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.

We present a terminating tableau calculus for graded hybrid logic with global modalities, reflexivity, transitivity and role hierarchies. Termination of the system is achieved through pattern-based blocking. Previous approaches to related logics all rely on chain-based blocking. Besides being conceptually simple and suitable for efficient implementation, the pattern-based approach gives us a NE...

Ergative case, the special case of transitive subjects, raises questions not only for the theory of case but also for theories of subjecthood and transitivity. This paper analyzes the case system of Nez Perce, a ”three-way ergative” language, with an eye towards a formalization of the category of transitive subject. I show that it is object agreement that is determinative of transitivity, and h...

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...

Digital memcomputing machines (DMMs) are non-linear dynamical systems designed so that their equilibrium points are solutions of the Boolean problem they solve. In a previous work [Chaos 27, 023107 (2017)] it was argued that when DMMs support solutions of the associated Boolean problem then strange attractors cannot coexist with such equilibria. In this work, we demonstrate such conjecture. In ...

Social networks based trust is a promising approach to supporting people and software agents to interact with “strangers” on the Web. A necessary condition for trust propagation in social networks is that trust is transitive. However, is trust transitive? What types of trust are transitive and why? There are few theories and models found to answer these fundamental questions in a formal manner....

Proofs of equalities may be built from assumptions using proof rules for reflexivity, symmetry, and transitivity. Reflexivity is an axiom proving x=x for any x; symmetry is a 1-premise rule taking a proof of x=y and returning a proof of y=x; and transitivity is a 2-premise rule taking proofs of x=y and y=z, and returning a proof of x=z. Define an equivalence relation to hold between proofs iff ...

We define a variant of Lamport’s Temporal Logic of Actions, extended by spatial modalities, that is intended for the specification of mobile systems with distributed state. We discuss notions of refinement appropriate for mobile systems, specifically concerning the topological structure of the system, and show how these can be represented in the logic via quantification and implication, ensurin...