In this paper, dual exponential possibility distributions, namely, upper and lower exponential possibility distributions, are identified from the given data to characterize a decision-maker's knowledge. A decision group's knowledge can be represented by a set of such dual possibility distributions. The inherent diversity of knowledge among decision-makers is characterized by a conflict index. A conflict resolution model is proposed based on the conflict index, which integrates multiple possibility distributions identified into a new one to represent compromised knowledge of a decision group. As an application, a portfolio selection problem with multiple decision-makers is considered.