On the relation of Fuzzy subsets, Postean and Boolean lattices . The λ-rainbow lattices. Transfinite Fuzzy subsets

Konstantinos Kyritsis (1)

1 TEI - Technological Educational Institute of Epirus

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

Mots clés: Boollean Lattices; Postean Lattices; Fuzzy-subsets lattices; Transfinite Real numbers; Surreal numbers; Ordinal Real numbers

Domaines: Mathématiques [math]

Konstantinos Kyritsis. On the relation of Fuzzy subsets, Postean and Boolean lattices . The λ-rainbow lattices. Transfinite Fuzzy subsets. VII congress of SIGEF - Decision Making under Uncertainty in the Global Environment of the 21st Century, Chania of Grete in Greece 18-20 September 2000, Sep 2000, Chania of Crete, Greece. pp.763 - 774. ⟨hal-01552355⟩