Conflict between Belief Functions: A New Measure Based on Their Non-conflicting Parts

Abstract

When combining belief functions by conjunctive rules of combination, conflicts often appear, which are assigned to empty set by the non-normalised conjunctive rule or normalised by Dempster’s rule of combination in Dempster-Shafer theory. Combination of conflicting belief functions and interpretation of their conflicts is often questionable in real applications; hence a series of alternative combination rules were suggested and a series of papers on conflicting belief functions have been published and conflicts of belief functions started to be investigated. This theoretical contribution introduces a new definition of conflict between two belief functions on a general finite frame of discernment. Its idea is based on H´ajek-Vald´es algebraic analysis of belief functions, on our previous study of conflicts of belief functions, where internal conflicts of belief functions are distinguished from a conflict between belief functions, and on the decomposition of a belief function into its conflicting and non-conflicting parts. Basic properties of this newly defined conflict are presented, analyzed and briefly compared with our previous approaches to conflict as well as with Liu’s degree of conflict.