Abstract
We consider comparative dissimilarity relations on pairs on fuzzy description profiles, the latter providing a fuzzy set-based representation of pairs of objects. Such a relation expresses the idea of “no more dissimilar than” and is used by a decision maker when performing a case-based decision task under vague information. We first limit ourselves to those relations admitting a weighted \(\varvec{L}^p\) distance representation, for which we provide an axiomatic characterization in case the relation is complete, transitive and defined on the entire space of pairs of fuzzy description profiles. Next, we switch to the more general class of comparative dissimilarity relations representable by a Choquet \(\varvec{L}^p\) distance, parameterized by a completely alternating normalized capacity.
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Acknowledgements
The first two authors are members of the INdAM-GNAMPA research group. The second author has been partially supported by the MUR PRIN 2022 project “Models for dynamic reasoning under partial knowledge to make interpretable decisions” (grant number 2022AP3B3B) funded by the European Union - Next Generation EU.
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Coletti, G., Petturiti, D. & Bouchon-Meunier, B. Weighted and Choquet \(L^p\) distance representation of comparative dissimilarity relations on fuzzy description profiles. Ann Math Artif Intell (2024). https://doi.org/10.1007/s10472-024-09924-y
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DOI: https://doi.org/10.1007/s10472-024-09924-y
Keywords
- Dissimilarity relation
- Fuzzy description profiles
- Weighted \(\varvec{L}^p\) distance
- Choquet \(\varvec{L}^p\) distance