Belief functions on ordered frames of discernment
Arnaud Martin (DRUID)
TL;DR
This paper explores how belief functions can be adapted to ordered frames of discernment, redefining key concepts like power space, union, and distances to better handle ordered responses in questionnaires.
Contribution
It introduces new definitions for belief functions on ordered frames, including a redefinition of the power space, union, and intersection for fuzzy ordered elements.
Findings
Redefinition of the power space for ordered elements
New approach to union and intersection of fuzzy ordered elements
Analysis of distances on ordered elements and their applications
Abstract
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.
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Taxonomy
TopicsMetaheuristic Optimization Algorithms Research · Water Systems and Optimization · Advanced Algebra and Logic