Study of some algebraical properties of adaptive combination rules

Dubois and Prade, Data Fusion in Robotics and Machine Intelligence, Academic Press, New York, 1992, have proposed an adaptive combination rule that moves gradually from conjunctive mode to disjunctive mode as soon as the conflict between sources increases. The authors also proposed in Dubois and Prade, Control Eng. Practice 2 (1994) pp. 812-823, a generalization of the previous rule to more than two sources based upon restricting the number of reliable sources between an optimistic case and a pessimistic case. In this paper, we are particularly interested in studying these two rules in the light of some appealing algebraical properties. Particularly, we will study the link of these rules with commutativity, associativity, compromise, convexity, autoduality, ignorance and impossible cases. We also investigate their link with the MICA operators introduced by Yager [Fuzzy Sets and Systems 67 (1994) pp. 129-146]. Finally, we propose some extension of the rules. (C) 2000 Elsevier Science B.V. All rights reserved.