Abstract
We study the problem of a vector space over \(\mathbb {R}\) whose Euclidean scalar product is unknown. From piece of evidence given by certain experts, we are able to build suitable belief and plausibility functions on the space of scalar products. We pay special attention to study contradictions and degrees of conflict. As a possible application, for a random variable of the vector space, we are able to get the related belief and plausibility functions for its variance.
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Notes
- 1.
Analogously for \(G^-(g_j)\).
- 2.
A non-negative scalar which is invariant under change of basis.
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Salamanca, J.J. (2018). Belief and Plausibility Functions on the Space of Scalar Products and Applications. In: Destercke, S., Denoeux, T., Cuzzolin, F., Martin, A. (eds) Belief Functions: Theory and Applications. BELIEF 2018. Lecture Notes in Computer Science(), vol 11069. Springer, Cham. https://doi.org/10.1007/978-3-319-99383-6_28
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DOI: https://doi.org/10.1007/978-3-319-99383-6_28
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