Parameterizing the Semantics of Fuzzy Attribute Implications by Systems of Isotone Galois Connections

2014/10/25 by Vilém Vychodil, Vilem Vychodil
Computer Science · Mathematics · #Advanced Algebra and Logic #Artificial intelligence #Computer science #Data mining #Discrete mathematics #Fuzzy logic #Fuzzy set #Galois connection #Logic, Reasoning, and Knowledge #Mathematics #Programming language #Rough Sets and Fuzzy Logic #Semantics (computer science) #Theoretical computer science #acm:03B52 #acm:06A15 #acm:68P20 #cs.AI #msc:03B52 #msc:06A15 #msc:68P20

paper · pdf · doi:10.1109/tfuzz.2015.2470530

published as IEEE Trans. Fuzzy Systems 24(3): 645-660 (2016)

arxiv created 2014/10/25 · openalex publication_date 2015/08/19 · arxiv updated 2016/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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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