František Včelař and Zuzana Pátíková
On Tarski’s Type Theorems for LFuzzy Isotone and LFuzzy Relatively Isotone Maps on LComplete Propelattices
143 - 150
2016
10
3
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/10005160
https://publications.waset.org/vol/111
World Academy of Science, Engineering and Technology
Recently a new type of very general relational
structures, the so called (L)complete propelattices, was introduced.
These significantly generalize complete lattices and completely lattice
Lordered sets, because they do not assume the technically very
strong property of transitivity. For these structures also the main part
of the original Tarski’s fixed point theorem holds for (Lfuzzy) isotone
maps, i.e., the part which concerns the existence of fixed points and
the structure of their set. In this paper, fundamental properties of
(L)complete propelattices are recalled and the so called Lfuzzy
relatively isotone maps are introduced. For these maps it is proved
that they also have fixed points in Lcomplete propelattices, even if
their set does not have to be of an awaited analogous structure of
a complete propelattice.
Open Science Index 111, 2016