Distances Between Partial Preference Orderings
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909272579768320 |
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| author | Dezert, Jean Shekhovtsov, Andrii Salabun, Wojciech |
| author_facet | Dezert, Jean Shekhovtsov, Andrii Salabun, Wojciech |
| contents | This paper proposes to establish the distance between partial preference orderings based on two very different approaches. The first approach corresponds to the brute force method based on combinatorics. It generates all possible complete preference orderings compatible with the partial preference orderings and calculates the Frobenius distance between all fully compatible preference orderings. Unfortunately, this first method is not very efficient in solving high-dimensional problems because of its big combinatorial complexity. That is why we propose to circumvent this problem by using a second approach based on belief functions, which can adequately model the missing information of partial preference orderings. This second approach to the calculation of distance does not suffer from combinatorial complexity limitation. We show through simple examples how these two theoretical methods work. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_19869 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distances Between Partial Preference Orderings Dezert, Jean Shekhovtsov, Andrii Salabun, Wojciech Artificial Intelligence This paper proposes to establish the distance between partial preference orderings based on two very different approaches. The first approach corresponds to the brute force method based on combinatorics. It generates all possible complete preference orderings compatible with the partial preference orderings and calculates the Frobenius distance between all fully compatible preference orderings. Unfortunately, this first method is not very efficient in solving high-dimensional problems because of its big combinatorial complexity. That is why we propose to circumvent this problem by using a second approach based on belief functions, which can adequately model the missing information of partial preference orderings. This second approach to the calculation of distance does not suffer from combinatorial complexity limitation. We show through simple examples how these two theoretical methods work. |
| title | Distances Between Partial Preference Orderings |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2407.19869 |