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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.07714 |
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| _version_ | 1866916091375124480 |
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| author | Gorokhovik, V. V. |
| author_facet | Gorokhovik, V. V. |
| contents | The paper deals with partial and weak preference relations defined on infinite-dimensional vector spaces and compatible with algebraic operations. By a partial preference we mean an asymmetric and transitive binary relation, while a weak preference is such a partial preference for which the indifference relation corresponding it is transitive (an indifference relation is the complement to the union of a partial preference and the reverse to it). Our first aim is to study the internal structure of compatible partial and weak preferences. Using these results we then prove that a compatible weak preference admits an analytical representation by means of a step-linear function, while a compatible partial preference can be analytically represent by the family of step-linear functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_07714 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Internal structure and analytical representation of preference relations defined on infinite-dimensional real vector spaces Gorokhovik, V. V. Optimization and Control 91B08 (Primary) 90B50, 06A06, 06A05 (Secondary) The paper deals with partial and weak preference relations defined on infinite-dimensional vector spaces and compatible with algebraic operations. By a partial preference we mean an asymmetric and transitive binary relation, while a weak preference is such a partial preference for which the indifference relation corresponding it is transitive (an indifference relation is the complement to the union of a partial preference and the reverse to it). Our first aim is to study the internal structure of compatible partial and weak preferences. Using these results we then prove that a compatible weak preference admits an analytical representation by means of a step-linear function, while a compatible partial preference can be analytically represent by the family of step-linear functions. |
| title | Internal structure and analytical representation of preference relations defined on infinite-dimensional real vector spaces |
| topic | Optimization and Control 91B08 (Primary) 90B50, 06A06, 06A05 (Secondary) |
| url | https://arxiv.org/abs/2312.07714 |