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.