Consensus for Decomposable Measures

Abstract

In this paper we extend some previous works on the consensus of probabilities, possibilities and homogeneous families of decomposable measures. First, we show that the eventwise aggregation of different types of decomposable measures can be meaningful if and only if the underlying t-conorms belong to the same equivalence class of a naturally defined equivalence relation. Then we give weighted forms of consensus functions for such t-conorm-based decomposable measures. As a consequence, we obtain that the unanimity condition can be preserved only if all the considered t-conorms are the same.