The notion of a transitive closure of a fuzzy relation is very useful for clustering in pattern recognition, for fuzzy databases, etc. It is based on translating the standard definition of transitivity and transitive closure into fuzzy terms. This definition works fine, but to some extent it does not fully capture our understanding of transitivity. The reason is that this definition is based on...

Since the Transitivity Hypothesis was introduced thirty four years ago, it has become one of the most influential approaches to the functioning of transitivity in natural language. Despite the huge impact of the approach, at least within functional linguistics, some fundamental theoretical and methodological problems still remain unsolved; this seriously undermines the entire approach. The aim ...

The counterfactual tradition to defining actual causation has come a long way since Lewis started it off. However there are still important open problems that need to be solved. One of them is the (in)transitivity of causation. Endorsing transitivity was a major source of trouble for the approach taken by Lewis, which is why currently most approaches reject it. But transitivity has never lost i...

A general framework for studying the transitivity of reciprocal relations is presented. The key feature is the cyclic evaluation of transitivity: triangles (i.e. any three points) are visited in a cyclic manner. An upper bound function acting upon the ordered weights encountered provides an upper bound for the ‘sum minus 1’ of these weights. Commutative quasi-copulas allow to translate a genera...

The concepts of fuzzy transitivity of a fuzzy relation on a given universe and the measure of fuzzy transitivity are studied with the use of Gödel fuzzy implicator.

One of the most prominent properties in real-world networks is the presence of a community structure, i.e. dense and loosely interconnected groups of nodes called communities. In an attempt to better understand this concept, we study the relationship between the strength of the community structure and the network transitivity (or clustering coefficient). Although intuitively appealing, this ana...

The structural-analytic literature of the past decade indicates that transitivity in social networks is an important concern. However, existing structural analytic methods are frequently unable to deal directly with the substantive and methodological problems posed by transitive relations in social structures (Berkowitz, 1982). These difficulties typically surface in one of two contexts. First,...

The concept of topological transitivity goes back to G. D. Birkhoff [1]

the value of good X (x-axis) and such that the response is menu dependent (red when X is offered against Y, blue when X is offered against Z). Transitivity violations (i.e., cases where x-axis orderings are not conserved on the y-axis) are possible, as for X1, X2, X3. However, if the representation is menu invariant (i.e., if red and blue lines coincide), transitivity violations cannot occur. I...

This paper introduces fundamental ideas of bitopological dynamical systems. Here, notions transitivity, point pairwise iterated compactness, weakly etc. are introduced. Later, it is shown that under homeomorphism, transitivity implies transitivity. Moreover, homeomorphism; compactness and found to be equivalent. we apply our results in the development process a human embryo from zygote until bi...