By Dr Costas Kyritsis. Technical University of Crete
,Proceedings of the VII Congress of
Sigef 2000.(1992)

This
paper was written during 1992.In
this paper is proved a kind of equivalence between Boolean (2-valued logic),
Postean (3-valued logic), and
Fuzzy-subsets (Fuzzy logic) lattices.

As
Fuzzy logic is considered an extension of 3-valued logic we introduce an
extension of the Postean lattices based on an order type λ, as spectrum of logical valuations, under the name λ-rainbow lattices. We introduce, also, a kind of
arithmetical representation of the λ-Fuzzy
subsets lattices, in a manner much the same that an geometric line segment is an interval of real numbers. We make use
of the transfinite real numbers of A. Glayzal that later became known and
rediscovered by J.H.Conway as surreal numbers.