We characterize totally ordered sets within the class of all ordered sets containing at least four-element chains. We use a simple relationship between their isotone transformations and the so called 1-endomorphism which is introduced in the paper. Later we describe 1-, 2-, 3-, 4-homomorphisms of ordered sets in the language of super strong mappings.
A distributive pseudocomplemented set [2] is called Stone if for all the condition holds. It is shown that in a finite case is Stone iff the join of all distinct minimal prime ideals of is equal to .
Two operators are constructed which make it possible to transform ternary relations into binary relations defined on binary relations and vice versa. A possible graphical representation of ternary relations is described.
The aim of this paper is to define and study cardinal (direct) and ordinal operations of addition, multiplication, and exponentiation for -ary relational systems. -ary ordered sets are defined as special -ary relational systems by means of properties that seem to suitably generalize reflexivity, antisymmetry, and transitivity from the case of or 3. The class of -ary ordered sets is then closed under the cardinal and ordinal operations.
By applying the solution of the internal direct product decomposition we investigate the relations between convex isomorphisms and direct product decompositions of directed multilattices.
We show that the study of topological T0-spaces with a finite number of points agrees essentially with the study of polyhedra, by means of the geometric realization of finite spaces. In this paper all topological spaces are assumed to be T0.
Under suitable conditions we prove the existence of fixed points of fuzzy monotone multifunctions.
We prove the existence of a fixed point of non-expanding fuzzy multifunctions in -fuzzy preordered sets. Furthermore, we establish the existence of least and minimal fixed points of non-expanding fuzzy multifunctions in -fuzzy ordered sets.
In this paper further development of Chebyshev type inequalities for Sugeno integrals based on an aggregation function and a scale transformation is given. Consequences for T-(S-)evaluators are established.