Partial Order and Related Disciplines

Abstract

It is always hard to try a positioning. Nevertheless, it may help interested readers to find their way through the jungle of concepts, relations, and equations of this text. Certainly, partial order has to do with graph theory in discrete mathematics, as its visualization is a digraph and questions like connectivity or identification of articulation points and of separated subsets are typical of graph theory; see, e.g., Wagner and Bodendiek 1989) and Patil and Taillie (2004). There is also a connection to the network domain, as partial order constitutes a directed graph, which is one of the characteristics of networks. In our applications here, there is always a matrix, which quantifies the multi-indicator system, the data matrix. With or without the interim step of deriving the rank matrix, we arrive at a partial order. Once, however, the poset is derived, it may be analyzed as a mathematical object on its own right.