In this short note the main results are: 1) They are introduced axiomatically the λ-rainbow lattices. It is proved that the λ-Fuzzy subsets lattices are distributive λ-rainbow lattices and other relations of these two classes of lattices. 2) They are introduced the transfinite real, complex, quaternion. Fuzzy subsets. They can be considered as a kind of Arithmetisation of the abstract λ-Fuzzy subsets lattices. The transfinite real Fuzzy subsets are special λ-Fuzzy subsets with good properties. 3) It is proved a mutual isomorphic representation of the Boolean (2-valued logic) Postean (3-valued logic) and Fuzzy-subsets (Fuzzy-logic) lattices
Publié le : 2000-09-18
Classification:
Boollean Lattices,
Postean Lattices,
Fuzzy-subsets lattices,
Transfinite Real numbers,
Surreal numbers,
Ordinal Real numbers,
[MATH]Mathematics [math]
@article{hal-01552355,
author = {Kyritsis, Konstantinos},
title = {On the relation of Fuzzy subsets, Postean and Boolean lattices . The $\lambda$-rainbow lattices. Transfinite Fuzzy subsets},
journal = {HAL},
volume = {2000},
number = {0},
year = {2000},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01552355}
}
Kyritsis, Konstantinos. On the relation of Fuzzy subsets, Postean and Boolean lattices . The λ-rainbow lattices. Transfinite Fuzzy subsets. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-01552355/