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适宜于展开模糊推理的两类模糊度量空间
引用本文:王国俊,段景瑶. 适宜于展开模糊推理的两类模糊度量空间[J]. 中国科学:技术科学, 2014, 0(5): 623-632
作者姓名:王国俊  段景瑶
作者单位:[1]陕西师范大学数学研宄所,西安710062 [2]宝鸡文理学院数学系,宝鸡721013
基金项目:国家自然科学基金(批准号:11171200)、中央高校特别支持项目(批准号:GK201403001)、宝鸡文理学院重点项目(批准号:ZK14059)和中央高校教师自由探索项目(批准号:GK201402006)资助.
摘    要:
给出了衡量模糊推理鲁棒性的度量应有的结构,建立了基于左连续三角模的4类模糊度量空间,证明了基于Lukasiewicz蕴涵和Goguen乘积蕴涵的模糊度量空间是最适宜于展开模糊推理的两类模糊度量空间.

关 键 词:模糊推理  鲁棒性  正则度量  Goguen型蕴涵  Lukasiewicz型蕴涵

Two types of fuzzy metric spaces suitable for fuzzy reasoning
WANG GuoJun,DUAN JingYao. Two types of fuzzy metric spaces suitable for fuzzy reasoning[J]. Scientia Sinica Techologica, 2014, 0(5): 623-632
Authors:WANG GuoJun  DUAN JingYao
Affiliation:1 Department of Mathematics and Information Sciences, Shaanxi Normal University, Xi'an 710062, China 2 Department of Mathematics, Baoji University of Arts and Sciences, Baoji 721013, China)
Abstract:
The metric structures for measure the robustness of fuzzy reasoning are given. Based on the left continuous triangular norms, four types of fuzzy metric spaces are constructed. Finally, it proved that the fuzzy metric spaces related to Lukasiewicz implication and Goguen implication are more suitable for fuzzy reasoning.
Keywords:fuzzy reasoning robustness   regular metric   Goguen implication   Lukasiewicz implication
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