Journal
IEEE TRANSACTIONS ON FUZZY SYSTEMS
Volume 24, Issue 3, Pages 645-660Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TFUZZ.2015.2470530
Keywords
Attribute implication; complete axiomatization; data dependence; formal concept analysis; fuzzy logic; IF-THEN rule; nonredundant base; residuated lattice
Funding
- Czech Science Foundation [P202/14-11585S]
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We study the semantics of fuzzy IF-THEN rules called fuzzy attribute implications parameterized by systems of isotone Galois connections. The rules express dependences 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.
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