Competitive learning of possibility distributions

Possibility theory offers an interesting frame to process uncertain data. It allows one to build expert or decision systems that take into account uncertainty or unreliability. Self learning from uncertain data would make it easier to build such systems : find fuzzy rules that underlie these data and adjust them to optimize the representation of a set of examples. In this paper, the authors propose a scheme for clustering n-tuples of possibility distributions. The authors apply an unsupervised technique that has its roots in competitive learning of neural networks. This technique is designed to find clusters in a set of examples. Each cluster is represented by a prototype, which is of the same kind as the examples. The prototypes evolve according to the examples. The technique is defined to work on possibility distributions and in such a way that the different steps of the algorithm may be interpreted in terms of possibility theory. Moreover, new prototypes are added when needed. In the first part of the paper, for simplicity of presentation, the algorithm is described in detail step by step for single possibility distribution prototypes. It is then extended to n-tuples. In the second part, a simulated example makes use of the algorithm for clustering data coming from two possibilistic sensors