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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 64, Issue 3


On D-posets of fuzzy sets

Roman Frič
Published Online: 2014-07-05 | DOI: https://doi.org/10.2478/s12175-014-0224-8


D-posets of fuzzy sets constitute a natural simple mathematical structure in which relevant notions of generalized probability theory can be formalized. We present a classification of D-posets leading to a hierarchy of distinguished subcategories of D-posets related to probability and study their relationships. This contributes to a better understanding of the transition from classical probability theory to fuzzy probability theory. In particular, we describe the transition from the Boolean cogenerator {0, 1} to the fuzzy cogenerator [0, 1] and prove that the generated Łukasiewicz tribes form an epireflective subcategory of the bold algebras.

MSC: Primary 06A11, 60A86, 06D72; Secondary 28C99, 54C20, 06D35

Keywords: probability domain; D-poset; D-poset of fuzzy sets; sequentially continuous D-homomorphism; MV-algebra; bold algebra; Łukasiewicz tribe; cogenerator; epireflective subcategory

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About the article

Published Online: 2014-07-05

Published in Print: 2014-06-01

Citation Information: Mathematica Slovaca, Volume 64, Issue 3, Pages 545–554, ISSN (Online) 1337-2211, DOI: https://doi.org/10.2478/s12175-014-0224-8.

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© 2014 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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