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Fuzzy Galois Connections
Author(s) -
Bêlohlávek Radim
Publication year - 1999
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19990450408
Subject(s) - mathematics , galois connection , galois module , embedding problem , fuzzy logic , galois extension , galois group , residuated lattice , fuzzy subalgebra , algebra over a field , fundamental theorem of galois theory , connection (principal bundle) , pure mathematics , discrete mathematics , fuzzy number , fuzzy set , artificial intelligence , computer science , geometry
The concept of Galois connection between power sets is generalized from the point of view of fuzzy logic. Studied is the case where the structure of truth values forms a complete residuated lattice. It is proved that fuzzy Galois connections are in one‐to‐one correspondence with binary fuzzy relations. A representation of fuzzy Galois connections by (classical) Galois connections is provided.