We present a graphical criterion for reading dependencies from the minimal directed independence map G of a graphoid p, under the assumption that G is a polytree and p satisfies weak transitivity. We prove that the criterion is sound and complete. We argue that assuming weak transitivity is not too restrictive.

In cluster analysis context is of major interest to induce an order that allow us to compare the groups generated by cluster analysis itself. Using the sample similarities obtained in this analysis like possibilities in fuzzy sets context provide us to induce a transitivity property in cluster analysis, producing a similarities matrix that meets to the transitivity conditions and that resembles...

It is important to see what kinds of properties of graphs can be transfer to the product of them. Here we will prove that the colour automorphism vertex transitivity can be transfer, and bring a special proof for vertex transitivity property of Cayley graphs of semigroups as well.

Fuzzy implicators are the basic ingredients of many applications. So it becomes essential to study the various features of an implicator before implementing it in any practical application. This paper discusses the properties of transitivity of a fuzzy relation on a given universe and measure of fuzzy transitivity defined in terms of the Reichenbach fuzzy implicator which is an s-implicator.

PURPOSE Deformable image registration (DIR) is necessary for accurate dose accumulation between multiple radiotherapy image sets. DIR algorithms can suffer from inverse and transitivity inconsistencies. When using deformation vector fields (DVFs) that exhibit inverse-inconsistency and are nontransitive, dose accumulation on a given image set via different image pathways will lead to different a...

this paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. it incorporates the most important settings of lattice-valued topology, including poslat topology of s.~e.~rodabaugh, $(l,m)$-fuzzy topology of t.~kubiak and a.~v{s}ostak, and $m$-fuzzy topology on $l$-fuzzy sets of c.~guido. moreover, its respe...

In this paper, we introduce the concept of the generalized topological molecular lattices as a generalization of Wang's topological molecular lattices,  topological spaces, fuzzy topological spaces, L-fuzzy topological spaces and soft topological spaces. Topological molecular lattices were defined by closed elements, but in this new structure we present the concept of the open elements and defi...

in this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. it gives some criterions to study locally convex topological spaces in a discrete approach.

We present a graphical criterion for reading dependencies from the minimal directed independence map G of a graphoid p when G is a polytree and p satisfies composition and weak transitivity. We prove that the criterion is sound and complete. We argue that assuming composition and weak transitivity is not too restrictive.

Section 2. Then we present ProtoNet. ProtoNet is centered around the concept of homology transitivity. ProtoNet clusters protein sequences into a hierarchy based on sequence similarity and homology transitivity. Thus the hierarchy parallels the evolutionary history of these protein sequences. We then illustrate—using Histone proteins—the application of ProtoNet to detect remote protein relatives.