On monotonicity of comonotonically maxitive functional
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917990101942272 |
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| author | Radul, Taras |
| author_facet | Radul, Taras |
| contents | The comonotonic maxitivity property of functionals frequently appears in the characterization of fuzzy integrals based on the maximum operation. In some special cases, comonotonic maxitivity implies monotonicity of functionals. The question of whether this implication holds in general was posed by T. Radul (2023). It was shown in that paper that the implication is valid for finite compacta. In this article, we provide a negative answer to the general problem and discuss additional properties that need to be imposed to ensure the implication holds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13761 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On monotonicity of comonotonically maxitive functional Radul, Taras General Topology Functional Analysis 28E10 The comonotonic maxitivity property of functionals frequently appears in the characterization of fuzzy integrals based on the maximum operation. In some special cases, comonotonic maxitivity implies monotonicity of functionals. The question of whether this implication holds in general was posed by T. Radul (2023). It was shown in that paper that the implication is valid for finite compacta. In this article, we provide a negative answer to the general problem and discuss additional properties that need to be imposed to ensure the implication holds. |
| title | On monotonicity of comonotonically maxitive functional |
| topic | General Topology Functional Analysis 28E10 |
| url | https://arxiv.org/abs/2504.13761 |