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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
Abstract 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.