title: |
Pavelka-style fuzzy logic for attribute implications |
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publication: |
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part of series: |
Advances in Intelligent Systems Research | |
ISBN: |
978-90-78677-01-7 | |
ISSN: |
1951-6851 | |
DOI: |
doi:10.2991/jcis.2006.282 (how to use a DOI) | |
author(s): |
Radim Belohlavek, Vilem Vychodil |
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corresponding author: |
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publication date: |
October 2006 |
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keywords: |
attribute dependency, fuzzy logic, attribute implication, Armstrong axioms, graded completeness |
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abstract: |
We present Pavelka-style fuzzy logic for reasoning about
attribute implications, i.e. formulas $A\Rightarrow B$. Fuzzy attribute implications allow for two different interpretations, namely,
in data tables with graded (fuzzy) attributes and in data tables over domains
with similarity relations. The axioms of our logic are inspired by well-known Armstrong axioms
but the logic allows us to infer partially true formulas from partially
true formulas.
We prove soundness and completeness of our logic in graded style,
i.e. we prove that a degree to which an attribute implication $A\Rightarrow B$
semantically follows from a collection $T$ of partially true attribute
implications equals a degree to which $A\Rightarrow B$ is provable
from $T$.
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copyright: |
©
Atlantis Press. This article is distributed under the
terms of the Creative Commons Attribution License, which permits
non-commercial use, distribution and reproduction in any medium,
provided the original work is properly cited. |
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full text: |