Metrics in multiset spaces

被引：2
|
作者：
Petrovsky, Alexey B. [1 ,2 ,3 ,4 ]
机构：
[1] Russian Acad Sci, Fed Res Ctr Comp Sci & Control, Prospekt 60-Let Oktyabrya, Moscow, Russia
[2] Belgorod State Natl Res Univ, Belgorod, Russia
[3] VG Shukhov Belgorod State Technol Univ, Belgorod, Russia
[4] Volgograd State Tech Univ, Volgograd, Russia
来源：
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS | 2019年 / 36卷 / 04期
基金：
俄罗斯基础研究基金会;
关键词：
Multiset; space of multisets; metric; pseudometric; quasimetric; symmetric; multi-attribute objects; similarity and dissimilarity of objects; group multiple criteria decision making; group verbal decision analysis;
D O I：
10.3233/JIFS-18525
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
The paper considers new classes of spaces of finite, bounded, measurable multisets with different metrics, pseudometrics, quasimetrics, symmetrics, and some properties of these metrics. We discuss the possibilities to apply new types of metrics for estimating proximity of objects with many numerical and/or verbal attributes. We use the introduced indexes of similarity and dissimilarity of objects represented as multisets in new methods of group multiple criteria decision making.
引用
收藏
页码：3073 / 3085
页数：13
相关论文
共 50 条
  • [21] Positive metrics on reductive spaces
    Prudhon, Nicolas
    COMPTES RENDUS MATHEMATIQUE, 2007, 345 (07) : 369 - 372
  • [22] UNBOUNDED METRICS ON NONCOMPACT SPACES
    NIX, ED
    PERVIN, WJ
    AMERICAN MATHEMATICAL MONTHLY, 1964, 71 (09): : 1054 - &
  • [23] Homogenous metrics in cosmogonic spaces
    Kosambi, DD
    COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES, 1938, 206 : 1086 - 1088
  • [24] Fuzzy polynucleotide spaces and metrics
    Nieto, Juan J.
    Torres, A.
    Georgiou, D. N.
    Karakasidis, T. E.
    BULLETIN OF MATHEMATICAL BIOLOGY, 2006, 68 (03) : 703 - 725
  • [25] Monotone metrics on matrix spaces
    Department of Mathematics, Faculty of Chemical Engineering, Technical University Budapest, Sztoczek u. 2, H-1521 Budapest XI, Hungary
    不详
    Linear Algebra Its Appl, (81-96):
  • [26] Monotone metrics on matrix spaces
    Petz, D
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1996, 244 : 81 - 96
  • [27] ON DENSE SUBSETS IN SPACES OF METRICS
    Ishiki, Yoshito
    COLLOQUIUM MATHEMATICUM, 2022, 170 (01) : 27 - 39
  • [28] NATURAL METRICS ON SMALE SPACES
    FRIED, D
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1983, 297 (01): : 77 - 79
  • [29] OPTIMAL METRICS ON METRIZABLE SPACES
    JANOS, L
    ARCHIV DER MATHEMATIK, 1971, 22 (06) : 660 - &
  • [30] Fuzzy polynucleotide spaces and metrics
    Juan J. Nieto
    A. Torres
    D. N. Georgiou
    T. E. Karakasidis
    Bulletin of Mathematical Biology, 2006, 68 : 703 - 725
12345