On Possibilistic and Probabilistic Information Fusion

Introduction

Information used in decision making generally comes from multiple sources. We are interested in the problem of multi-source information fusion in the case when the information provided has some uncertainty. Two important types of sources of information are electro-mechanical sensors and human observers/experts; this is particularly the case in security environments. We note that sensor-provided information generally has a probabilistic type of uncertainty. Human-observer-provided information, which is generally linguistic in nature, typically introduces a possibilistic type of uncertainty. Here we are faced with a problem in which we must fuse information with different modes of uncertainty. Here we shall discuss an approach to attaining capability based on the use of probability-possibility transformation. We first discuss the basic features of information provided in terms of possibilistic uncertainty. We point out the entailment principle, a tool that allows one to infer less specific from a given piece of information. We also discuss the problem of fusing multiple pieces of possibilistic information. We describe a procedure for transforming information between possibilistic and probabilistic representations. We use this to form the basis for a technique for fusing multiple pieces of uncertain information some of which is possibilistic and some probabilistic. We provide a normalization procedure for addressing the problems that arise when the information to be fused has some conflict.

The most well-known uncertainty representation is the probabilistic model. Assume V is some variable taking its value in the space X. In probabilistic uncertainty we associate with each x_i ∈ X a value p_i ∈ [0, 1] indicating the probability that x_i is the value of V. We denote the collection of these as the probability distribution P. For any subset A of X the probability that V lies in A is . In the probabilistic framework the normalization property that Prob(X) = 1 requires that Σ_i p_i = 1. Probabilistic uncertainty is essentially based on ratio scale information. That is, if we know the ratio then we can completely determine the probability distribution. Within the framework of probability theory the Shannon entropy is used to quantify the amount of uncertainty associated with a probability distribution P