Set operations on maxitive belief structures

This paper studies the set operations on maxitive belief structures. Unlike Dempster-Shafer structures, we show that different maxitive belief structures can induce the same upper and lower possibilities. Then the operations on the set of maxitive belief structures might not be the operations on their induced upper and lower possibilities. We call those operations on maxitive belief structures which are also the operations on their induced upper and lower possibilities the nice operations. We introduce the set operations on maxitive belief structures, including weighted sum, intersection, union, complement, projection, cylindrical extension and Cartesian product operations. We show that the weighted sum, union, projection and cylindrical extension are nice operations, and the intersection, complement and Cartesian product operations are not nice.

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