Residuated lattice structures, Properties, Partial fuzzy set theory, Partial fuzzy logic, Undefined values

This paper concentrates on investigating the preservation of the axioms and essential properties of residuated lattices in partial fuzzy set theory. We consider seven mostknown partial algebras dealing with undefined values such as the Bochvar, Bochvar external, Sobocinski, McCarthy, Nelson, ´ Kleene, Łukasiewicz, and additional, two recent ones, namely the Lower estimation algebra and the Dragonfly algebra. We provide the sketch of proofs in details for the preservation of considered axioms and properties in these algebras. The paper concludes with the tables summarizing the results, which visibly show how close is a partial algebra to a residuated lattice.