On rearrangement inequalities for T-norm logics
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909186644770816 |
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| author | Wu, Chai Wah |
| author_facet | Wu, Chai Wah |
| contents | The rearrangement inequality states that the sum of products of permutations of 2 sequences of real numbers are maximized when the terms are similarly ordered and minimized when the terms are ordered in opposite order. We show that similar inequalities exist for multi-valued logic with the multiplication and addition operation replaced with various T-norms and T-conorms respectively. For instance, we show that the rearrangement inequality holds when the T-norms and T-conorms are derived from Archimedean copulas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_06051 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On rearrangement inequalities for T-norm logics Wu, Chai Wah Logic 06D30, 06D72, 62H05, 05A20, 05E40, 03B52 The rearrangement inequality states that the sum of products of permutations of 2 sequences of real numbers are maximized when the terms are similarly ordered and minimized when the terms are ordered in opposite order. We show that similar inequalities exist for multi-valued logic with the multiplication and addition operation replaced with various T-norms and T-conorms respectively. For instance, we show that the rearrangement inequality holds when the T-norms and T-conorms are derived from Archimedean copulas. |
| title | On rearrangement inequalities for T-norm logics |
| topic | Logic 06D30, 06D72, 62H05, 05A20, 05E40, 03B52 |
| url | https://arxiv.org/abs/2204.06051 |