山东大学学报(理学版)
山東大學學報(理學版)
산동대학학보(이학판)
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
2014年
10期
72-77
,共6页
区间值模糊拟度量空间%区间值模糊拟度量双完备化%双柯西序列%等距同构
區間值模糊擬度量空間%區間值模糊擬度量雙完備化%雙柯西序列%等距同構
구간치모호의도량공간%구간치모호의도량쌍완비화%쌍가서서렬%등거동구
interval-valued fuzzy quasi-metric spaces%interval-valued fuzzy quasi-metric bicompletion%bi-Cauchy sequence%isometry
在拟度量的背景下推广了区间值模糊度量的概念,主要结果如下:(1)给出了区间值模糊拟度量空间等距同构的扩张定理;(2)证明了每个区间值模糊拟度量空间有双完备化且它是唯一达到等距同构的;(3)得到了区间值模糊拟度量空间双完备化的构造方法和区间值模糊拟度量空间可双完备化的等价刻画。
在擬度量的揹景下推廣瞭區間值模糊度量的概唸,主要結果如下:(1)給齣瞭區間值模糊擬度量空間等距同構的擴張定理;(2)證明瞭每箇區間值模糊擬度量空間有雙完備化且它是唯一達到等距同構的;(3)得到瞭區間值模糊擬度量空間雙完備化的構造方法和區間值模糊擬度量空間可雙完備化的等價刻畫。
재의도량적배경하추엄료구간치모호도량적개념,주요결과여하:(1)급출료구간치모호의도량공간등거동구적확장정리;(2)증명료매개구간치모호의도량공간유쌍완비화차타시유일체도등거동구적;(3)득도료구간치모호의도량공간쌍완비화적구조방법화구간치모호의도량공간가쌍완비화적등개각화。
We generalize the notions of interval-valued fuzzy metric in the quasi-metric background.The main results of this paper are:(1 )the isometric extension theorem of interval-valued fuzzy quasi-metric space is given;(2 )it is proved that every interval-valued fuzzy quasi-metric space has bicompletion and is unique up to isometry;(3 )a method to construct the interval-valued fuzzy quasi-metric space bicompletion is given,and a equivalent characterization of in-terval-value fuzzy quasi-metric spaces is obtained which can be bicompletable.