[1]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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Logical metric spaces for interval-valued fuzzy reasoning

CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume: 18 Number of periods: 2023 3 Page number: 613-618 Column: 学术论文—人工智能基础 Public date: 2023-07-05
Title:
Logical metric spaces for interval-valued fuzzy reasoning
Author(s):
LUO Minxia;  XU Donghui
School of Sciences, China Jiliang University, Hangzhou 310018, China
Keywords:
fuzzy sets; interval-valued fuzzy set; interval-valued fuzzy reasoning; triangular norm; residual implication; distance metric; logical metric space; full implication method
CLC:
TP18
DOI:
10.11992/tis.202110019
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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