Combination Rule Based on Proportional Redistribution of Generalized Conflict for Evidence Theory

Dempster's rule is a powerful tool for combining multiple distinct pieces of evidence in evidence theory. When conflict between pieces of evidence is high, the combination result of Dempster's rule is counterintuitive. Many alternative combination rules have been proposed. Most of these alternative combination rules are based on the redistribution of Shafer's conflicting mass. The quantitative definition of generalized conflict is given. Based on Proportional generalized conflict redistribution (PGCR), a new class of evidence combination rules is proposed and the links with some existed rules are established. A special instance of the PGCR rules referred to as PGCR-A is proposed by using the subsets' average support degrees as the proportional coefficients. PGCR-A rule can deal with the combination of high conflict evidence. During the process of combination, PGCR-A rule can also automatically determine the weights of the basic belief mass converging to the more specific subsets according to the focal elements' cardinalities. Since PGCR-A rule is not associative, a modified version is proposed to make it quasi-associative.