[1]罗敏霞,徐东辉.区间值模糊推理的逻辑度量空间[J].智能系统学报,2023,18(3):613-618.[doi:10.11992/tis.202110019]
LUO Minxia,XU Donghui.Logical metric spaces for interval-valued fuzzy reasoning[J].CAAI Transactions on Intelligent Systems,2023,18(3):613-618.[doi:10.11992/tis.202110019]
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LUO Minxia,XU Donghui.Logical metric spaces for interval-valued fuzzy reasoning[J].CAAI Transactions on Intelligent Systems,2023,18(3):613-618.[doi:10.11992/tis.202110019]
区间值模糊推理的逻辑度量空间
《智能系统学报》[ISSN 1673-4785/CN 23-1538/TP] 卷:
18
期数:
2023年第3期
页码:
613-618
栏目:
学术论文—人工智能基础
出版日期:
2023-07-05
- Title:
- Logical metric spaces for interval-valued fuzzy reasoning
- Keywords:
- fuzzy sets; interval-valued fuzzy set; interval-valued fuzzy reasoning; triangular norm; residual implication; distance metric; logical metric space; full implication method
- 分类号:
- TP18
- 摘要:
- 为了探寻适合区间值模糊推理的条件，本文研究区间值逻辑度量空间。本文提出一种新的基于区间值双剩余蕴涵算子的区间值模糊集的距离度量。由4个著名的区间值双剩余诱导相应的距离度量，做成4个度量空间，分别研究4个度量空间的性质。进一步，证明基于区间值?ukasiewicz剩余蕴涵的度量空间和区间值Goguen剩余蕴涵的度量空间适合做区间值模糊推理。最后，在基于区间值?ukasiewicz剩余蕴涵度量空间中，证明基于区间值?ukasiewicz剩余蕴涵的模糊推理全蕴涵算法是鲁棒的，为区间值模糊推理算法的应用提供了坚实的理论基础。
- Abstract:
- In order to find the condition suitable for interval-valued fuzzy reasoning, this paper studies the interval-valued logical metric space. This paper presents a new distance metric of interval-valued fuzzy sets based on interval-valued biresiduals. Four famous interval-valued biresiduals are used to induce corresponding distance metrics to produce four metric spaces, and the properties of the four metric spaces are studied respectively. Furthermore, it is proved that the metric space based on interval-valued ?ukasiewicz residual implication and the metric space based on interval-valued Goguen residual implication are suitable for interval-valued fuzzy reasoning. Finally, in the interval-valued Ukasiewicz residual implication metric space, it is proved that the full implication algorithm of fuzzy reasoning based on interval-valued Ukasiewicz residual implication is robust, which provides a solid theoretical basis for the application of interval-valued fuzzy reasoning algorithm.
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备注/Memo
收稿日期:2021-10-18。
基金项目:国家自然科学基金项目(12171445, 61773019).
作者简介:罗敏霞,教授,博士,中国人工智能学会人工智能基础专业委员会常务委员,中国逻辑学会非经典逻辑与计算专委会委员,国际信息研究学会中国分会泛逻辑与智能信息处理专业委员会副主任,国际信息研究学会中国分会人工智能专业委员会专家委员。主要研究方向为非经典逻辑、近似推理与图像处理;发表学术论文130余篇,出版专著2部,教材1部;徐东辉,助教,主要研究方向为区间值模糊推理
通讯作者:罗敏霞.E-mail:mxluo@cjlu.eud.cn
更新日期/Last Update:
1900-01-01