Parameterizing the semantics of fuzzy attribute implications by systems of isotone Galois connections
This work addresses a theoretical problem in fuzzy logic and data mining for researchers, offering incremental improvements by generalizing existing parameterizations.
The paper tackles the problem of formalizing the semantics of fuzzy attribute implications in object-attribute data by introducing parameterizations based on systems of isotone Galois connections, which generalize earlier approaches using linguistic hedges, and provides characterizations for semantic entailment and bases derived from data.
We study the semantics of fuzzy if-then rules called fuzzy attribute implications parameterized by systems of isotone Galois connections. The rules express dependencies between fuzzy attributes in object-attribute incidence data. The proposed parameterizations are general and include as special cases the parameterizations by linguistic hedges used in earlier approaches. We formalize the general parameterizations, propose bivalent and graded notions of semantic entailment of fuzzy attribute implications, show their characterization in terms of least models and complete axiomatization, and provide characterization of bases of fuzzy attribute implications derived from data.