In this paper, some recent results established by Marin Borcut [M. Borcut, Tripled fixed point theorems for monotone mappings in partially ordered metric spaces, Carpathian J. Math. 28, 2 (2012), 207--214] and [M. Borcut, Tripled coincidence theorems for monotone mappings in partially ordered metric spaces, Creat. Math. Inform. 21, 2 (2012), 135--142] are generalized and improved, with much sho...

Representing and reasoning with an agent’s preferences is important in many applications of constraints formalisms. Such preferences are often only partially ordered. One class of soft constraints formalisms, semiring-based CSPs, allows a partially ordered set of preference degrees, but this set must form a distributive lattice; whilst this is convenient computationally, it considerably restric...

Results from the rich and well-developed theory of well-quasi-ordering have often been rediscovered and republished. The purpose of this paper is to describe this intriguing subject. To illustrate the theory, here are two definitions and an elementary result. A partially ordered set is called well-partially-ordered if every subset has at least one, but only a finite number, of minimal elements....

As an application of the dual equivalence between the category of L-spatialC-objects and the category of L-sober C-M-L-spaces, it is shown in this paper that for a fixed augmented partially ordered set A, there exists a dual equivalence between the category of A-spatial augmented partially ordered sets and the category of A-sober A-valued spaces. Then, with regard to this duality, for a fixed (...

In this paper, we show that if a partially ordered set has 2n elements and has dimension n, then it is isosnorphic to the set of n-l element subsets and lelement subsets of a sef, ordered by inclusion, or else it has six elements and is isomorphic to a partially ordered b;i we call the chevron or to its dual.

To take into account that expert’s degrees of certainty are not always comparable, researchers have used partially ordered set of degrees instead of the more traditional linearly (totally) ordered interval [0, 1]. In most cases, it is assumed that this partially ordered set is a lattice, i.e., every two elements have the greatest lower bound and the least upper bound. In this paper, we prove a ...