Probabilistic and fuzzy information fusion applied to radar system ranking

The decision making systems make use of heterogeneous information to identify an object class or a target, which are affected by various kinds of imperfection. First, information issued from measures (radar measures, images) of an observation is represented by X variables. Generally, on these X variables, each class can be described through a probability distribution function. These decision systems also integrate expert prior knowledge to assist the decision. Such information is defined by Y variables and is represented by fuzzy membership functions. The question is how to combine appropriately these two kinds of variables in order to improve the efficiency of the decision process. In this paper, we present a decision model combining probabilistic and fuzzy variables. The decision is defined using a fuzzy Bayesian approach, which takes into account these two imperfections. Only two classes are considered using one X variable and one Y variable. Then an extension is proposed to suit more complicated cases. To validate the interest of this approach, we compare it with the standard Bayesian classification and fuzzy classification, applied separately to synthetic data. In addition, we will see how our approach can be applied to the problem of radar system ranking, on which system resources are limited and as a consequence, decisions about priorities must be taken. Using the system information sources (i.e. probabilistic: radar measurements, fuzzy: prior expert knowledge, evidential), a comparison between Bayesian classification, fuzzy classification, system decision and the proposed approach is presented.