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arXiv · 2204.06051

On rearrangement inequalities for T-norm logics

Chai Wah Wu
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Abstract

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.

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Chai Wah Wu. 2022-04-12. On rearrangement inequalities for T-norm logics. https://doi.org/10.1007/s11787-023-00332-0

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