On \(D\)-posets of fuzzy sets. (Q2877067)
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scientific article; zbMATH DE number 6333340
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \(D\)-posets of fuzzy sets. |
scientific article; zbMATH DE number 6333340 |
Statements
21 August 2014
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probability domains
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\(D\)-posets of fuzzy sets
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sequentially continuous \(D\)-homomorphisms
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MV-algebras
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bold algebras
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Łukasiewicz tribes
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cogenerators
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epireflective subcategories
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0.9323579
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0.90318614
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On \(D\)-posets of fuzzy sets. (English)
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\(D\)-posets of fuzzy sets constitute a natural simple mathematical structure in which relevant notions of generalized probability theory can be formalized.NEWLINENEWLINE The paper discusses the classification of \(D\)-posets leading to a hierarchy of distinguished subcategories of \(D\)-posets related to probability and studies their relationships. This contributes to a better understanding of the transition from classical probability theory to fuzzy probability theory.NEWLINENEWLINE In particular, it is described the transition from the Boolean cogenerator \(\{0,1\}\) to the fuzzy cogenerator \([0,1]\) and it is proved that the generated Łukasiewicz tribes form an epireflective subcategory of the bold algebras.
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