Idempotent Conjunctive Combination of Belief Functions by Distance Minimization

When combining multiple belief functions, designing a combination rule that selects the least informative belief function among those more informative than each of the combined ones is a difficult task. Such rules, commonly depicted as "cautious", are typically required to be idempotent, since when one is cautious, combining identical information should not lead to the reinforcement of some hypothesis. However, applying the least commitment principle using partial orders is in general not straightforward, mainly due to the non-uniqueness of solutions. Building upon previous work, this paper investigates the use of distances compatible with such partial orders to determine a unique solution to the combination problem. The obtained operators are conjunctive, idempotent and commutative, but lack associativity. They are, however, quasi-associative allowing sequential combinations at no extra complexity.