Belief functions on ordered frames of discernment
This work addresses a specific issue in belief function theory for ordered data, representing an incremental advancement in the domain of uncertainty modeling.
The paper tackles the problem of applying belief functions to ordered responses in questionnaires by redefining the power space and union for disjunctive combination, and studying distances and fuzzy cardinality for ordered elements.
Most questionnaires offer ordered responses whose order is poorly studied via belief functions. In this paper, we study the consequences of a frame of discernment consisting of ordered elements on belief functions. This leads us to redefine the power space and the union of ordered elements for the disjunctive combination. We also study distances on ordered elements and their use. In particular, from a membership function, we redefine the cardinality of the intersection of ordered elements, considering them fuzzy.