Belief intervals aggregation

Abstract

The combination rule is the core of Dempster-Shafer theory (DST), and there is no uniform aggregation rule adapting to all conditions. The construction of such a rule is still an open and hot topic. In this article, we focus on this point. We focus on the belief interval, which is made up of belief function and plausibility function, in the form of [belief function, plausibility function], instead of basic belief assignment, to represent the DST. We aim at exploring a belief interval combination rule as the combination rule of DST. To do this, we contrast the belief interval with the intuitionistic fuzzy sets and construct the belief interval combination rule based on the intuitionistic fuzzy weighted averaging (IFWA) operator, which opens the door for DST combination rules to the aggregation operator perspective. Further, we find that directly using the IFWA operator as the belief interval combination rule poses three problems: the “‘one’ veto problem,” converge easily close to [1, 1] and the belief function from the belief interval combination rule is not normalized. To solve these problems, we add a normalization process in the belief interval combination rule to modify it, which can address all these three problems well. We also set up a series of examples to illustrate the belief interval combination rule, including a multisensor fusion scenario to compare it with some of the existing rules, which shows its superiorities in better stability and lower operational load.