On D-posets of fuzzy sets |
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Authors: | Roman Frič |
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Affiliation: | 1. Mathematical Institute, Slovak Academy of Sciences, Gre?ákova 6, SK-040 01, Ko?ice, Slovakia
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Abstract: | 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 ?ukasiewicz tribes form an epireflective subcategory of the bold algebras. |
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