Pavelka-style fuzzy logic for attribute implications
Radim Belohlavek 0, Vilem Vychodil
Available Online October 2006.
- https://doi.org/10.2991/jcis.2006.282How to use a DOI?
- attribute dependency, fuzzy logic, attribute implication, Armstrong axioms, graded completeness
- 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 $T$.
- Open Access
- This is an open access article distributed under the CC BY-NC license.
Cite this article
TY - CONF AU - Radim Belohlavek AU - Vilem Vychodil PY - 2006/10 DA - 2006/10 TI - Pavelka-style fuzzy logic for attribute implications PB - Atlantis Press SN - 1951-6851 UR - https://doi.org/10.2991/jcis.2006.282 DO - https://doi.org/10.2991/jcis.2006.282 ID - Belohlavek2006/10 ER -