Axiomatic characterization of transit functions of weak hierarchies

  • Manoj Changat University of Kerala, India
  • Prasanth G. Narasimha-Shenoi Government College Chittur, India
  • Peter F. Stadler Universit├Ąt Leipzig, Germany
Keywords: Transit functions, convexities, weak hierarchies, axiom systems

Abstract

Transit functions provide a unified approach to study notions of intervals, convexities, and betweenness. Recently, their scope has been extended to certain set systems associated with clustering. We characterize here the class of set systems that correspond to k-ary monotonic transit functions. Convexities form a subclass and are characterized in terms of transit functions by two additional axioms. We then focus on axiom systems associated with weak hierarchies as well as other generalizations of hierarchical set systems.

Published
2018-08-08
Section
Articles