The relation of Fuzzy subsets, Postean and Boolean lattices .The λ-rainbow lattices . The transfinite real Fuzzy subsets.

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.