区间值模糊推理的逻辑度量空间  

Logical metric spaces for interval-valued fuzzy reasoning

作　　者：罗敏霞 徐东辉 LUO Minxia;XU Donghui(School of Sciences,China Jiliang University,Hangzhou 310018,China)

机构地区：[1]中国计量大学理学院,浙江杭州310018

出　　处：《智能系统学报》2023年第3期613-618,共6页CAAI Transactions on Intelligent Systems

基　　金：国家自然科学基金项目(12171445,61773019).

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Łukasiewicz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Łukasiewicz剩余蕴涵度量空间中,证明基于区间值Łukasiewicz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。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-valuedŁukasiewicz 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.

关 键 词：模糊集 区间值模糊集 区间值模糊推理 三角范数 剩余蕴涵 距离度量 逻辑度量空间 全蕴涵算法 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]