzzy \(\sigma\)-algebras (Q1313012)
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scientific article; zbMATH DE number 496168
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(P\)-measures on soft fuzzy \(\sigma\)-algebras |
scientific article; zbMATH DE number 496168 |
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\(P\)-measures on soft fuzzy \(\sigma\)-algebras (English)
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13 February 1994
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The authors establish a certain isomorphism between the space of all \(P\)- measures of soft fuzzy \(\sigma\)-algebras [\textit{K. Piasecki}, Fuzzy Sets Syst. 17, 271-284 (1985; Zbl 0604.60005)] and the space of all probability measures on a Boolean \(\sigma\)-algebra. The proof utilizes the well-known Loomis-Sikorski theorem. As a by-product, the authors provide a negative answer to a question of \textit{A. Dvurečenskij} [Fuzzy Sets Syst. 43, No. 2, 173-181 (1991; Zbl 0742.28009)] by showing that there are soft fuzzy \(\sigma\)-algebras that do not admit \(P\)- measures.
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\(P\)-measures
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soft fuzzy \(\sigma\)-algebras
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probability measures on a Boolean \(\sigma\)-algebra
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