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| Format: | Preprint |
| Veröffentlicht: |
2001
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| Online-Zugang: | https://arxiv.org/abs/cs/0112008 |
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| _version_ | 1866915559864532992 |
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| author | Burgin, Mark |
| author_facet | Burgin, Mark |
| contents | Many mathematical models utilize limit processes. Continuous functions and the calculus, differential equations and topology, all are based on limits and continuity. However, when we perform measurements and computations, we can achieve only approximate results. In some cases, this discrepancy between theoretical schemes and practical actions changes drastically outcomes of a research and decision-making resulting in uncertainty of knowledge. In the paper, a mathematical approach to such kind of uncertainty, which emerges in computation and measurement, is suggested on the base of the concept of a fuzzy limit. A mathematical technique is developed for differential models with uncertainty. To take into account the intrinsic uncertainty of a model, it is suggested to use fuzzy derivatives instead of conventional derivatives of functions in this model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_cs_0112008 |
| institution | arXiv |
| publishDate | 2001 |
| record_format | arxiv |
| spellingShingle | Representation of Uncertainty for Limit Processes Burgin, Mark Artificial Intelligence Numerical Analysis G.1; E.1 Many mathematical models utilize limit processes. Continuous functions and the calculus, differential equations and topology, all are based on limits and continuity. However, when we perform measurements and computations, we can achieve only approximate results. In some cases, this discrepancy between theoretical schemes and practical actions changes drastically outcomes of a research and decision-making resulting in uncertainty of knowledge. In the paper, a mathematical approach to such kind of uncertainty, which emerges in computation and measurement, is suggested on the base of the concept of a fuzzy limit. A mathematical technique is developed for differential models with uncertainty. To take into account the intrinsic uncertainty of a model, it is suggested to use fuzzy derivatives instead of conventional derivatives of functions in this model. |
| title | Representation of Uncertainty for Limit Processes |
| topic | Artificial Intelligence Numerical Analysis G.1; E.1 |
| url | https://arxiv.org/abs/cs/0112008 |