On the determination of strength of belief for decision support under uncertainty—Part II: fusing strengths of belief

Valuation functions are used in decision making under uncertainty to enable comparisons of alternatives. They are based on a weighted averaging of the n possible payoffs available under an alternative. The weighting vectors used are a reflection of the decision-making agentʹs strength of belief a given outcome will occur. Our concern is with developing methods to fuse multiple sources of these weighting vectors. We first suggest a method based on a normalized product. Some methods are suggested for handling completely conflicting beliefs. We abstract the basic features of this product fusion method. Particularly notably among these properties is the fact that a source with all weights equal, 1/n, acts as an identity in the fusion process. We consider next a fusion method using a uninorm aggregation operator with identity 1/n. We carefully look at this new type of method for multi-source fusion and suggest some generations and modifications. Finally we consider the situation when the contributing sources have differing credibilities.