Quasi-ultrafilters and Weak-ultrafilters: Their Properties and Maximality

The concept of a Quasi-Ultrafilter provides an axiomatic analysis of incomplete social judgments. The weak filter (or weak ultrafilter) was introduced by K. Schlechta in the 1990s as a relaxed version of an ultrafilter. A pair (X, f) of a finite set X and a symmetric submodular function f is called a connectivity system. This concept is commonly used in discussions of graph width parameters, such as branch-width and tree-width, to analyze graph structures. In this paper, we discussed Quasi-Ultrafilter and Maximal Quasi-filter on Connectivity System.