Some characterizations on the chain recurrence, chain transitivity, chain mixing property,shadowing and $h$-shadowing for Zadeh's extension are obtained. Besides, it is provedthat a dynamical system is spatiotemporally chaotic provided that the Zadeh's extensionis Li-Yorke sensitive.

In this paper, the new concept of non-autonomous iterated function system is introduced and also shown that non-autonomous iterated function system IFS(f_(1,∞)^0,f_(1,∞)^1) is topologically transitive for the metric space of X whenever the system has average shadowing property and its minimal points on X are dense. Moreover, such a system is topologically transitive, whenever, there is a point ...

When is a cause of a cause of an effect also a cause of that effect? The right answer is either “Sometimes” or “Always”. In favour of “Always”, transitivity is considered by some to be necessary for distinguishing causes from redundant noncausal events. Moreover transitivity may be motivated by an interest in an unselective notion of causation, untroubled by principles of invidious discriminati...

Parthood is a relation of fundamental importance in a number of disciplines including cognitive science, linguistics and conceptual modeling. However, one classical problem for conceptual modeling theories of parthood is deciding on the transitivity of these relations. This issue is of great importance since transitivity plays a fundamental role both conceptually (e.g., to afford inferences in ...