We present a sound and complete graphical criterion for reading dependencies from the minimal undirected independence map of a graphoid that satisfies weak transitivity. We argue that assuming weak transitivity is not too restrictive.

Ethicists and economists commonly assume that if A is all things considered better than B, and B is all things considered better than C, then A is all things considered better than C. Call this principle Transitivity. Although it has great conceptual, intuitive, and empirical appeal, I will argue against it. Some philosophers believe that the concept of better than implies Transitivity, so Tran...

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.