Lukasiewicz-based merging possibilistic networks

•The Lukasiewicz t-norm is characterized by its high effect of reinforcement.•The process of fusion is established for the possibilistic networks having same or different graphical structures.•The certainty degree is increased after applying fusion.•The extension process of possibilistic networks in a common structure may produce cycles.•A possibilistic adaptation of the arc reversal method is proposed.

Possibility theory provides a good framework for dealing with merging problems when information is pervaded with uncertainty and inconsistency. Many merging operators in possibility theory have been proposed. This paper develops a new approach to merging uncertain information modeled by possibilistic networks. In this approach we restrict our attention to show how a “triangular norm” establishes a lower bound on the degree to which an assessment is true when it is obtained by a set of initial hypothesis represented by a joint possibility distribution. This operator is characterized by its high effect of reinforcement. A strongly conjunctive operator is suitable to merge networks that are not involved in conflict, especially those supported by both sources. In this paper, the Lukasiewicz t-norm is first applied to a set of possibility measures to combine networks having the same and different graphical structures. We then present a method to merge possibilistic networks dealing with cycles.