Extensionality in Graded Properties of Fuzzy Relations

@inproceedings{Behounek2006ExtensionalityIG,
  title={Extensionality in Graded Properties of Fuzzy Relations},
  author={Libor Behounek},
  year={2006}
}
New definitions of graded reflexivity, symmetry, transitivity, antisymmetry, and functionality of fuzzy relations are proposed which are relative to an indistinguishability relation E on the universe of discourse. It is shown that if considered nongraded (i.e., either fully present or else fully absent), the new definitions reduce to the usual ones under full extensionality of the relation w.r.t. E. However, if graded properties of R (e.g., transitivity to some degree) are taken into account… CONTINUE READING
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