Onn-ordered sets and order completeness

Parameter Determination of ONN (Ordered Neural Networks)

Infimum and supremum completeness properties of ordered sets without axioms

In this paper, by using the ideas of the second author, we establish several intimate connections among the most simple infimum and supremum completeness properties of a generalized ordered set. That is, an arbitrary set equipped with an arbitrary inequality relation. In particular, we obtain straightforward extensions of some basic theorems on partially ordered sets. Due to the equalities inf ...

Tripled partially ordered sets

In this paper, we introduce tripled partially ordered sets and monotone functions on tripled partiallyordered sets. Some basic properties on these new dened sets are studied and some examples forclarifying are given.

Order Norms on Bounded Partially Ordered Sets

In this paper, we extend the domains of affirmation and negation operators, and more important, of triangular (semi)norms and (semi)conorms from the unit interval to bounded partially ordered sets. The fundamental properties of the original operators are proven to be conserved under this extension. This clearly shows that they are essentially based upon order-theoretic notions. Consequently, a ...

FUZZY ORDERED SETS AND DUALITY FOR FINITE FUZZY DISTRIBUTIVE LATTICES

The starting point of this paper is given by Priestley’s papers, where a theory of representation of distributive lattices is presented. The purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. In this way, some results of Priestley’s papers are extended. In the main theorem, we show that the category of finite fuzzy Priestley space...